![Robot Localization and Map Building
2
Moreover, traditional EKF localisation techniques are computationally efficient, but they may
also fail with quadruped walking robots present poor odometry, in situations such as leg slip-
page and loss of balance. Furthermore, we propose a hybrid localisation method to eliminate
inconsistencies and fuse inaccurate odometry data with costless visual data. The proposed
FM-EKF localisation algorithm makes use of a fuzzy cell to speed up convergence and to
maintain an efficient localisation. Subsequently, the performance of the proposed method was
tested in three experimental comparisons: (i) simple movements along the pitch, (ii) localising
and playing combined behaviours and c) kidnapping the robot.
The rest of the chapter is organised as follows. Following the brief introduction of Section 1,
Section 2 describes the proposed observer module as an updating process of a Bayesian lo-
calisation method. Also, robot motion and measurement models are presented in this section
for real-time landmark detection. Section 3 investigates the proposed localisation methods.
Section 4 presents the system architecture. Some experimental results on landmark modelling
and localisation are presented in Section 5 to show the feasibility and performance of the pro-
posed localisation methods. Finally, a brief conclusion is given in Section 6.
2. Observer design
This section describes a robot observer model for processing motion and measurement phases.
These phases, also known as Predict and Update, involve a state estimation in a time sequence
for robot localisation. Additionally, at each phase the state is updated by sensing information
and modelling noise for each projected state.
2.1 Motion Model
The state-space process requires a state vector as processing and positioning units in an ob-
server design problem. The state vector contains three variables for robot localisation, i.e., 2D
position (x, y) and orientation (θ). Additionally, the prediction phase incorporates noise from
robot odometry, as it is presented below:
x−
t
y−
t
θ−
t
=
xt−1
yt−1
θt−1
+
(ulin
t + wlin
t )cosθt−1 − (ulat
t + wlat
t )sinθt−1
(ulin
t + wlin
t )sinθt−1 + (ulat
t + wlat
t )cosθt−1
urot
t + wrot
t
(4.9)
where ulat, ulin and urot are the lateral, linear and rotational components of odometry, and
wlat, wlin and wrot are the lateral, linear and rotational components in errors of odometry.
Also, t − 1 refers to the time of the previous time step and t to the time of the current step.
In general, state estimation is a weighted combination of noisy states using both priori and
posterior estimations. Likewise, assuming that v is the measurement noise and w is the pro-
cess noise, the expected value of the measurement R and process noise Q covariance matrixes
are expressed separately as in the following equations:
R = E[vvt
] (4.10)
Q = E[wwt
] (4.11)
The measurement noise in matrix R represents sensor errors and the Q matrix is also a con-
fidence indicator for current prediction which increases or decreases state uncertainty. An
odometry motion model, ut−1 is adopted as shown in Figure 1. Moreover, Table 1 describes
all variables for three dimensional (linear, lateral and rotational) odometry information where
(
x,
y) is the estimated values and (x, y) the actual states.](https://image.slidesharecdn.com/1056389-250527054255-ee582a8b/85/Robot-Localization-And-Map-Building-Hanafiah-Yussof-Ed-14-320.jpg)
![Visual Localisation of quadruped walking robots 7
where Ll refers to all possible operators from the current landmark model, σm is the
standard deviation for each sampled entity im in a sample set and l is a landmark de-
scriptor value.
3. Localisation Methods
Robot localisation is an environment analysis task determined by an internal state obtained
from robot-environment interaction combined with any sensed observations. The traditional
state assumption relies on the robot’s influence over its world and on the robot’s perception
of its environment.
Both steps are logically divided into independent processes which use a state transition for
integrating data into a predictive and updating state. Therefore, the implemented localisation
methods contain measurement and control phases as part of state integration and a robot
pose conformed through a Bayesian approach. On the one hand, the control phase is assigned
to robot odometry which translates its motion into lateral, linear and rotational velocities. On
the other hand, the measurement phase integrates robot sensed information by visual features.
The following sections describe particular phase characteristics for each localisation approach.
3.1 Fuzzy Markov Method
As it is shown in the FM grid-based method of (Buschka et al., 2000) and (Herrero-Pérez et al.,
2004), a grid Gt contains a number of cells for each grid element Gt(x, y) for holding a proba-
bility value for a possible robot position in a range of [0, 1]. The fuzzy cell (fcell) is represented
as a fuzzy trapezoid (Figure 3) defined by a tuple θ, ∆, α, h, b , where θ is robot orientation
at the trapezoid centre with values in a range of [0, 2π]; ∆ is uncertainty in a robot orientation
θ; h corresponds to fuzzy cell (fcell) with a range of [0, 1]; α is a slope in the trapezoid, and b is
a correcting bias.
Fig. 3. Graphic representation of robot pose in an f uzzy cell
Since a Bayesian filtering technique is implemented, localisation process works in predict-
observe-update phases for estimating robot state. In particular, the Predict step adjusts to
motion information from robot movements. Then, the Observe step gathers sensed infor-
mation. Finally, the Update step incorporates results from the Predict and Observe steps for
obtaining a new estimation of a fuzzy grid-map. The process sequence is described as follows:
1. Predict step. During this step, robot movements along grid-cells are represented by a
distribution which is continuously blurred. As described in previous work in (Herrero-
Pérez et al., 2004), the blurring is based on odometry information reducing grid occu-
pancy for robot movements as shown in Figure 4(c)). Thus, the grid state G
t is obtained
by performing a translation and rotation of Gt−1 state distribution according to motion
u. Subsequently, this odometry-based blurring, Bt, is uniformly calculated for including
uncertainty in a motion state.](https://image.slidesharecdn.com/1056389-250527054255-ee582a8b/85/Robot-Localization-And-Map-Building-Hanafiah-Yussof-Ed-19-320.jpg)
![Robot Localization and Map Building
10
where AtPt−1 AT
t is a progression of Pt−1 along a new movement and At is defined as follows:
At = f s =
1 0 −ulat
t cosθt − ulin
t senθt−1
0 1 ulin
t cosθt − ulat
t senθt−1
0 0 1
(4.19)
and WtQt−1WT
t represents odometry noise, Wt is Jacobian motion state approximation and Qt
is a covariance matrix as follows:
Qt = E[wtwT
t ] (4.20)
The Sony AIBO robot may not be able to obtain a landmark observation at each localisation
step but it is constantly executing a motion movement. Therefore, it is assumed that frequency
of odometry calculation is higher than visually sensed measurements. For this reason, con-
trol steps are executed independently from measurement states (Kiriy Buehler, 2002) and
covariance matrix actualisation is presented as follows:
st = s−
t (4.21)
Pt = P−
t (4.22)
2. Updating step. During this phase, sensed data and noise covariance Pt are used for obtain-
ing a new state vector. The sensor model is also updated using measured landmarks m1···6,(x,y)
as environmental descriptive data. Thus, each zi
t of the i landmarks is measured as distance
and angle with a vector (ri
t, φi
t). In order to obtain an updated state, the next equation is used:
st = st−1 + Ki
t(zi
t − ẑi
t) = st−1 + Ki
t(zi
t − hi
(st−1)) (4.23)
where hi(st−1) is a predicted measurement calculated from the following non-linear functions:
ẑi
t = hi
(st−1) =
(mi
t,x − st−1,x)2 + (mi
t,y − st−1,y)
atan2(mi
t,x − st−1,x, mi
t,y − st−1,y) − st−1,θ
(4.24)
Then, the Kalman gain, Ki
t, is obtained from the next equation:
Ki
t = Pt−1(Hi
t)T
(Si
t)−1
(4.25)
where Si
t is the uncertainty for each predicted measurement ẑi
t and is calculated as follows:
Si
t = Hi
tPt−1(Hi
t)T
+ Ri
t (4.26)
Then Hi
t describes changes in the robot position as follows:
Hi
t = hi(st−1)st
=
−
mi
t,x−st−1,x
(mi
t,x−st−1,x)2+(mi
t,y−st−1,y)2
−
mi
t,y−st−1,y
(mi
t,x−st−1,x)2+(mi
t,y−st−1,y)2
0
mi
t,y−st−1,y
(mi
t,x−st−1,x)2+(mi
t,y−st−1,y)2 −
mi
t,x−st−1,x
(mi
t,x−st−1,x)2+(mi
t,y−st−1,y)2 −1
0 0 0
(4.27)
where Ri
t represents the measurement noise which was empirically obtained and Pt is calcu-
lated using the following equation:](https://image.slidesharecdn.com/1056389-250527054255-ee582a8b/85/Robot-Localization-And-Map-Building-Hanafiah-Yussof-Ed-22-320.jpg)
![1
2
transformed in consequence of her cruelty to her lover. (Ellis’s Metrical
Romances, I, 130.) This story was introduced into Europe, therefore, much
about the time at which it was enrolled among the contents of the Vṛihat
Kathá in Cashmir. The metempsychosis is so much more obvious an
explanation of the change of forms, that it renders it probable the story was
originally Hindu. It was soon copied in Europe, and occurs in Le Grand as
La vieille qui séduisit la jeune fille. III. 148 [ed. III. Vol. IV. 50]. The
parallel is very close and the old woman gives “une chienne à manger des
choses fortement saupoudrèes de senève qui lai picotait le palais et les
narines et l’animal larmoyait beaucoup.” She then shows her to the young
woman and tells her the bitch was her daughter. “Son malheur fut d’avoir le
cœur dur; un jeune homme l’aimait, elle le rebuta. Le malheureux après
avoir tout tenté pour l’attendrir, désespéré de sa dureté en prit tant de
chagrin qu’il tomba malade et mourut. Dieu l’a bien vengè; voyez en quel
état pour la punir il a reduit ma pauvre fille, et comment elle pleure sa
faute.” The lesson was not thrown away. The story occurs also in the Gesta
Romanorum as “The Old Woman and her Dog” [in Bohn’s edition it is Tale
XXVIII], and it also finds a place where we should little have expected to
find it, in the Promptuarium of John Herolt of Basil, an ample repository of
examples for composing sermons: the compiler a Dominican friar,
professing to imitate his patron saint, who always abundabat exemplis in
his discourses.” [In Bohn’s edition we are told that it appears in an English
garb amongst a translation of Æsop’s Fables published in 1658.] Dr. Rost
refers us to Th. Wright, Latin Stories, London, 1842, p. 218. Loiseleur
Deslongchamps Essai sur les Fables Indiennes, Paris, 1838, p. 106 ff. F. H.
Von der Hagen, Gesammtabenteuer, 1850 I, cxii. ff and Grässe, I. 1, 374 ff.
In Gonzenbach’a Sicilianische Märchen, No. 55, Vol. I, p. 359, Epomata
plays some young men much the same trick as Devasmitá, and they try in
much the same way to conceal their disgrace. The story is the second in my
copy of the Śuka Saptati.
Cp. the way in which Rüdiger carries off the daughter of king Osantrix, Hagen’s
Helden-Sagen, Vol. I, p. 227.
τηρήσαντες νύκτα χειμέριον ὕδατι καὶ ἀνέμῳ καὶ ἅμ’ ἀσέληνον ἐξῇσαν. Thucyd. III.
22.](https://image.slidesharecdn.com/1056389-250527054255-ee582a8b/85/Robot-Localization-And-Map-Building-Hanafiah-Yussof-Ed-80-320.jpg)
Robot Localization And Map Building Hanafiah Yussof Ed
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- 5. I Robot Localization and Map Building
- 7. Robot Localization and Map Building Edited by Hanafiah Yussof In-Tech intechweb.org
- 8. Published by In-Teh In-Teh Olajnica 19/2, 32000 Vukovar, Croatia Abstracting and non-profit use of the material is permitted with credit to the source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside. After this work has been published by the In-Teh, authors have the right to republish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work. © 2010 In-teh www.intechweb.org Additional copies can be obtained from: publication@intechweb.org First published March 2010 Printed in India Technical Editor: Sonja Mujacic Cover designed by Dino Smrekar Robot Localization and Map Building, Edited by Hanafiah Yussof p. cm. ISBN 978-953-7619-83-1
- 9. V Preface Navigation of mobile platform is a broad topic, covering a large spectrum of different technologies and applications. As one of the important technology highlighting the 21st century, autonomous navigation technology is currently used in broader spectra, ranging from basic mobile platform operating in land such as wheeled robots, legged robots, automated guided vehicles (AGV) and unmanned ground vehicle (UGV), to new application in underwater and airborne such as underwater robots, autonomous underwater vehicles (AUV), unmanned maritime vehicle (UMV), flying robots and unmanned aerial vehicle (UAV). Localization and mapping are the essence of successful navigation in mobile platform technology. Localization is a fundamental task in order to achieve high levels of autonomy in robot navigation and robustness in vehicle positioning. Robot localization and mapping is commonly related to cartography, combining science, technique and computation to build a trajectory map that reality can be modelled in ways that communicate spatial information effectively. The goal is for an autonomous robot to be able to construct (or use) a map or floor plan and to localize itself in it. This technology enables robot platform to analyze its motion and build some kind of map so that the robot locomotion is traceable for humans and to ease future motion trajectory generation in the robot control system. At present, we have robust methods for self-localization and mapping within environments that are static, structured, and of limited size. Localization and mapping within unstructured, dynamic, or large-scale environments remain largely an open research problem. Localization and mapping in outdoor and indoor environments are challenging tasks in autonomous navigation technology. The famous Global Positioning System (GPS) based on satellite technology may be the best choice for localization and mapping at outdoor environment. Since this technology is not applicable for indoor environment, the problem of indoor navigation is rather complex. Nevertheless, the introduction of Simultaneous Localization and Mapping (SLAM) technique has become the key enabling technology for mobile robot navigation at indoor environment. SLAM addresses the problem of acquiring a spatial map of a mobile robot environment while simultaneously localizing the robot relative to this model. The solution method for SLAM problem, which are mainly introduced in this book, is consists of three basic SLAM methods. The first is known as extended Kalman filters (EKF) SLAM. The second is using sparse nonlinear optimization methods that based on graphical representation. The final method is using nonparametric statistical filtering techniques known as particle filters. Nowadays, the application of SLAM has been expended to outdoor environment, for use in outdoor’s robots and autonomous vehicles and aircrafts. Several interesting works related to this issue are presented in this book. The recent rapid
- 10. VI progress in sensors and fusion technology has also benefits the mobile platforms performing navigation in term of improving environment recognition quality and mapping accuracy. As one of important element in robot localization and map building, this book presents interesting reports related to sensing fusion and network for optimizing environment recognition in autonomous navigation. This book describes comprehensive introduction, theories and applications related to localization, positioning and map building in mobile robot and autonomous vehicle platforms. It is organized in twenty seven chapters. Each chapter is rich with different degrees of details and approaches, supported by unique and actual resources that make it possible for readers to explore and learn the up to date knowledge in robot navigation technology. Understanding the theory and principles described in this book requires a multidisciplinary background of robotics, nonlinear system, sensor network, network engineering, computer science, physics, etc. The book at first explores SLAM problems through extended Kalman filters, sparse nonlinear graphical representation and particle filters methods. Next, fundamental theory of motion planning and map building are presented to provide useful platform for applying SLAM methods in real mobile systems. It is then followed by the application of high-end sensor network and fusion technology that gives useful inputs for realizing autonomous navigation in both indoor and outdoor environments. Finally, some interesting results of map building and tracking can be found in 2D, 2.5D and 3D models. The actual motion of robots and vehicles when the proposed localization and positioning methods are deployed to the system can also be observed together with tracking maps and trajectory analysis. Since SLAM techniques mostly deal with static environments, this book provides good reference for future understanding the interaction of moving and non-moving objects in SLAM that still remain as open research issue in autonomous navigation technology. Hanafiah Yussof Nagoya University, Japan Universiti Teknologi MARA, Malaysia
- 11. VII Contents Preface V 1. Visual Localisation of quadruped walking robots 001 Renato Samperio and Huosheng Hu 2. Ranging fusion for accurating state of the art robot localization 027 Hamed Bastani and Hamid Mirmohammad-Sadeghi 3. Basic Extended Kalman Filter – Simultaneous Localisation and Mapping 039 Oduetse Matsebe, Molaletsa Namoshe and Nkgatho Tlale 4. Model based Kalman Filter Mobile Robot Self-Localization 059 Edouard Ivanjko, Andreja Kitanov and Ivan Petrović 5. Global Localization based on a Rejection Differential Evolution Filter 091 M.L. Muñoz, L. Moreno, D. Blanco and S. Garrido 6. Reliable Localization Systems including GNSS Bias Correction 119 Pierre Delmas, Christophe Debain, Roland Chapuis and Cédric Tessier 7. Evaluation of aligning methods for landmark-based maps in visual SLAM 133 Mónica Ballesta, Óscar Reinoso, Arturo Gil, Luis Payá and Miguel Juliá 8. Key Elements for Motion Planning Algorithms 151 Antonio Benitez, Ignacio Huitzil, Daniel Vallejo, Jorge de la Calleja and Ma. Auxilio Medina 9. Optimum Biped Trajectory Planning for Humanoid Robot Navigation in Unseen Environment 175 Hanafiah Yussof and Masahiro Ohka 10. Multi-Robot Cooperative Sensing and Localization 207 Kai-Tai Song, Chi-Yi Tsai and Cheng-Hsien Chiu Huang 11. Filtering Algorithm for Reliable Localization of Mobile Robot in Multi-Sensor Environment 227 Yong-Shik Kim, Jae Hoon Lee, Bong Keun Kim, Hyun Min Do and Akihisa Ohya 12. Consistent Map Building Based on Sensor Fusion for Indoor Service Robot 239 Ren C. Luo and Chun C. Lai
- 12. VIII 13. Mobile Robot Localization and Map Building for a Nonholonomic Mobile Robot 253 Songmin Jia and AkiraYasuda 14. Robust Global Urban Localization Based on Road Maps 267 Jose Guivant, Mark Whitty and Alicia Robledo 15. Object Localization using Stereo Vision 285 Sai Krishna Vuppala 16. Vision based Systems for Localization in Service Robots 309 Paulraj M.P. and Hema C.R. 17. Floor texture visual servo using multiple cameras for mobile robot localization 323 Takeshi Matsumoto, David Powers and Nasser Asgari 18. Omni-directional vision sensor for mobile robot navigation based on particle filter 349 Zuoliang Cao, Yanbin Li and Shenghua Ye 19. Visual Odometry and mapping for underwater Autonomous Vehicles 365 Silvia Botelho, Gabriel Oliveira, Paulo Drews, Mônica Figueiredo and Celina Haffele 20. A Daisy-Chaining Visual Servoing Approach with Applications in Tracking, Localization, and Mapping 383 S. S. Mehta, W. E. Dixon, G. Hu and N. Gans 21. Visual Based Localization of a Legged Robot with a topological representation 409 Francisco Martín, Vicente Matellán, José María Cañas and Carlos Agüero 22. Mobile Robot Positioning Based on ZigBee Wireless Sensor Networks and Vision Sensor 423 Wang Hongbo 23. A WSNs-based Approach and System for Mobile Robot Navigation 445 Huawei Liang, Tao Mei and Max Q.-H. Meng 24. Real-Time Wireless Location and Tracking System with Motion Pattern Detection 467 Pedro Abreua, Vasco Vinhasa, Pedro Mendesa, Luís Paulo Reisa and Júlio Gargantab 25. Sound Localization for Robot Navigation 493 Jie Huang 26. Objects Localization and Differentiation Using Ultrasonic Sensors 521 Bogdan Kreczmer 27. Heading Measurements for Indoor Mobile Robots with Minimized Drift using a MEMS Gyroscopes 545 Sung Kyung Hong and Young-sun Ryuh 28. Methods for Wheel Slip and Sinkage Estimation in Mobile Robots 561 Giulio Reina
- 13. Visual Localisation of quadruped walking robots 1 0 Visual Localisation of quadruped walking robots Renato Samperio and Huosheng Hu School of Computer Science and Electronic Engineering, University of Essex United Kingdom 1. Introduction Recently, several solutions to the robot localisation problem have been proposed in the sci- entific community. In this chapter we present a localisation of a visual guided quadruped walking robot in a dynamic environment. We investigate the quality of robot localisation and landmark detection, in which robots perform the RoboCup competition (Kitano et al., 1997). The first part presents an algorithm to determine any entity of interest in a global reference frame, where the robot needs to locate landmarks within its surroundings. In the second part, a fast and hybrid localisation method is deployed to explore the characteristics of the proposed localisation method such as processing time, convergence and accuracy. In general, visual localisation of legged robots can be achieved by using artificial and natural landmarks. The landmark modelling problem has been already investigated by using prede- fined landmark matching and real-time landmark learning strategies as in (Samperio & Hu, 2010). Also, by following the pre-attentive and attentive stages of previously presented work of (Quoc et al., 2004), we propose a landmark model for describing the environment with "in- teresting" features as in (Luke et al., 2005), and to measure the quality of landmark description and selection over time as shown in (Watman et al., 2004). Specifically, we implement visual detection and matching phases of a pre-defined landmark model as in (Hayet et al., 2002) and (Sung et al., 1999), and for real-time recognised landmarks in the frequency domain (Maosen et al., 2005) where they are addressed by a similarity evaluation process presented in (Yoon & Kweon, 2001). Furthermore, we have evaluated the performance of proposed localisation methods, Fuzzy-Markov (FM), Extended Kalman Filters (EKF) and an combined solution of Fuzzy-Markov-Kalman (FM-EKF),as in (Samperio et al., 2007)(Hatice et al., 2006). The proposed hybrid method integrates a probabilistic multi-hypothesis and grid-based maps with EKF-based techniques. As it is presented in (Kristensen & Jensfelt, 2003) and (Gutmann et al., 1998), some methodologies require an extensive computation but offer a reliable posi- tioning system. By cooperating a Markov-based method into the localisation process (Gut- mann, 2002), EKF positioning can converge faster with an inaccurate grid observation. Also. Markov-based techniques and grid-based maps (Fox et al., 1998) are classic approaches to robot localisation but their computational cost is huge when the grid size in a map is small (Duckett & Nehmzow, 2000) and (Jensfelt et al., 2000) for a high resolution solution. Even the problem has been partially solved by the Monte Carlo (MCL) technique (Fox et al., 1999), (Thrun et al., 2000) and (Thrun et al., 2001), it still has difficulties handling environmental changes (Tanaka et al., 2004). In general, EKF maintains a continuous estimation of robot po- sition, but can not manage multi-hypothesis estimations as in (Baltzakis & Trahanias, 2002). 1
- 14. Robot Localization and Map Building 2 Moreover, traditional EKF localisation techniques are computationally efficient, but they may also fail with quadruped walking robots present poor odometry, in situations such as leg slip- page and loss of balance. Furthermore, we propose a hybrid localisation method to eliminate inconsistencies and fuse inaccurate odometry data with costless visual data. The proposed FM-EKF localisation algorithm makes use of a fuzzy cell to speed up convergence and to maintain an efficient localisation. Subsequently, the performance of the proposed method was tested in three experimental comparisons: (i) simple movements along the pitch, (ii) localising and playing combined behaviours and c) kidnapping the robot. The rest of the chapter is organised as follows. Following the brief introduction of Section 1, Section 2 describes the proposed observer module as an updating process of a Bayesian lo- calisation method. Also, robot motion and measurement models are presented in this section for real-time landmark detection. Section 3 investigates the proposed localisation methods. Section 4 presents the system architecture. Some experimental results on landmark modelling and localisation are presented in Section 5 to show the feasibility and performance of the pro- posed localisation methods. Finally, a brief conclusion is given in Section 6. 2. Observer design This section describes a robot observer model for processing motion and measurement phases. These phases, also known as Predict and Update, involve a state estimation in a time sequence for robot localisation. Additionally, at each phase the state is updated by sensing information and modelling noise for each projected state. 2.1 Motion Model The state-space process requires a state vector as processing and positioning units in an ob- server design problem. The state vector contains three variables for robot localisation, i.e., 2D position (x, y) and orientation (θ). Additionally, the prediction phase incorporates noise from robot odometry, as it is presented below: x− t y− t θ− t = xt−1 yt−1 θt−1 + (ulin t + wlin t )cosθt−1 − (ulat t + wlat t )sinθt−1 (ulin t + wlin t )sinθt−1 + (ulat t + wlat t )cosθt−1 urot t + wrot t (4.9) where ulat, ulin and urot are the lateral, linear and rotational components of odometry, and wlat, wlin and wrot are the lateral, linear and rotational components in errors of odometry. Also, t − 1 refers to the time of the previous time step and t to the time of the current step. In general, state estimation is a weighted combination of noisy states using both priori and posterior estimations. Likewise, assuming that v is the measurement noise and w is the pro- cess noise, the expected value of the measurement R and process noise Q covariance matrixes are expressed separately as in the following equations: R = E[vvt ] (4.10) Q = E[wwt ] (4.11) The measurement noise in matrix R represents sensor errors and the Q matrix is also a con- fidence indicator for current prediction which increases or decreases state uncertainty. An odometry motion model, ut−1 is adopted as shown in Figure 1. Moreover, Table 1 describes all variables for three dimensional (linear, lateral and rotational) odometry information where ( x, y) is the estimated values and (x, y) the actual states.
- 15. Visual Localisation of quadruped walking robots 3 Fig. 1. The proposed motion model for Aibo walking robot According to the empirical experimental data, the odometry system presents a deviation of 30% on average as shown in Equation (4.12). Therefore, by applying a transformation matrix Wt from Equation (4.13), noise can be addressed as robot uncertainty where θ points the robot heading. Qt = (0.3ulin t )2 0 0 0 (0.3ulat t )2 0 0 0 (0.3urot t + √ (ulin t )2+(ulat t )2 500 )2 (4.12) Wt = f w = cosθt−1 −senθt−1 0 senθt−1 cosθt−1 0 0 0 1 (4.13) 2.2 Measurement Model In order to relate the robot to its surroundings, we make use of a landmark representation. The landmarks in the robot environment require notational representation of a measured vector f i t for each i-th feature as it is described in the following equation: f (zt) = {f1 t , f2 t , ...} = { r1 t b1 t s1 t , r2 t b2 t s2 t , ...} (4.14) where landmarks are detected by an onboard active camera in terms of range ri t, bearing bi t and a signature si t for identifying each landmark. A landmark measurement model is defined by a feature-based map m, which consists of a list of signatures and coordinate locations as follows: m = {m1, m2, ...} = {(m1,x, m1,y), (m2,x, m2,y), ...} (4.15)
- 16. Robot Localization and Map Building 4 Variable Description xa x axis of world coordinate system ya y axis of world coordinate system xt−1 previous robot x position in world coordinate system yt−1 previous robot y position in world coordinate system θt−1 previous robot heading in world coordinate system xt−1 previous state x axis in robot coordinate system yt−1 previous state y axis in robot coordinate system ulin,lat t lineal and lateral odometry displacement in robot coordinate system urot t rotational odometry displacement in robot coordinate system xt current robot x position in world coordinate system yt current robot y position in world coordinate system θt current robot heading in world coordinate system xt current state x axis in robot coordinate system yt current state y axis in robot coordinate system Table 1. Description of variables for obtaining linear, lateral and rotational odometry informa- tion. where the i-th feature at time t corresponds to the j-th landmark detected by a robot whose pose is xt = x y θ T the implemented model is: ri t(x, y, θ) bi t(x, y, θ) si t(x, y, θ) = (mj,x − x)2 + (mj,y − y)2 atan2(mj,y − y, mj,x − x)) − θ sj (4.16) The proposed landmark model requires an already known environment with defined land- marks and constantly observed visual features. Therefore, robot perception uses mainly de- fined landmarks if they are qualified as reliable landmarks. 2.2.1 Defined Landmark Recognition The landmarks are coloured beacons located in a fixed position and are recognised by image operators. Figure 2 presents the quality of the visual detection by a comparison of distance errors in the observations of beacons and goals. As can be seen, the beacons are better recog- nised than goals when they are far away from the robot. Any visible landmark in a range from 2m to 3m has a comparatively less error than a near object. Figure 2.b shows the angle errors for beacons and goals respectively, where angle errors of beacons are bigger than the ones for goals. The beacon errors slightly reduces when object becomes distant. Contrastingly, the goal errors increases as soon the robot has a wider angle of perception. These graphs also illustrates errors for observations with distance and angle variations. In both graphs, error measurements are presented in constant light conditions and without oc- clusion or any external noise that can affect the landmark perception. 2.2.2 Undefined Landmark Recognition A landmark modelling is used for detecting undefined environment and frequently appearing features. The procedure is accomplished by characterising and evaluating familiarised shapes from detected objects which are characterised by sets of properties or entities. Such process is described in the following stages:
- 17. Visual Localisation of quadruped walking robots 5 Fig. 2. Distance and angle errors in landmarks observations for beacons and goals of proposed landmark model. • Entity Recognition The first stage of dynamic landmark modelling relies on feature identification from constantly observed occurrences. The information is obtained from colour surface descriptors by a landmark entity structure. An entity is integrated by pairs or triplets of blobs with unique characteristics constructed from merging and com- paring linear blobs operators. The procedure interprets surface characteristics for ob- taining range frequency by using the following operations: 1. Obtain and validate entity’s position from the robot’s perspective. 2. Get blobs’ overlapping values with respect to their size. 3. Evaluate compactness value from blobs situated in a bounding box. 4. Validate eccentricity for blobs assimilated in current the entity. • Model Evaluation The model evaluation phase describes a procedure for achieving landmark entities for a real time recognition. The process makes use of previously defined models and merges them for each sensing step. The process is described in Algorithm 1: From the main loop algorithm is obtained a list of candidate entities {E} to obtain a col- lection of landmark models {L}. This selection requires three operations for comparing an entity with a landmark model: – Colour combination is used for checking entities with same type of colours as a landmark model. – Descriptive operators, are implemented for matching features with a similar char- acteristics. The matching process merges entities with a ±0.3 range ratio from defined models. – Time stamp and Frequency are recogised every minute for filtering long lasting models using a removing and merging process of non leading landmark models. The merging process is achieved using a bubble sort comparison with a swapping stage modified for evaluating similarity values and it also eliminates 10% of the landmark
- 18. Robot Localization and Map Building 6 Algorithm 1 Process for creating a landmark model from a list of observed features. Require: Map of observed features {E} Require: A collection of landmark models {L} {The following operations generate the landmark model information.} 1: for all {E}i ⊆ {E} do 2: Evaluate ColourCombination({E}i) {C}i 3: Evaluate BlobDistances({E}i) di 4: Obtain TimeStamp({E}ii) ti 5: Create Entity({C}i, di, ti) j 6: for {L}k MATCHON{L} do {If information is similar to an achieved model } 7: if j ∈ {L}k then 8: Update {L}k(j) {Update modelled values and} 9: Increase {L}k frequency {Increase modelled frequency} 10: else {If modelled information does not exist } 11: Create {L}k+1(j) {Create model and} 12: Increase {L}k+1 frequency {Increase modelled frequency} 13: end if 14: if time 1 min then {After one minute } 15: MergeList({L}) {Select best models} 16: end if 17: end for 18: end for candidates. The similarity values are evaluated using Equation 3.4 and the probability of perception using Equation 3.5: p(i, j) = M(i, j) N ∑ k=1 M(k, j) (3.4) M(i, j) = P ∑ l=1 E(i, j, l) (3.5) where N indicates the achieved candidate models, i is the sampled entity, j is the compared landmark model, M(i, j) is the landmark similarity measure obtained from matching an entity’s descriptors and assigning a probability of perception as described in Equation 3.6, P is the total descriptors, l is a landmark descriptor and E(i, j, l) is the Euclidian distance of each landmark model compared, estimated using Equation 3.7: N ∑ k=1 M(k, j) = 1 (3.6) E(i, j, l) = Ll ∑ m=1 (im − lm)2 σ2 m (3.7)
- 19. Visual Localisation of quadruped walking robots 7 where Ll refers to all possible operators from the current landmark model, σm is the standard deviation for each sampled entity im in a sample set and l is a landmark de- scriptor value. 3. Localisation Methods Robot localisation is an environment analysis task determined by an internal state obtained from robot-environment interaction combined with any sensed observations. The traditional state assumption relies on the robot’s influence over its world and on the robot’s perception of its environment. Both steps are logically divided into independent processes which use a state transition for integrating data into a predictive and updating state. Therefore, the implemented localisation methods contain measurement and control phases as part of state integration and a robot pose conformed through a Bayesian approach. On the one hand, the control phase is assigned to robot odometry which translates its motion into lateral, linear and rotational velocities. On the other hand, the measurement phase integrates robot sensed information by visual features. The following sections describe particular phase characteristics for each localisation approach. 3.1 Fuzzy Markov Method As it is shown in the FM grid-based method of (Buschka et al., 2000) and (Herrero-Pérez et al., 2004), a grid Gt contains a number of cells for each grid element Gt(x, y) for holding a proba- bility value for a possible robot position in a range of [0, 1]. The fuzzy cell (fcell) is represented as a fuzzy trapezoid (Figure 3) defined by a tuple θ, ∆, α, h, b , where θ is robot orientation at the trapezoid centre with values in a range of [0, 2π]; ∆ is uncertainty in a robot orientation θ; h corresponds to fuzzy cell (fcell) with a range of [0, 1]; α is a slope in the trapezoid, and b is a correcting bias. Fig. 3. Graphic representation of robot pose in an f uzzy cell Since a Bayesian filtering technique is implemented, localisation process works in predict- observe-update phases for estimating robot state. In particular, the Predict step adjusts to motion information from robot movements. Then, the Observe step gathers sensed infor- mation. Finally, the Update step incorporates results from the Predict and Observe steps for obtaining a new estimation of a fuzzy grid-map. The process sequence is described as follows: 1. Predict step. During this step, robot movements along grid-cells are represented by a distribution which is continuously blurred. As described in previous work in (Herrero- Pérez et al., 2004), the blurring is based on odometry information reducing grid occu- pancy for robot movements as shown in Figure 4(c)). Thus, the grid state G t is obtained by performing a translation and rotation of Gt−1 state distribution according to motion u. Subsequently, this odometry-based blurring, Bt, is uniformly calculated for including uncertainty in a motion state.
- 20. Robot Localization and Map Building 8 Thus, state transition probability includes as part of robot control, the blurring from odometry values as it is described in the following equation: G t = f (Gt | Gt−1, u) ⊗ Bt (4.30) 2. Observe step. In this step, each observed landmark i is represented as a vector zi, which includes both range and bearing information obtained from visual perception. For each observed landmark zi, a grid-map Si,t is built such that Si,t(x, y, θ| zi) is matched to a robot position at (x, y, θ) given an observation r at time t. 3. Update step. At this step, grid state G t obtained from the prediction step is merged with each observation step St,i. Afterwards, a fuzzy intersection is obtained using a product operator as follows: Gt = f (zt | Gt) (4.31) Gt = G t × St,1 × St,2 × · · · × St,n (4.32) (a) (b) (c) (d) (e) (f) Fig. 4. In this figure is shown a simulated localisation process of FM grid starting from ab- solute uncertainty of robot pose (a) and some initial uncertainty (b) and (c). Through to an approximated (d) and finally to an acceptable robot pose estimation obtained from simulated environment explained in (Samperio Hu, 2008). A simulated example of this process is shown in Figure 4. In this set of Figures, Figure 4(a) illustrates how the system is initialised with absolute uncertainty of robot pose as the white areas. Thereafter, the robot incorporates landmark and goal information where each grid state Gt is updated whenever an observation can be successfully matched to a robot position, as
- 21. Visual Localisation of quadruped walking robots 9 illustrated in Figure 4(b). Subsequently, movements and observations of various landmarks enable the robot to localise itself, as shown from Figure 4(c) to Figure 4(f). This method’s performance is evaluated in terms of accuracy and computational cost during a real time robot execution. Thus, a reasonable fcell size of 20 cm2 is addressed for less accuracy and computing cost in a pitch space of 500cmx400cm. This localisation method offers the following advantages, according to (Herrero-Pérez et al., 2004): • Fast recovery from previous errors in the robot pose estimation and kidnappings. • Multi-hypotheses for robot pose (x, y) . • It is much faster than classical Markovian approaches. However, its disadvantages are: • Mono-hypothesis for orientation estimation. • It is very sensitive to sensor errors. • The presence of false positives makes the method unstable in noisy conditions. • Computational time can increase dramatically. 3.2 Extended Kalman Filter method Techniques related to EKF have become one of the most popular tools for state estimation in robotics. This approach makes use of a state vector for robot positioning which is related to environment perception and robot odometry. For instance, robot position is adapted using a vector st which contains (x, y) as robot position and θ as orientation. s = xrobot yrobot θrobot (4.17) As a Bayesian filtering method, EKF is implemented Predict and Update steps, described in detail below: 1. Prediction step. This phase requires of an initial state or previous states and robot odometry information as control data for predicting a state vector. Therefore, the current robot state s− t is affected by odometry measures, including a noise approximation for error and control estimations P− t . Initially, robot control probability is represented by using: s− t = f (st−1, ut−1, wt) (4.18) where the nonlinear function f relates the previous state st−1, control input ut−1 and the pro- cess noise wt. Afterwards, a covariance matrix P− t is used for representing errors in state estimation obtained from the previous step’s covariance matrix Pt−1 and defined process noise. For that reason, the covariance matrix is related to the robot’s previous state and the transformed control data, as described in the next equation: P− t = AtPt−1 AT t + WtQt−1WT t (4.19)
- 22. Robot Localization and Map Building 10 where AtPt−1 AT t is a progression of Pt−1 along a new movement and At is defined as follows: At = f s = 1 0 −ulat t cosθt − ulin t senθt−1 0 1 ulin t cosθt − ulat t senθt−1 0 0 1 (4.19) and WtQt−1WT t represents odometry noise, Wt is Jacobian motion state approximation and Qt is a covariance matrix as follows: Qt = E[wtwT t ] (4.20) The Sony AIBO robot may not be able to obtain a landmark observation at each localisation step but it is constantly executing a motion movement. Therefore, it is assumed that frequency of odometry calculation is higher than visually sensed measurements. For this reason, con- trol steps are executed independently from measurement states (Kiriy Buehler, 2002) and covariance matrix actualisation is presented as follows: st = s− t (4.21) Pt = P− t (4.22) 2. Updating step. During this phase, sensed data and noise covariance Pt are used for obtain- ing a new state vector. The sensor model is also updated using measured landmarks m1···6,(x,y) as environmental descriptive data. Thus, each zi t of the i landmarks is measured as distance and angle with a vector (ri t, φi t). In order to obtain an updated state, the next equation is used: st = st−1 + Ki t(zi t − ẑi t) = st−1 + Ki t(zi t − hi (st−1)) (4.23) where hi(st−1) is a predicted measurement calculated from the following non-linear functions: ẑi t = hi (st−1) = (mi t,x − st−1,x)2 + (mi t,y − st−1,y) atan2(mi t,x − st−1,x, mi t,y − st−1,y) − st−1,θ (4.24) Then, the Kalman gain, Ki t, is obtained from the next equation: Ki t = Pt−1(Hi t)T (Si t)−1 (4.25) where Si t is the uncertainty for each predicted measurement ẑi t and is calculated as follows: Si t = Hi tPt−1(Hi t)T + Ri t (4.26) Then Hi t describes changes in the robot position as follows: Hi t = hi(st−1)st = − mi t,x−st−1,x (mi t,x−st−1,x)2+(mi t,y−st−1,y)2 − mi t,y−st−1,y (mi t,x−st−1,x)2+(mi t,y−st−1,y)2 0 mi t,y−st−1,y (mi t,x−st−1,x)2+(mi t,y−st−1,y)2 − mi t,x−st−1,x (mi t,x−st−1,x)2+(mi t,y−st−1,y)2 −1 0 0 0 (4.27) where Ri t represents the measurement noise which was empirically obtained and Pt is calcu- lated using the following equation:
- 23. Visual Localisation of quadruped walking robots 11 Pt = (I − Ki tHi t)Pt−1 (4.28) Finally, as not all ẑi t values are obtained at every observation, zi t values are evaluated for each observation and δi t is a confidence measurement obtained from Equation (4.29). The confi- dence observation measurement has a threshold value between 5 and 100, which varies ac- cording to localisation quality. δi t = (zi t − ẑi t)T (Si t)−1 (zi t − ẑi t) (4.29) 3.3 FM-EKF method Merging the FM and EKF algorithms is proposed in order to achieve computational efficiency, robustness and reliability for a novel robot localisation method. In particular, the FM-EKF method deals with inaccurate perception and odometry data for combining method hypothe- ses in order to obtain the most reliable position from both approaches. The hybrid procedure is fully described in Algorithm 2, in which the fcell grid size is (50-100 cm) which is considerably wider than FM’s. Also the fcell is initialised in the space map centre. Subsequently, a variable is iterated for controlling FM results and it is used for comparing robot EKF positioning quality. The localisation quality indicates if EKF needs to be reset in the case where the robot is lost or the EKF position is out of FM range. Algorithm 2 Description of the FM-EKF algorithm. Require: positionFM over all pitch Require: positionEKF over all pitch 1: while robotLocalise do 2: {Execute”Predict”phases f orFMandEKF} 3: Predict positionFM using motion model 4: Predict positionEKF using motion model 5: {Execute”Correct”phases f orFMandEKF} 6: Correct positionFM using perception model 7: Correct positionEKF using perception model 8: {Checkqualityo f localisation f orEKFusingFM} 9: if (quality(positionFM) quality(positionEKF) then 10: Initialise positionEKF to positionFM 11: else 12: robot position ← positionEKF 13: end if 14: end while The FM-EKF algorithm follows the predict-observe-update scheme as part of a Bayesian ap- proach. The input data for the algorithm requires similar motion and perception data. Thus, the hybrid characteristics maintain a combined hypothesis of robot pose estimation using data that is independently obtained. Conversely, this can adapt identical measurement and control information for generating two different pose estimations where, under controlled circum- stances one depends on the other. From one viewpoint, FM localisation is a robust solution for noisy conditions. However, it is also computationally expensive and cannot operate efficiently in real-time environments
- 24. Robot Localization and Map Building 12 with a high resolution map. Therefore, its computational accuracy is inversely proportional to the fcell size. From a different perspective, EKF is an efficient and accurate positioning system which can converge computationally faster than FM. The main drawback of EKF is a misrepresentation in the multimodal positioning information and method initialisation. Fig. 5. Flux diagram of hybrid localisation process. The hybrid method combines FM grid accuracy with EKF tracking efficiency. As it is shown in Figure 5, both methods use the same control and measurement information for obtaining a robot pose and positioning quality indicators. The EKF quality value is originated from the eigenvalues of the error covariance matrix and from noise in the grid- map. As a result, EKF localisation is compared with FM quality value for obtaining a robot pose estimation. The EKF position is updated whenever the robot position is lost or it needs to be initialised. The FM method runs considerably faster though it is less accurate. This method implements a Bayesian approach for robot-environment interaction in a locali- sation algorithm for obtaining robot position and orientation information. In this method a wider fcell size is used for the FM grid-map implementation and EKF tracking capabilities are developed to reduce computational time. 4. System Overview The configuration of the proposed HRI is presented in Figure 6. The user-robot interface man- ages robot localisation information, user commands from a GUI and the overhead tracking, known as the VICON tracking system for tracking robot pose and position. This overhead tracking system transmits robot heading and position data in real time to a GUI where the information is formatted and presented to the user. The system also includes a robot localisation as a subsystem composed of visual perception, motion and behaviour planning modules which continuously emits robot positioning infor- mation. In this particular case, localisation output is obtained independently of robot be- haviour moreover they share same processing resources. Additionally, robot-visual informa- tion can be generated online from GUI from characterising environmental landmarks into robot configuration. Thus, the user can manage and control the experimental execution using online GUI tasks. The GUI tasks are for designing and controlling robot behaviour and localisation methods,
- 25. Visual Localisation of quadruped walking robots 13 Fig. 6. Complete configuration of used human-robot interface. and for managing simulated and experimental results. Moreover, tracking results are the ex- periments’ input and output of a grand truth that is evaluating robot self-localisation results. 5. Experimental Results The presented experimental results contain the analysis of the undefined landmark models and a comparison of implemented localisation methods. The undefined landmark modelling is designed for detecting environment features that could support the quality of the locali- sation methods. All localisation methods make use of defined landmarks as main source of information. The first set of experiments describe the feasibility for employing a not defined landmark as a source for localisation. These experiments measure the robot ability to define a new landmark in an indoor but dynamic environment. The second set of experiments compare the quality of localisation for the FM, EKF and FM-EKF independently from a random robot behaviour and environment interaction. Such experiments characterise particular situations when each of the methods exhibits an acceptable performance in the proposed system. 5.1 Dynamic landmark acquisition The performance for angle and distance is evaluated in three experiments. For the first and second experiments, the robot is placed in a fixed position on the football pitch where it con- tinuously pans its head. Thus, the robot maintains simultaneously a perception process and a dynamic landmark creation. Figure 7 show the positions of 1683 and 1173 dynamic models created for the first and second experiments over a duration of five minutes. Initially, newly acquired landmarks are located at 500 mm and with an angle of 3Π/4rad from the robot’s centre. Results are presented in Table ??. The tables for Experiments 1 and 2, illustrate the mean (x̃) and standard deviation (σ) of each entity’s distance, angle and errors from the robot’s perspective. In the third experiment, landmark models are tested during a continuous robot movement. This experiment consists of obtaining results at the time the robot is moving along a circular
- 26. Robot Localization and Map Building 14 Fig. 7. Landmark model recognition for Experiments 1, 2 and 3
- 27. Visual Localisation of quadruped walking robots 15 Experpiment 1 Distance Angle Error in Distance Error in Angle Mean 489.02 146.89 256.46 2.37 StdDev 293.14 9.33 133.44 8.91 Experpiment 2 Distance Angle Error in Distance Error in Angle Mean 394.02 48.63 86.91 2.35 StdDev 117.32 2.91 73.58 1.71 Experpiment 3 Distance Angle Error in Distance Error in Angle Mean 305.67 12.67 90.30 3.61 StdDev 105.79 4.53 54.37 2.73 Table 2. Mean and standard deviation for experiment 1, 2 and 3. trajectory with 20 cm of bandwidth radio, and whilst the robot’s head is continuously panning. The robot is initially positioned 500 mm away from a coloured beacon situated at 0 degrees from the robot’s mass centre. The robot is also located in between three defined and one undefined landmarks. Results obtained from dynamic landmark modelling are illustrated in Figure 7. All images illustrate the generated landmark models during experimental execution. Also it is shown darker marks on all graphs represent an accumulated average of an observed landmark model. This experiment required 903 successful landmark models detected over five minute duration of continuous robot movement and the results are presented in the last part of the table for Experiment 3. The results show magnitudes for mean (x̃) and standard deviation (σ), distance, angle and errors from the robot perspective. Each of the images illustrates landmark models generated during experimental execution, represented as the accumulated average of all observed models. In particular for the first two experiments, the robot is able to offer an acceptable angular error estimation in spite of a variable proximity range. The results for angular and distance errors are similar for each experiment. However, landmark modelling performance is susceptible to perception errors and obvious proximity difference from the perceived to the sensed object. The average entity of all models presents a minimal angular error in a real-time visual pro- cess. An evaluation of the experiments is presented in Box and Whisker graphs for error on position, distance and angle in Figure 8. Therefore, the angle error is the only acceptable value in comparison with distance or po- sitioning performance. Also, the third experiment shows a more comprehensive real-time measuring with a lower amount of defined landmark models and a more controllable error performance. 5.2 Comparison of localisation methods The experiments were carried out in three stages of work: (i) simple movements; (ii) com- bined behaviours; and (iii) kidnapped robot. Each experiment set is to show robot positioning abilities in a RoboCup environment. The total set of experiment updates are of 15, with 14123 updates in total. In each experimental set, the robot poses estimated by EKF, FM and FM-EKF localisation methods are compared with the ground truth generated by the overhead vision system. In addition, each experiment set is compared respectively within its processing time. Experimental sets are described below:
- 28. Robot Localization and Map Building 16 Fig. 8. Error in angle for Experiments 1, 2 and 3. 1. Simple Movements. This stage includes straight and circular robot trajectories in for- ward and backward directions within the pitch. 2. Combined Behaviour. This stage is composed by a pair of high level behaviours. Our first experiment consists of reaching a predefined group of coordinated points along the pitch. Then, the second experiment is about playing alone and with another dog to obtain localisation results during a long period. 3. Kidnapped Robot. This stage is realised randomly in sequences of kidnap time and pose. For each kidnap session the objective is to obtain information about where the robot is and how fast it can localise again. All experiments in a playing session with an active localisation are measured by showing the type of environment in which each experiment is conducted and how they directly affect robot behaviour and localisation results. In particular, the robot is affected by robot displacement, experimental time of execution and quantity of localisation cycles. These characteristics are described as follows and it is shown in Table 3: 1. Robot Displacement is the accumulated distance measured from each simulated method step from the perspective of the grand truth mobility.
- 29. Visual Localisation of quadruped walking robots 17 2. Localisation Cycles include any completed iteration from update-observe-predict stages for any localisation method. 3. Time of execution refers to total amount of time taken for each experiment with a time of 1341.38 s for all the experiments. Exp. 1 Exp. 2 Exp. 3 Displacement (mm) 15142.26 5655.82 11228.42 Time of Execution (s) 210.90 29.14 85.01 Localisation Cycles (iterations) 248 67 103 Table 3. Experimental conditions for a simulated environment. The experimental output depends on robot behaviour and environment conditions for obtain- ing parameters of performance. On the one side, robot behaviour is embodied by the specific robot tasks executed such as localise, kick the ball, search for the ball, search for landmarks, search for players, move to a point in the pitch, start, stop, finish, and so on. On the other side, robot control characteristics describe robot performance on the basis of values such as: robot displacement, time of execution, localisation cycles and landmark visibility. Specifically, robot performance crite- ria are described for the following environment conditions: 1. Robot Displacement is the distance covered by the robot for a complete experiment, obtained from grand truth movement tracking. The total displacement from all experi- ments is 146647.75 mm. 2. Landmark Visibility is the frequency of the detected true positives for each landmark model among all perceived models. Moreover, the visibility ranges are related per each localisation cycle for all natural and artificial landmarks models. The average landmark visibility obtained from all the experiments is in the order of 26.10 % landmarks per total of localisation cycles. 3. Time of Execution is the time required to perform each experiment. The total time of execution for all the experiments is 902.70 s. 4. Localisation Cycles is a complete execution of a correct and update steps through the localisation module. The amount of tries for these experiments are 7813 cycles. The internal robot conditions is shown in Table ??: Exp 1 Exp 2 Exp 3 Displacement (mm) 5770.72 62055.79 78821.23 Landmark Visibility (true positives/total obs) 0.2265 0.3628 0.2937 Time of Execution (s) 38.67 270.36 593.66 Localisation Cycles (iterations) 371 2565 4877 Table 4. Experimental conditions for a real-time environment. In Experiment 1, the robot follows a trajectory in order to localise and generate a set of visi- ble ground truth points along the pitch. In Figures 9 and 10 are presented the error in X and Y axis by comparing the EKF, FM, FM-EKF methods with a grand truth. In this graphs it is shown a similar performance between the methods EKF and FM-EKF for the error in X and Y
- 30. Robot Localization and Map Building 18 Fig. 9. Error in X axis during a simple walk along the pitch in Experiment 1. Fig. 10. Error in Y axis during a simple walk along the pitch in Experiment 1. Fig. 11. Error in θ axis during a simple walk along the pitch in Experiment 1. Fig. 12. Time performance for localisation methods during a walk along the pitch in Exp. 1.
- 31. Visual Localisation of quadruped walking robots 19 Fig. 13. Robot trajectories for EKF, FM, FM-EKF and the overhead camera in Exp. 1. axis but a poor performance of the FM. However for the orientation error displayed in Figure 11 is shown that whenever the robot walks along the pitch without any lack of information, FM-EKF improves comparatively from the others. Figure 12 shows the processing time for all methods, in which the proposed FM-EKF method is faster than the FM method, but slower than the EKF method. Finally, in Figure 13 is presented the estimated trajectories and the over- head trajectory. As can be seen, during this experiment is not possible to converge accurately for FM but it is for EKF and FM-EKF methods where the last one presents a more accurate robot heading. For Experiment 2, is tested a combined behaviour performance by evaluating a playing ses- sion for a single and multiple robots. Figures 14 and 15 present as the best methods the EKF and FM-EKF with a slightly improvement of errors in the FM-EKF calculations. In Figure 16 is shown the heading error during a playing session where the robot visibility is affected by a constantly use of the head but still FM-EKF, maintains an more likely performance compared to the grand truth. Figure 17 shows the processing time per algorithm iteration during the robot performance with a faster EKF method. Finally, Figure 18 shows the difference of robot trajectories estimated by FM-EKF and overhead tracking system. In the last experiment, the robot was randomly kidnapped in terms of time, position and orientation. After the robot is manually deposited in a different pitch zone, its localisation performance is evaluated and shown in the figures for Experiment 3. Figures 19 and 20 show positioning errors for X and Y axis during a kidnapping sequence. Also, FM-EKF has a similar development for orientation error as it is shown in Figure 21. Figure 22 shows the processing
- 32. Robot Localization and Map Building 20 Fig. 14. Error in X axis during a simple walk along the pitch in Experiment 2. Fig. 15. Error in Y axis during a simple walk along the pitch in Experiment 2. Fig. 16. Error in θ axis during a simple walk along the pitch in Experiment 2. Fig. 17. Time performance for localisation methods during a walk along the pitch in Exp. 2.
- 33. Visual Localisation of quadruped walking robots 21 Fig. 18. Robot trajectories for EKF, FM, FM-EKF and the overhead camera in Exp. 2. time per iteration for all algorithms a kidnap session. Finally, in Figure 23 and for clarity rea- sons is presented the trajectories estimated only by FM-EKF, EKF and overhead vision system. Results from kidnapped experiments show the resetting transition from a local minimum to fast convergence in 3.23 seconds. Even EKF has the most efficient computation time, FM-EKF offers the most stable performance and is a most suitable method for robot localisation in a dynamic indoor environment. 6. Conclusions This chapter presents an implementation of real-time visual landmark perception for a quadruped walking robot in the RoboCup domain. The proposed approach interprets an object by using symbolic representation of environmental features such as natural, artificial or undefined. Also, a novel hybrid localisation approach is proposed for fast and accurate robot localisation of an active vision platform. The proposed FM-EKF method integrates FM and EKF algorithms using both visual and odometry information. The experimental results show that undefined landmarks can be recognised accurately during static and moving robot recognition sessions. On the other hand, it is clear that the hybrid method offers a more stable performance and better localisation accuracy for a legged robot which has noisy odometry information. The distance error is reduced to ±20 mm and the orientation error is 0.2 degrees. Further work will focus on adapting for invariant scale description during real time image processing and of optimising the filtering of recognized models. Also, research will focus on
- 34. Robot Localization and Map Building 22 Fig. 19. Error in X axis during a simple walk along the pitch in Experiment 3. Fig. 20. Error in Y axis during a simple walk along the pitch in Experiment 3. Fig. 21. Error in θ axis during a simple walk along the pitch in Experiment 3. Fig. 22. Time performance for localisation methods during a walk along the pitch in Exp. 3.
- 35. Visual Localisation of quadruped walking robots 23 Fig. 23. Robot trajectories for EKF, FM, FM-EKF and the overhead camera in Exp. 3., where the thick line indicates kidnapped period. the reinforcement of the quality in observer mechanisms for odometry and visual perception, as well as the improvement of landmark recognition performance. 7. Acknowledgements We would like to thank TeamChaos (http://www.teamchaos.es) for their facilities and pro- gramming work and Essex technical team (http://essexrobotics.essex.ac.uk) for their support in this research. Part of this research was supported by a CONACyT (Mexican government) scholarship with reference number 178622. 8. References Baltzakis, H. Trahanias, P. (2002). Hybrid mobile robot localization using switching state- space models., Proc. of IEEE International Conference on Robotics and Automation, Wash- ington, DC, USA, pp. 366–373. Buschka, P., Saffiotti, A. Wasik, Z. (2000). Fuzzy landmark-based localization for a legged robot, Proc. of IEEE Intelligent Robots and Systems, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1205 – 1210. Duckett, T. Nehmzow, U. (2000). Performance comparison of landmark recognition systems for navigating mobile robots, Proc. 17th National Conf. on Artificial Intelligence (AAAI- 2000), AAAI Press/The MIT Press, pp. 826 – 831.
- 36. Robot Localization and Map Building 24 Fox, D., Burgard, W., Dellaert, F. Thrun, S. (1999). Monte carlo localization: Efficient position estimation for mobile robots, AAAI/IAAI, pp. 343–349. URL: http://citeseer.ist.psu.edu/36645.html Fox, D., Burgard, W. Thrun, S. (1998). Markov localization for reliable robot navigation and people detection, Sensor Based Intelligent Robots, pp. 1–20. Gutmann, J.-S. (2002). Markov-kalman localization for mobile robots., ICPR (2), pp. 601–604. Gutmann, J.-S., Burgard, W., Fox, D. Konolige, K. (1998). An experimental comparison of localization methods, Proc. of IEEE/RSJ International Conference on Intelligen Robots and Systems, Vol. 2, pp. 736 – 743. Hatice, K., C., B. A., L. (2006). Comparison of localization methodsfor a robot soccer team, International Journal of Advanced Robotic Systems 3(4): 295–302. Hayet, J., Lerasle, F. Devy, M. (2002). A visual landmark framework for indoor mobile robot navigation, IEEE International Conference on Robotics and Automation, Vol. 4, pp. 3942 – 3947. Herrero-Pérez, D., Martínez-Barberá, H. M. Saffiotti, A. (2004). Fuzzy self-localization using natural features in the four-legged league, in D. Nardi, M. Riedmiller C. Sammut (eds), RoboCup 2004: Robot Soccer World Cup VIII, LNAI, Springer-Verlag, Berlin, DE. Online at http://www.aass.oru.se/˜asaffio/. Jensfelt, P., Austin, D., Wijk, O. Andersson, M. (2000). Feature based condensation for mo- bile robot localization, Proc. of IEEE International Conference on Robotics and Automa- tion, pp. 2531 – 2537. Kiriy, E. Buehler, M. (2002). Three-state extended kalman filter for mobile robot localization, Technical Report TR-CIM 05.07, McGill University, Montreal, Canada. Kitano, H., Asada, M., Kuniyoshi, Y., Noda, I. Osawa, E. (1997). Robocup: The robot world cup initiative, International Conference on Autonomous Agents archive, Marina del Rey, California, United States, pp. 340 – 347. Kristensen, S. Jensfelt, P. (2003). An experimental comparison of localisation methods, Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 992 – 997. Luke, R., Keller, J., Skubic, M. Senger, S. (2005). Acquiring and maintaining abstract land- mark chunks for cognitive robot navigation, IEEE/RSJ International Conference on In- telligent Robots and Systems, pp. 2566– 2571. Maosen, W., Hashem, T. Zell, A. (2005). Robot navigation using biosonar for natural land- mark tracking, IEEE International Symposium on Computational Intelligence in Robotics and Automation, pp. 3 – 7. Quoc, V. D., Lozo, P., Jain, L., Webb, G. I. Yu, X. (2004). A fast visual search and recogni- tion mechanism for real-time robotics applications, Lecture notes in computer science 3339(17): 937–942. XXII, 1272 p. Samperio, R. Hu, H. (2008). An interactive HRI for walking robots in robocup, In Proc. of the International Symposium on Robotics and Automation IEEE, ZhangJiaJie, Hunan, China. Samperio, R. Hu, H. (2010). Implementation of a localisation-oriented HRI for walking robots in the robocup environment, International Journal of Modelling, Identification and Control (IJMIC) 12(2). Samperio, R., Hu, H., Martin, F. Mantellan, V. (2007). A hybrid approach to fast and accurate localisation for legged robots, Robotica . Cambridge Journals (In Press). Sung, J. A., Rauh, W. Recknagel, M. (1999). Circular coded landmark for optical 3d- measurement and robot vision, IEEE/RSJ International Conference on Intelligent Robots and Systems, Vol. 2, pp. 1128 – 1133.
- 37. Visual Localisation of quadruped walking robots 25 Tanaka, K., Kimuro, Y., Okada, N. Kondo, E. (2004). Global localization with detection of changes in non-stationary environments, Proc. of IEEE International Conference on Robotics and Automation, pp. 1487 – 1492. Thrun, S., Beetz, M., Bennewitz, M., Burgard, W., Cremers, A., Dellaert, F., Fox, D., Hahnel, D., Rosenberg, C., Roy, N., Schulte, J. Schulz, D. (2000). Probabilistic algorithms and the interactive museum tour-guide robot minerva, International Journal of Robotics Research 19(11): 972–999. Thrun, S., Fox, D., Burgard, W. Dellaert, F. (2001). Robust monte carlo localization for mobile robots, Journal of Artificial Intelligence 128(1-2): 99–141. URL: http://citeseer.ist.psu.edu/thrun01robust.html Watman, C., Austin, D., Barnes, N., Overett, G. Thompson, S. (2004). Fast sum of absolute differences visual landmark, IEEE International Conference on Robotics and Automation, Vol. 5, pp. 4827 – 4832. Yoon, K. J. Kweon, I. S. (2001). Artificial landmark tracking based on the color histogram, IEEE/RSJ Intl. Conference on Intelligent Robots and Systems, Vol. 4, pp. 1918–1923.
- 38. Robot Localization and Map Building 26
- 39. Ranging fusion for accurating state of the art robot localization 27 X Ranging fusion for accurating state of the art robot localization Hamed Bastani1 and Hamid Mirmohammad-Sadeghi2 1Jacobs University Bremen, Germany 2Isfahann University of Technology, Iran 1. Introduction Generally speaking, positioning and localization give somehow the same comprehension in terminology. They can be defined as a mechanism for realizing the spatial relationship between desired features. Independent from the mechanisms themselves, they all have certain requirements to fulfil. Scale of measurements and granularity is one important aspect to be investigated. There are limitations, and on the other hand expectations, depending on each particular application. Accuracy gives the closeness of the estimated solution with respect to the associated real position of a feature in the work space (a.k.a ground truth position). Consistency of the realized solution and the ground truth, is represented by precision. Other parameters are still existing which leave more space for investigation depending on the technique used for localization, parameters such as refresh rate, cost (power consumption, computation, price, infrastructure installation burden, ...), mobility and adaptively to the environment (indoor, outdoor, space robotics, underwater vehicles, ...) and so on. From the mobile robotics perspective, localization and mapping are deeply correlated. There is the whole field of Simultaneous Localization and Mapping (SLAM), which deals with the employment of local robot sensors to generate good position estimates and maps; see (Thrun, 2002) for an overview. SLAM is also intensively studied from the multi robot perspective. This is while SLAM requires high end obstacle detection sensors such as laser range finders and it is computationally quite expensive. Aside from SLAM, there are state of the art positioning techniques which can be anyhow fused in order to provide higher accuracy, faster speed and to be capable of dealing with systems with higher degrees of complexity. Here, the aim is to first of all survey an introductory overview on the common robot localization techniques, and particularly then focus on those which employ a rather different approach, i.e ranging by means of specially radio wireless technology. It will be shortly seen that mathematical tools and geometrical representation of a graph model containing multiple robots as the network nodes, can be considered a feature providing higher positioning accuracy compared to the traditional methods. Generally speaking, such improvements are scalable and also provide robustness against variant inevitable disturbing environmental features and measurement noise. 2
- 40. Robot Localization and Map Building 28 2. State of the Art Robot Localization Localization in the field of mobile robotics is vast enough to fall into unique judgements and indeed categorization. There are plenty of approaches tackling the problem from different perspectives. In order to provide a concrete understanding of grouping, we start facing the localization mechanisms with a form of categorization as follows. • Passive Localization: where already present signals are observed and processed by the system in order to deduce location of desired features. Clearly, depending on the signal’s specifications, special sensory system as well as available computation power, certain exibility is required due to passiveness. • Active Localization: in which, the localization mechanism itself generates and uses its own signals for the localization purpose. Preference is up to the particular application where it may choose a solution which falls in either of the above classes. However, a surface comparison says the second approach would be more environmental independent and therefore, more reliable for a wider variety of applications. This again will be a tradeoff for some overhead requirements such as processing power, computation resources and possibly extra auxiliary hardware subunits. From another side of assessment, being utilized hardware point of view, we can introduce the techniques below, which each itself is either passive or active: 1. Dead reckoning: uses encoders, principally to realize translational movements from rotational measurements based on integration. Depending on the application, there are different resolutions defined. This class is the most basic but at the same time the most common one, applied in mobile robotics. Due to its inherit characteristics, this method is considered noisy and less robust. On the other hand, due to its popularity, there has been enough research investment to bring about sufficient improvements for the execution and results quality of this technique (e.g. (Lee) and (Heller) can be referred to). 2. INS methods: which are based on inertial sensors, accelerometers and detectors for electromagnetic field and gravity. They are also based on integration on movement elements, therefore, may eventually lead to error accumulation especially if drift prune sensors are used. Due to vast field of applications, these methods also enjoyed quite enough completeness, thanks to the developed powerful mathematical tools. (Roos, 2002) is for example offering one of these complementary enhancements. 3. Vision and visual odometery: utilizing a single camera, stereo vision or even omni directional imaging, this solution can potentially be useful in giving more information than only working as the localization routine. This solution can considerably become more computationally expensive, especially if employed in a dynamic environment or expected to deal with relatively-non-stationary features. It is however, considered a popular and effective research theme lately, and is enhanced significantly by getting backup support from signal processing techniques, genetic algorithms, as well as evolutionary and learning algorithms.
- 41. Ranging fusion for accurating state of the art robot localization 29 4. Ranging: employing a distance measurement media that can be either laser, infrared, acoustic or radio signals. Ranging can be done using different techniques; recording signal’s Time of Flight, Time Difference of Arrival or Round Trip Time of Flight of the beamed signal, as well as its Angle of Arrival. This class is under main interest to be fused properly for increasing efficiency and accuracy of the traditional methods. There are some less common approaches which indirectly can still be categorized in the classes above. Itemized reference to them is as the following. Doppler sensors can measure velocity of the moving objects. Principally speaking, a sinusoidal signal is emitted from a moving platform and the echo is sensed at a receiver. These sensors can use ultra sound signal as carrier or radio waves, either. Related to the wavelength, resolution and accuracy may differ; a more resolution is achieved if smaller wavelength (in other words higher frequency) is operational. Here again, this technique works based on integrating velocity vectors over time. Electromagnetic trackers can determine objects’ locations and orientations with a high accuracy and resolution (typically around 1mm in coordinates and 0.2◦ in orientation). Not only they are expensive methods, but also electromagnetic trackers have a short range (a few meters) and are very sensitive to presence of metallic objects. These limitations only make them proper for some fancy applications such as body tracking computer games, animation studios and so on. Optical trackers are very robust and typically can achieve high levels of accuracy and resolution. However, they are most useful in well-constrained environments, and tend to be expensive and mechanically complex. Example of this class of positioning devices are head tracker system (Wang et. al, 1990). Proper fusion of any of the introduced techniques above, can give higher precision in localization but at the same time makes the positioning routine computationally more expensive. For example (Choi Oh, 2005) combines sonar and vision, (Carpin Birk, 2004) fuses odometery, INS and ranging, (Fox et. al, 2001) mixes dead reckoning with vision, and there can be found plenty of other practical cases. Besides, each particular method can not be generalized for all applications and might fail under some special circumstances. For instance, using vision or laser rangenders, should be planned based on having a rough perception about the working environment beforehand (specially if system is working in a dynamic work space. If placed out and not moving, the strategy will differ, eg. in (Bastani et. al, 2005)). Solutions like SLAM which overcome the last weakness, need to detect some reliable features from the work space in order to build the positioning structure (i.e. an evolving representation called as the map) based on them. This category has a high complexity and price of calculation. In this vain, recent technique such as pose-graph put significant effort on improvements (Pfingsthhorn Birk, 2008). Concerning again about the environmental perception; INS solutions and accelerometers, may fail if the work space is electromagnetically noisy. Integrating acceleration and using gravity specifications in addition to the dynamics of the system, will cause a potentially large accumulative error in positioning within a long term use, if applied alone.
- 42. Robot Localization and Map Building 30 3. Ranging Technologies and Wireless Media The aim here is to refer to ranging techniques based on wireless technology in order to provide some network modelling and indeed realization of the positions of each node in the network. These nodes being mobile robots, form a dynamic (or in short time windows static) topology. Different network topologies require different positioning system solutions. Their differences come from physical layer specifications, their media access control layer characteristics, some capabilities that their particular network infrastructure provides, or on the other hand, limitations that are imposed by the network structure. We first very roughly categorizes an overview of the positioning solutions including variety of the global positioning systems, those applied on cellular and GSM networks, wireless LANs, and eventually ad hoc sensor networks. 3.1 Wireless Media Two communicating nodes compose the simplest network where there is only one established link available. Network size can grow by increasing the number of nodes. Based on the completeness of the topology, each node may participate in establishing various number of links. This property is used to define degree of a node in the network. Link properties are relatively dependent on the media providing the communication. Bandwidth, signal to noise ratio (SNR), environmental propagation model, transmission power, are some of such various properties. Figure 1 summarizes most commonly available wireless communication media which currently are utilized for network positioning, commercially or in the research fields. With respect to the platform, each solution may provide global or local coordinates which are eventually bidirectionally transformable. Various wireless platforms – based on their inherent specifications and capabilities, may be used such that they fit the environmental conditions and satisfy the localization requirements concerning their accessibility, reliability, maximum achievable resolution and the desired accuracy. Fig. 1. Sweeping the environment from outdoor to indoor, this figure shows how different wireless solutions use their respective platforms in order to provide positioning. They all indeed use some ranging technique for the positioning purpose, no matter time of flight or received signal strength. Depending on the physical size of the cluster, they provide local or global positions. Anyhow these two are bidirectional transformable.
- 43. Ranging fusion for accurating state of the art robot localization 31 Obviously, effectiveness and efficiency of a large scale outdoor positioning system is rather different than a small scale isolated indoor one. What basically differs is the environment which they may fit better for, as well as accuracy requirements which they afford to fulfil. On the x-axis of the diagram in figure 1, moving from outdoor towards indoor environment, introduced platforms become less suitable specially due to the attenuation that indoor environmental conditions apply to the signal. This is while from right to left of the x-axis in the same diagram, platforms and solutions have the potential to be customized for outdoor area as well. The only concern is to cover a large enough area outdoor, by pre-installing the infrastructure. The challenge is dealing with accurate indoor positioning where maximum attenuation is distorting the signal and most of the daily, surveillance and robotics applications are utilized. In this vein, we refer to the WLAN class and then for providing enhancement and more competitive accuracy, will turn to wireless sensor networks. 3.2 Wireless Local Area Networks Very low price and their common accessibility have motivated development of wireless LAN-based indoor positioning systems such as Bluetooth and Wi-Fi. (Salazar, 2004) comprehensively compares typical WLAN systems in terms of markets, architectures, usage, mobility, capacities, and industrial concerns. WLAN-based indoor positioning solutions mostly depend on signal strength utilization. Anyhow they have either a client-based or client-assisted design. Client-based system design: Location estimation is usually performed by RF signal strength characteristics, which works much like pattern matching in cellular location systems. Because signal strength measurement is part of the normal operating mode of wireless equipment, as in Wi-Fi systems, no other hardware infrastructure is required. A basic design utilizes two phases. First, in the offline phase, the system is calibrated and a model is constructed based on received signal strength (RSS) at a finite number of locations within the targeted area. Second, during an online operation in the target area, mobile units report the signal strengths received from each access point (AP) and the system determines the best match between online observations and the offline model. The best matching point is then reported as the estimated position. Client-assisted system design: To ease burden of system management (provisioning, security, deployment, and maintenance), many enterprises prefer client-assisted and infrastructure- based deployments in which simple sniffers monitor client’s activity and measure the signal strength of transmissions received from them (Krishnan, 2004). In client-assisted location system design, client terminals, access points, and sniffers, collaborate to locate a client in the WLAN. Sniffers operate in passive scanning mode and sense transmissions on all channels or on predetermined ones. They listen to communication from mobile terminals and record time-stamped information. The sniffers then put together estimations based on a priory model. A client’s received signal strength at each sniffer is compared to this model using nearest neighbour searching to estimate the clients location (Ganu, 2004). In terms of system deployment, sniffers can either be co-located with APs, or, be located at other
- 44. Robot Localization and Map Building 32 positions and function just like the Location Management Unit in a cellular-based location system. 3.3 Ad hoc Wireless Sensor Networks Sensor networks vary signicantly from traditional cellular networks or similars. Here, nodes are assumed to be small, inexpensive, homogeneous, cooperative, and autonomous. Autonomous nodes in a wireless sensor network (WSN) are equipped with sensing (optional), computation, and communication capabilities. The key idea is to construct an ad hoc network using such wireless nodes whereas nodes’ locations can be realized. Even in a pure networking perspective, location-tagged information can be extremely useful for achieving some certain optimization purposes. For example (Kritzler, 2006) can be referred to which proposes a number of location-aware protocols for ad hoc routing and networking. It is especially difficult to estimate nodes’ positions in ad hoc networks without a common clock as well as in absolutely unsynchronized networks. Most of the localization methods in the sensor networks are based on RF signals’ properties. However, there are other approaches utilizing Ultra Sound or Infra Red light instead. These last two, have certain disadvantages. They are not omnidirectional in broadcasting and their reception, and occlusion if does not completely block the communication, at least distorts the signal signicantly. Due to price exibilities, US methods are still popular for research applications while providing a high accuracy for in virtu small scale models. Not completely inclusive in the same category however there are partially similar techniques which use RFID tags and readers, as well as those WSNs that work based on RF UWB communication, all have proven higher potentials for indoor positioning. An UWB signal is a series of very short baseband pulses with time durations of only a few nanoseconds that exist on all frequencies simultaneously, resembling a blast of electrical noise (Fontanaand, 2002). The fine time resolution of UWB signals makes them promising for use in high-resolution ranging. In this category, time of flight is considered rather than the received signal strength. It provides much less unambiguity but in contrast can be distorted by multipath fading. A generalized maximum-likelihood detector for multipaths in UWB propagation measurement is described in (Lee, 2002). What all these techniques are suffering from is needing a centralized processing scheme as well as a highly accurate and synchronized common clock base. Some approaches are however tackling the problem and do not concern time variant functions. Instead, using for example RFID tags and short-range readers, enables them to provide some proximity information and gives a rough position of the tag within a block accuracy/resolution (e.g. the work by (Fontanaand, 2002) with very short range readers for a laboratory environment localization). The key feature which has to be still highlighted in this category is the overall cost of implementation. 4. Infra Structure Principles In the field of positioning by means of radio signals, there are various measurement techniques that are used to determine position of a node. In a short re-notation they are divided into three groups: • Distance Measurements: ToF, TDoA, RSS • Angle Measurements: AoA • Fingerprinting: RSS patterns (radio maps)
- 45. Ranging fusion for accurating state of the art robot localization 33 Distance and angle measurement methods are the mostly used metrics for outdoor location systems. Distance measurements use the path loss model and ToF measurements to determine a location. Angle Measurements are based on knowing the angle of incidence of the received signal. However, this class requires directional antennas and antenna arrays to measure the angle of incidence. That makes this option not very viable for a node with high- mobility. For smaller scale applications, this method can be utilized by means of ESPAR (Electronically Steerable Parasitic Array Radiator) antennas. Such an antenna steers autonomously its beam toward the arrival direction of desired radio waves and steers the nulls of the beam toward the undesired interfering waves (Ging, 2005). The versatile beam forming capabilities of the ESPAR antenna allows to reduce multipath fading and makes accurate reading for direction of arrival. There are not too much of applicable experiences for indoor mobile robotics, (Shimizu, 2005) for example, applies it on search and rescue robotics for urban indoor environment. Distance and Angle measurements work only with direct line-of-sight signals from the transmitter to the receiver, indeed being widely practical for outdoor environments. For indoors, channel consists of multipath components, and the mobile station is probably surrounded by scattering objects. For these techniques to work, a mobile node has to see at least three signal sources, necessarily required for triangulation. Distance measurement techniques in the simplest case, will end up to multilateration in order to locate position of a desired point, no matter being a transmitter or a receiver. Collaborative multilateration (also referred to as N-hop multilateration) consists of a set of mechanisms that enables nodes to nd several hops away from beacon nodes to collaborate with each other and potentially estimate their locations within desired accuracy limits. Collaborative multilateration is presented in two edges of computation models, centralized and distributed. These can be used in a wide variety of network setups from fully centralized where all the computation takes place at a base station, locally centralized (i.e., computation takes place at a set of cluster heads) to fully distributed where computation takes place at every node. 5. RSS Techniques A popular set of approaches tries to employ the received signal strength (RSS) as distance estimate between a wireless sender and a receiver. If the physical signal itself can not be measured, packet loss can be used to estimate RSS (Royer, 1999). But the relation between the RF signal strength and spatial distances is very complex as real world environments do not only consist of free space. They also include various objects that cause absorption, reflection, diffraction, and scattering of the RF signals (Rappaport, 1996). The transmitted signal therefore most often reaches the receiver by more than one path, resulting in a phenomenon known as multi path fading (Neskovic et. al, 2000). The quality of these techniques is hence very limited; the spatial resolution is restricted to about a meter and there are tremendous error rates (Xang et. al. 2005). They are hence mainly suited for Context-Awareness with room or block resolution (Yin et. al, 2005). Due to the principle problems with RSS, there are attempts to develop dedicated hardware for localizing objects over medium range.
- 46. Robot Localization and Map Building 34 5.1 Properties The indoor environment poses additional challenges compared to the outdoor environment. The channel is complex; having various multipath, scattering and diffraction effects that make estimating the signal strength highly probabilistic. Traditional methods working based on AoA and ToF principles can not be used with this technology, additionally special hardware is required to get a time synchronized network out of the available standard access points. Therefore the only applicable method is the received signal strength technique. RSS is the simplest RF measurement technique as its values are easily accessible through a WLAN interface. It is more preferred than the Signal to Noise ratio (SNR) to be used for the radio signature, because it is more location dependant (Bahl Padmanabhan, 2000). Noise can vary considerably from location to location and may heavily depend on the external factors, while this is not the case for the received signal strength. Since the RSS values still signicantly fluctuate over time for a given location, they can be considered as a random variable, and hence, are described in a statistical fashion in order to estimate the distribution parameters. The fundamentals of the RSS techniques come from the Frii’s Transmission Equation. The reason that Friis’ formula does not work satisfactorily for indoor propagation is that communicating points may suffer from nonl Line of Sight condition (nLoS). Strength decay of the received signal not only comes from path loss, but also shadowing and fading distort the received signal quality. They both depend on the environmental features, barriers and occlusion. Short scale fading due to multipath, adds random high frequency terms with large amplitude (Rappaport, 1996). This issue is more effective indoors. Still because of less complexity that the hardware design and implementation phases need, the RSS solution has been in the field of interest amongst most of the localization researches. 5.2 Techniques Apart from the statistical or probabilistic representation of signals, there are essentially two categories of RSS based techniques for positioning using WLAN: Trilateration and Location Fingerprinting. The prerequisite of the trilateration method is using a signal propagation model to convert RSS measurement to a transmitter-receiver (T-R) separate distance estimate. Utilizing the general empirical model can only obtain a very inaccurate distance of T-R, therefore a more accurate and correction-enforced model is required. Before a positioning system can estimate the location, a ngerprint database (also referred to as a radio map) constructed. In other words, a ”Location Fingerprinting” localization system consists of two phases, the offline (training) and the online (localization) phase. During the online phase a site survey is performed by measuring the RSS values from multiple APs. The floor is divided into predefined grid points. The RSS values are measured at desired locations on the grid. Multiple measurements are taken and the average values are stored in a database. The location ngerprint refers to the vector of RSS values from each access point and their corresponding location on the grid. A reference carpet refers to the collection of ngerprints and their associated locations for a given area. The drawback here is the extensive training values that have to be predetermined, separately for each particular indoor environment. Understanding the statistical properties of the location ngerprint (aka. RSS vector) is important for the design of a positioning system due to several reasons. It can provide insights into how many APs are needed to uniquely identify a location (Kaemarungsi
- 47. Ranging fusion for accurating state of the art robot localization 35 Krishnamurthy, 2004) with a given accuracy and precision, and, whether preprocessing of the RSS measurements can improve such accuracy. Within the same perspective, (Li et. al, 2005) has proposed a hybrid method compose of two stages. Area localization has been seen as a more viable alternative compared to point based localization mainly due to the fact that they can better describe localization uncertainty (Elnahraway et. al, 2004). They can easily trade accuracy for precision. Accuracy is the likelihood of the object being within the returned area, while precision is the size of the returned area. Point based algorithms on the other hand have difficulty in describing this behaviour. It was found that although area based approaches better described the localization uncertainty, their absolute performance is similar to point based approaches (Elnahraway et. al, 2004). 6. Physical and Logical Topology of WSN Field of networked robotics is envisioned to be one of the key research areas in robotics recently (Bekey et. al, -). This research field, flourishing in the last decade or so, is gaining additional momentum thanks to the advent of cheap, easy to deploy and low power nodes to build sensor networks. Richness of different sensors, and their prompt availability open new scenarios to solve some long standing problems. In this scenario, plenty of wireless sensors are deployed to the environment, in order to build up a network. This network first of all aims for holding a full connectivity which in most of applications can be represented by a graph. Plenty of theories and properties of graphs can merge to the scenario and open new doors for improvements (Gotsman Koren, 2005). However full network connectivity has its own advantages, local connectivities in order to extract connected clusters also are shown to be sufficient under some circumstances (Chan et. al, 2005). Assume a scenario that builds a mobile wireless (-sensor) network with possibly physical dynamic topology. If there are enough relative distances information available, it is not quite complicated to use some multilateration technique for finding a position, but it is conditioned on the availability of enough anchors to be used as references (Khan et. al, 2006). In this class, many solutions assume the availability of detectable landmarks at known positions in order to implement, for example, Kalman based localization methods (Leonard Durrant, 1991) and (Pillonetto Carpin, 2007), while some other approaches are developed based on anchor-free combinations (Pryantha et. al, 2003). Here, we explicitly solve the following layout problem: Given a set of mobile robots (simply named nodes) which are equipped with wireless transceivers and a mechanism by which each node can estimate its distance to a few nearby ones (or even through the whole network), the goal is to determine coordinates of every node via local or global communication. In general, radio communication constraints are a set of geometry rules to bound position estimates. Such constraints are a combination of radial and angular limitations. Latter aspects are out of the interests of this research. Ranging information is adequately sufficient in for these achievements. It goes to the fact that if all internode wireless links are established and their associative lengths are known, their graph representation is indeed uniquely realized. When only one subset of distances is known, more sophisticated techniques must be used. In contrast, when multiple solutions exist, the main phenomenon observed is that of foldovers, where entire pieces of the graph fold over on top of others,
- 48. Robot Localization and Map Building 36 without violating any of the partial distance constraints. A main challenge is to generate a solution which is fold-free. Occasionally, final result may suffer from translation, rotation and reflection degrees of freedom, but either of these are not important, because can be resolved by assigning some known coordinates to any three arbitrary nodes. Problem of reconstructing a geometric graph given its edges' lengths, has received some attention in discrete as well as computational geometry communities, whereas it is also relevant for molecule construction and protein folding applications, psychology, networking and also mobile robotics. Our main aim here is to roughly show how to extend graph realization analogy with noisy edges, for localizing the nodes with higher likelihood of unambiguous realization. In an interconnected network of n nodes, if all distances are known exactly, it is only possible to determine the relative coordinates of the points, i.e., to calculate the point coordinates in some arbitrary system. To place the points in an absolute coordinate system, it is necessary to know the positions of at least D+1 points, where D indicates the dimension of the space. Consider that a set of k anchor points are having a known position in the 2D space. A set of n-k nodes with unknown positions can possibly be spatially localized based on the known positions of those anchors. If k=0, the positioning scenario is called relative or anchor-less localization. On the other hand, an incremental approach can deal with a large size network where nodes are having a limited range of communication and indeed ranging. This solution, assigns coordinates to a small core of nodes, and repeatedly, updates coordinates to more neighbors based on local calculations and then proceeds until the whole network is covered. This solution is totally error prone in the early stages, unless being reinforced by proper filtering methods and statistical approaches, is very likely to break the error upper supremum. 7. Conclusions In this chapter, after surveying traditional methods for robot localization, we more emphasized on the radio networks and their ranging capabilities including RSS in WLAN networks as well as ToF measurements of WSN topologies. Their positioning accuracy is comparable in practice where the latter provides quite better positioning results. Practical results indicate that the last approach, enforced with some more mathematical representation can be reliably used for variety of mobile robotics positioning applications both indoor and outdoors, relatively independent from size of the mobile robotics network, explicitly explained in (Bastani Birk, 2009). In other words, having ranging capabilities and specially by radio signals enables the robots to overcome localization problems, less dependently from error accumulation and environmental features. 8. References Thrun, S (2002). Robotic mapping: A survey, Exploring Artificial Intelligence in the New Millennium, Morgan Kaufmann. Lee, B; Cai, W,; Turner, J. Chen, L. (?). Adaptive Dead Reckoning Algorithms for distributed Interactive Simulation, Journal of SIMULATION, Vol. 1, No 1-2. Heller, A. K. Taylor, S. (?). Using Determinism to Improve the Accuracy of Dead Reckoning Algorithms. Australian National University, CANBERRA.
- 49. Ranging fusion for accurating state of the art robot localization 37 Roos, T. (2002). A probabilistic approach to wlan user location. Intl Journal of WirelessInformation Networks, Vol 9. Birk, A. (1996). Learning geometric concepts with an evolutionary algorithm. Procedings of The Fifth Annual Conference on Evolutionary Programming. The MIT Press, Cambridge. Salazar, A.E.S. (2004). Positioning bluetooth and Wi-Fi systems, IEEE Trans. Consumer Electron., Vol. 50, No. 1, pp. 151-157. Krishnan, P., Krishnakumar, A.S., Ju, W.H., Mallows, C. Ganu, S. (2004) A system for LEASE: System for location estimation assisted by stationary emitters for indoor RF wireless networks, Proceedings of IEEE Infocom, pp. 1001-1011. Hong Kong. Ganu, ., Krishnakumar, A.S. Krishnan, P. (2004). Infrastructure-based location estimation in WLAN, Proceedings of IEEE Wireless Communications and Networking Conf. (WCNC 2004), pp. 465-470. Kritzler, M.; Lewejohann, L.; Krger, A.; Raubal, M. Sachser, N. (2006). An RFID-based Tracking System for Laboratory Mice in a Semi-Natural Environment, Proceedings In PTA2006 Workshop, Pervasive Technology Applied Real-World Experiences with RFID and Sensor Networks. Fontanaand, R. Gunderson, S. (2002). Ultra wideband precision asset location system, Proc. IEEE Conf. Ultra Wideband Systems and Technologies, pp. 147-150. Lee, J.Y. (2002). Ultra-wideband ranging in dense multipath environments, Ph.D. dissertation, Dept. Elect. Eng., Univ. Southern California. Royer, E.M. Toh, C.K. (1999). A review of current routing protocols for ad-hoc mobile wireless networks. IEEE Personal Communications Magazine, pp. 46-55. Rappaport, T.S. (1996). Wireless Comm. Principles and Practice. IEEE Press /Prentice Hall. Neskovic, A.; Nescovic, N. Paunovic, G. (2000). Modern approaches in modelling of mobile radio systems propagation environment. IEEE Communications Surveys. Xiang, Z.; Zhang, H.; Huang, J.; Song, S. Almeroth, K. (2005). A hidden environment model for constructing indoor radio maps. Sixth IEEE International Symposium on a World of Wireless Mobile and Multimedia Networks (WoWMoM 2005). pp. 395-400. Yin, J.; Yang, Q. Ni, L. (2005). Adaptive temporal radio maps for indoor location estimation. 3rd IEEE international conf. on Pervasive Computing and Communications, (PerCom 2005). pp. 85-94. Bahl, P Padmanabhan, V.N. (2000). RADAR: An in-building, RF based user location and tracking system, Proceedings of IEEE Infocom 2000, Vol. 2, pp. 775-784. Tel-Aviv, Israel. Rappaport, T. (1996). Wireless Communications Principle and Practice, Prentice Hall. Kaemarungsi, K. Krishnamurthy, P. (2004). Modeling of Indoor Positioning Systems Based on Location Fingerprinting. Proceedings of IEEE INFOCOM 2004. Li, B.; Dempster, A.; Rizos, C. Barnes, J. (2005). Hybrid Method for Localization Using WLAN. School of Surveying and Spatial Information System, University of New South Wales, Sydney. Elnahraway, E.; Li, X. Martin, R. P., (2004). The limits of localization using RSS. Proceedings of the 2nd international conference on Embedded networked sensor systems, pp. 283-284, New York, USA. Sklar. B.(1997). Rayleigh fading channels in mobile digital communication systems, IEEE Communications Magazine, Vol. 35, pp. 90-100. Thrun, S. (2000). An Online Mapping Algorithm for Teams of Mobile Robots, CMU-CS-00-167.
- 50. Robot Localization and Map Building 38 Bekey, G.; Ambrose, R.;V. Kumar ; A. Sanderson ; B. Wilcox, Y. Zheng. (?). International assessment of research and development in robotics. Gotsman C. Koren, Y. (2005). Distributed graph layout for sensor networks, Journal of graph algorithms and applications, Vol.9, No.1. Chan, H.; Luk M. Perrig, A. (2005). Using Clustering Information for Sensor Network Localization, LNCS, Springer, Distributed Computing in Sensor Systems, Vol. 3560, pp. 109-125. Khan, H.M. ; Olariu, S. Eltoweissy, M., (2006). Efficient single-anchor localization in sensor networks, Dependability and Security in Sensor Networks and Systems, DSSNS. Bastani, H. Birk, A. (2009). Precise Realtime Localization by RF Transceiver ToF Measurements, 14th International Conference on Advanced Robotics (ICAR), Germany. Leonard, J. Durrant-Whyte, H. (1991). Mobile robot localization by tracking geometric beacons, IEEE Transaction on Robotics and Automation, Vol.7, No. 3, pp.:376-382. Pillonetto, G. Carpin, S. (2007). Multirobot localization with unknown variance parameters using iterated Kalman filtering, IEEE/RSJ International Conference on Intelligent Robots and Systems. pp.: 1709-1714. Priyantha, N.; Balakrishnan, H.; Demanie, E. Teller, S. (2003). Anchor-free distributed localization in sensor networks, Proceedings of SenSys 03. Horn, K. (1987). Closed-form solution of absolute orientation using unit quaternion, Journal of Optical Society. USA, Vol.4, pp.: 629-638. Wang, J.; Chi, V. Fuchs, C. (1990). A Real-time Optical 3D Tracker for Head-mounted Display Systems, Computer Graphics, ACM SIGGRAPH, Vol. 24, No.2, pp.205-215. Choi, Y. Oh, S. (2005). Visual Sonar Based Localization Using Particle Attraction and Scattering, Proceedings of the IEEE International Conference on Mechatronics and Automation, Canada. Carpin, S. Birk, A. (2004). Stochastic map merging in rescue environments, In Robocup 2004. Springer. Fox, D.; Thrun, S.; Burgard, W. Dellaert, F. (2001). Particle filters for mobile robot localization. Sequential Monte Carlo Methods in Practice, Springer Verlag, pp. 499-516. Bastani, H. Mirmohammad Sadeghi, H.; Shariatmadari, A.; Azarnasab, E. Davarpanah Jazi, M. (2005). Design and Implementation of a Full Autonomous Mine Detecting Robot, 5th IFAC on Intelligent Autonomous Vehicles - IAV04, Elsevier, ISBN 008 044237 4. Pngsthorn, M. Birk, A. (2008). Efficiently Communicating Map Updates with the Pose Graph, International Conference on Intelligent Robots and Systems (IROS), 2008. Qing, H. (2005) A compact ESPAR antenna with planer parasitic elements on a dielectric cylinder, IEICE trans.communication. Vol.E88-B. Shimizu, M. (2005). Tiny Seekers, Robocup Rescue - Robot League Team, TDP in Robocup 2005 proceeding (CD format), Japan.
- 51. Basic Extended Kalman Filter – Simultaneous Localisation and Mapping 39 Basic Extended Kalman Filter – Simultaneous Localisation and Mapping 1 Oduetse Matsebe, 2 Molaletsa Namoshe and 3 Nkgatho Tlale 1,2,3 Council for Scientific and Industrial Research, Mechatronics and Micro Manufacturing Pretoria, South Africa 1. Introduction Most real systems are non-linear. Extended Kalman Filter (EKF) uses non-linear models of both the process and observation models while the Kalman Filter (KF) uses linear models. EKF is a good way to learn about Simultaneous Localisation and Mapping (SLAM). Much of the literature concentrates on advanced SLAM methods which stems from EKF or uses probabilistic techniques. This makes it difficult for new researchers to understand the basics of this exciting area of research. SLAM asks if it is possible for a robot, starting with no prior information, to move through its environment and build a consistent map of the entire environment. Additionally, the vehicle must be able to use the map to navigate and hence plan and control its trajectory during the mapping process. The applications of a robot capable of navigating, with no prior map, are diverse indeed. Domains in which 'man in the loop' systems are impractical or difficult such as sub-sea surveys and disaster zones are obvious candidates. Beyond these, the sheer increase in autonomy that would result from reliable, robust navigation in large dynamic environments is simply enormous (Newman 2006). SLAM has been implemented in a number of different domains from indoor robots to outdoor, underwater, and airborne systems. In many applications the environment is unknown. A priori maps are usually costly to obtain, inaccurate, incomplete, and become outdated. It also means that the robot‘s operation is limited to a particular environment (Neira 2008). This goal of the chapter is to provide an opportunity for researchers who are new to, or interested in, this exciting area with the basics, background information, major issues, and the state-of-the-art as well as future challenges in SLAM with a bent towards EKF-SLAM. It will also be helpful in realizing what methods are being employed and what sensors are being used. It presents the 2 – Dimensional (2D) feature based EKF-SLAM technique used for generating robot pose estimates together with positions of features in the robot’s operating environment, it also highlights some of the basics for successful EKF – SLAM implementation: (1) Process and observation models, these are the underlying models required, (2) EKF-SLAM Steps, the three-stage recursive EKF-SLAM process comprising prediction, observation and update, (3) Feature Extraction and Environment modelling, a 3
- 52. Robot Localization and Map Building 40 process of extracting well defined entities or landmarks (features) which are recognisable and can be repeatedly detected to aid navigation, (4) Data Association, this consists of determining the origin of each measurement, in terms of map features, (5) Multi – Robot – EKF – SLAM, the two types of multi robot systems are described: Collaborative and Cooperative multi robot systems with more emphasis on the Cooperative SLAM Scheme. 2. Basic Structure of EKF - SLAM The EKF-SLAM process consists of a recursive, three-stage procedure comprising prediction, observation and update steps. The EKF estimates the pose of the robot made up of the position ( , ) r r x y and orientation r , together with the estimates of the positions of the N environmental features , f i x where N i .... 1 , using observations from a sensor onboard the robot (Williams et al. 2001). We will constrain ourselves to using the simplest feature model possible; a point feature such that the coordinates of the th i feature in the global reference frame are given by: , i f i i x y x (1) SLAM considers that all landmarks are stationary, hence the state transition model for the th i feature is given by: , , , ( ) ( 1) f i f i f i k k x x x (2) It is important to note that the evolution model for features does have any uncertainty since the features are considered static. 2.1 Process Model Implementation of EKF - SLAM requires that the underlying state and measurement models be developed. This section describes the process models necessary for this purpose. 2.1.1 Kinematic Model Modeling of the kinematic states involves the study of the geometrical aspects of motion. The motion of a robot through the environment can be modeled through the following discrete time non-linear model: ( ) ( ( 1), ( ), ) r r k k k k X f X u (3)
- 53. Basic Extended Kalman Filter – Simultaneous Localisation and Mapping 41 Thus, ( ) r k X is the state of the robot at time k , ( ) k u is the robot control input at time k . (,,) f is a function that relates the robot state at time 1 k , known control inputs to the robot state at time k . 1 . ( ) . N u k u u (4) Equation (4) above is a little unrealistic, we need to model uncertainty. One popular way to model uncertainty is to insert noise terms into the control input ( ) k u such that: ( ) ( ) ( ) n u k k k u u (5) Thus ( ) n k u is a nominal control input and ( ) u k is a vector of control noise which is assumed to be temporally uncorrelated, zero mean and Gaussian with standard deviation . 1 . ( ) . u N k (6) The strength (covariance) of the control noise is denoted u Q , and is given by: 2 2 1 . . u N diag Q (7) The complete discrete time non-linear kinematic model can now be expressed in general form as: ( ) ( ( 1), ( ) ( )) r r n u k f k k k X X u (8) 2.1.2 Using Dead-Reckoned Odometry Measurements Sometimes a navigation system will be given a dead reckoned odometry position as input without recourse to the control signals that were involved. The dead reckoned positions can be converted into a control input for use in the core navigation system. It would be a bad
- 54. Robot Localization and Map Building 42 idea to simply use a dead-reckoned odometry estimate as a direct measurement of state in a Kalman Filter (Newman 2006). Given a sequence (1), (2), (3)... ( ) o o o o k x x x x of dead reckoned positions, we need to figure out a way in which these positions could be used to form a control input into a navigation system. This is given by: ( ) ( 1) ( ) o o o k k k u x x (9) This is equivalent to going back along ( 1) o k x and forward along ( ) o k x . This gives a small control vector ( ) o k u derived from two successive dead reckoned poses. Equation (9) substracts out the common dead-reckoned gross error (Newman 2006). The plant model for a robot using a dead reckoned position as a control input is thus given by: ( ) ( ( 1), ( )) r r k k k X f X u (10) ( ) ( 1) ( ) r r o k k k X X u (11) and are composition transformations which allows us to express robot pose described in one coordinate frame, in another alternative coordinate frame. These composition transformations are given below: 1 2 1 2 1 1 2 1 2 1 2 1 1 2 cos sin sin cos x x y y x y x x (12) 1 1 1 1 1 1 1 1 1 1 cos sin sin cos x y x y x (13) 2.2 Measurement Model This section describes a sensor model used together with the above process models for the implementation of EKF - SLAM. Assume that the robot is equipped with an external sensor capable of measuring the range and bearing to static features in the environment. The measurement model is thus given by:
- 55. Other documents randomly have different content
- 56. thrown into a state of great excitement. Then the enraged subjects, out of love for the king of Vatsa, wanted to make a general3 assault on Ujjayiní. But Rumaṇvat checked the impetuous fury of the subjects by telling them that Chaṇḍamahásena was not to be overcome by force, for he was a mighty monarch, and besides that an assault was not advisable, for it might endanger the safety of the king of Vatsa; but their object must be attained by policy. Then the calm and resolute Yaugandharáyaṇa, seeing that the country was loyal, and would not swerve from its allegiance, said to Rumaṇvat and the others; “All of you must remain here, ever on the alert; you must guard this country, and when a fit occasion comes you must display your prowess; but I will go accompanied by Vasantaka only, and will without fail accomplish by my wisdom the deliverance of the king and bring him home. For he is a truly firm and resolute man whose wisdom shines forth in adversity, as the lightning flash is especially brilliant during pelting rain. I know spells for breaking through walls, and for rending fetters, and receipts for becoming invisible, serviceable at need.” Having said this, and entrusted to Rumaṇvat the care of the subjects, Yaugandharáyaṇa set out from Kauśámbí with Vasantaka. And with him he entered the Vindhya forest, full of life4 like his wisdom, intricate and trackless as his policy. Then he visited the palace of the king of the Pulindas, Pulindaka by name, who dwelt on a peak of the Vindhya range, and was an ally of the king of Vatsa. He first placed him, with a large force at his heels, in readiness to protect the king of Vatsa when he returned that way, and then he went on accompanied by Vasantaka and at last arrived at the burning-ground of Mahákála in Ujjayiní, which was densely tenanted by vampires5 that smelt of carrion, and hovered hither and thither, black as night, rivalling the smoke-wreaths of the funeral pyres. And there a Bráhman-Rákshasa of the name of Yogeśvara immediately came up to him, delighted to see him, and admitted him into his friendship; then Yaugandharáyaṇa by means of a charm, which he taught him, suddenly altered his shape. That charm immediately made him deformed, hunchbacked, and old, and besides gave him the appearance of a madman, so that he produced loud laughter in those who beheld him. And in the same way Yaugandharáyaṇa, by means of that very charm, gave Vasantaka a body full of outstanding veins, with a large stomach, and an ugly mouth with
- 57. projecting teeth;6 then he sent Vasantaka on in front to the gate of the king’s palace, and entered Ujjayiní with such an appearance as I have described. There he, singing and dancing, surrounded by Bráhman boys, beheld with curiosity by all, made his way to the king’s palace. And there he excited by that behaviour the curiosity of the king’s wives, and was at last heard of by Vásavadattá. She quickly sent a maid and had him brought to the concert- room. For youth is twin-brother to mirth. And when Yaugandharáyaṇa came there and beheld the king of Vatsa in fetters, though he had assumed the appearance of a madman, he could not help shedding tears. And he made a sign to the king of Vatsa, who quickly recognized him, though he had come in disguise. Then Yaugandharáyaṇa by means of his magic power made himself invisible to Vásavadattá and her maids. So the king alone saw him, and they all said with astonishment, “that maniac has suddenly escaped somewhere or other.” Then the king of Vatsa hearing them say that, and seeing Yaugandharáyaṇa in front of him, understood that this was due to magic, and cunningly said to Vásavadattá; “Go my good girl, and bring the requisites for the worship of Sarasvatí.” When she heard that, she said, “So I will,” and went out with her companions. Then Yaugandharáyaṇa approached the king and communicated to him, according to the prescribed form, spells for breaking chains; and at the same time he furnished him with other charms for winning the heart of Vásavadattá, which were attached to the strings of the lute; and informed him that Vasantaka had come there and was standing outside the door in a changed form, and recommended him to have that Bráhman summoned to him; at the same time he said—“When this lady Vásavadattá shall come to repose confidence in you, then you must do what I tell you, at the present remain quiet.” Having said this, Yaugandharáyaṇa quickly went out, and immediately Vásavadattá entered with the requisites for the worship of Sarasvatí. Then the king said to her, “There is a Bráhman standing outside the door, let him be brought in to celebrate this ceremony in honour of Sarasvatí, in order that he may obtain a sacrificial fee.” Vásavadattá consented, and had Vasantaka, who wore a deformed shape, summoned from the door into the music-hall. And when he was brought and saw the king of Vatsa, he wept for sorrow, and then the king said to him, in order that the secret might not be discovered, “O Bráhman, I will remove all this deformity of thine produced by sickness; do
- 58. not weep, remain here near me.” And then Vasantaka said—“It is a great condescension on thy part, O king.” And the king seeing how he was deformed could not keep his countenance. And when he saw that, Vasantaka guessed what was in the king’s mind, and laughed so that the deformity of his distorted face was increased; and thereupon Vásavadattá, beholding him grinning like a doll, burst out laughing also, and was much delighted; then the young lady asked Vasantaka in fun the following question: “Bráhman, what science are you familiar with, tell us?” So he said, “Princess, I am an adept at telling tales.” Then she said, “Come, tell me a tale.” Then in order to please that princess, Vasantaka told the following tale, which was charming by its comic humour and variety. Story of Rúpiṇiká. There is in this country a city named Mathurá, the birthplace of Kṛishṇa, in it there was a hetæra known by the name of Rúpiṇiká; she had for a mother an old kuṭṭiní named Makaradanshṭrá, who seemed a lump of poison in the eyes of the young men attracted by her daughter’s charms. One day Rúpiṇiká went at the time of worship to the temple to perform her duty,7 and beheld from a distance a young man. When she saw that handsome young fellow, he made such an impression upon her heart, that all her mother’s instructions vanished from it. Then she said to her maid, “Go and tell this man from me, that he is to come to my house to-day.” The maid said, “So I will,” and immediately went and told him. Then the man thought a little and said to her; “I am a Bráhman named Lohajangha8; I have no wealth; then what business have I in the house of Rúpiṇiká which is only to be entered by the rich.” The maid said,—“My mistress does not desire wealth from you,”—whereupon Lohajangha consented to do as she wished. When she heard that from the maid, Rúpiṇiká went home in a state of excitement, and remained with her eyes fixed on the path by which he would come. And soon Lohajangha came to her house, while the kuṭṭiní
- 59. Makaradanshṭrá looked at him, and wondered where he came from. Rúpiṇiká, for her part, when she saw him, rose up to meet him herself with the utmost respect, and clinging to his neck in her joy, led him to her own private apartments. Then she was captivated with Lohajangha’s wealth of accomplishments, and considered that she had been only born to love him. So she avoided the society of other men, and that young fellow lived with her in her house in great comfort. Rúpiṇiká’s mother, Makaradanshṭrá, who had trained up many hetæræ, was annoyed when she saw this, and said to her in private; “My daughter, why do you associate with a poor man? Hetæræ of good taste embrace a corpse in preference to a poor man. What business has a hetæra like you with affection? How have you come to forget that great principle? The light of a red9 sunset lasts but a short time, and so does the splendour of a hetæra who gives way to affection. A hetæra, like an actress, should exhibit an assumed affection in order to get wealth; so forsake this pauper, do not ruin yourself.” When she heard this speech of her mother’s, Rúpiṇiká said in a rage, “Do not talk in this way, for I love him more than my life. And as for wealth, I have plenty, what do I want with more? So you must not speak to me again, mother, in this way.” When she heard this, Makaradanshṭrá was in a rage, and she remained thinking over some device for getting rid of this Lohajangha. Then she saw coming along the road a certain Rájpút, who had spent all his wealth, surrounded by retainers with swords in their hands. So she went up to him quickly and taking him aside, said—“My house is beset by a certain poor lover. So come there yourself to-day, and take such order with him that he shall depart from my house, and do you possess my daughter.” “Agreed,” said the Rájpút, and entered that house. At that precise moment Rúpiṇiká was in the temple, and Lohajangha meanwhile was absent somewhere, and suspecting nothing, he returned to the house a moment afterwards. Immediately the retainers of the Rájpút ran upon him, and gave him severe kicks and blows on all his limbs, and then they threw him into a ditch full of all kinds of impurities, and Lohajangha with difficulty escaped from it. Then Rúpiṇiká returned to the house, and when she heard what had taken place, she was distracted with grief, so the Rájpút, seeing that, returned as he came.
- 60. Lohajangha, after suffering this brutal outrage by the machinations of the kuṭṭiní, set out for some holy place of pilgrimage, in order to leave his life there, now that he was separated from his beloved. As he was going along in the wild country,10 with his heart burning with anger against the kuṭṭiní, and his skin with the heat of the summer, he longed for shade. Not being able to find a tree, he lighted on the body of an elephant, which had been stripped of all its flesh11 by jackals making their way into it by the hind- quarters; accordingly Lohajangha being worn out crept into this carcase, which was a mere shell, as only the skin remained, and went to sleep in it, as it was kept cool by the breeze which freely entered. Then suddenly clouds arose from all sides, and began to pour down a pelting shower of rain; that rain made the elephant’s skin contract so that no aperture was left, and immediately a copious inundation came that way, and carrying off the elephant’s hide swept it into the Ganges; so eventually the inundation bore it into the sea. And there a bird of the race of Garuḍa saw that hide, and supposing it to be carrion, took it to the other side of the sea; there it tore open the elephant’s hide with its claws, and, seeing that there was a man inside it, fled away. But Lohajangha was awaked by the bird’s pecking and scratching, and came out through the aperture made by its beak. And finding that he was on the other side of the sea, he was astonished, and looked upon the whole thing as a day-dream; then he saw there to his terror two horrible Rákshasas, and those two for their part contemplated him from a distance with feelings of fear. Remembering how they were defeated by Ráma, and seeing that Lohajangha was also a man who had crossed the sea, they were once more alarmed in their hearts. So, after they had deliberated together, one of them went off immediately and told the whole occurrence to king Vibhíshaṇa; king Vibhíshaṇa too, as he had seen the prowess of Ráma, being terrified at the arrival of a man, said to that Rákshasa; “Go, my good friend, and tell that man from me in a friendly manner, that he is to do me the favour of coming to my palace.” The Rákshasa said, “I will do so,” and timidly approached Lohajangha, and told him that request of his sovereign’s. Lohajangha for his part accepted that invitation with unruffled calm, and went to Lanká with that Rákshasa and his companion. And when he arrived in Lanká, he was astonished at beholding numerous splendid edifices of gold, and entering the king’s palace, he saw Vibhíshaṇa. The
- 61. king welcomed the Bráhman who blessed him in return, and then Vibhíshaṇa said, “Bráhman, how did you manage to reach this country?” Then the cunning Lohajangha said to Vibhíshaṇa—“I am a Bráhman of the name of Lohajangha residing in Mathurá; and I, Lohajangha being afflicted at my poverty, went to the temple of the god, and remaining fasting, for a long time performed austerities in the presence of Náráyaṇa.12 Then the adorable Hari12 commanded me in a dream, saying, ‘Go thou to Vibhíshaṇa, for he is a faithful worshipper of mine, and he will give thee wealth.’ Then, I said, ‘Vibhíshaṇa is where I cannot reach him’—but the lord continued, ‘To-day shalt thou see that Vibhíshaṇa.’ So the lord spake to me, and immediately I woke up and found myself upon this side of the sea. I know no more.” When Vibhíshaṇa heard this from Lohajangha, reflecting that Lanká was a difficult place to reach, he thought to himself—“Of a truth this man possesses divine power.” And he said to that Bráhman,—“Remain here, I will give you wealth.” Then he committed him to the care of the man-slaying Rákshasas as an inviolable deposit; and sent some of his subjects to a mountain in his kingdom called Swarṇamúla, and brought from it a young bird belonging to the race of Garuḍa; and he gave it to that Lohajangha, (who had to take a long journey to Mathurá,) to ride upon, in order that he might in the meanwhile break it in. Lohajangha for his part mounted on its back, and riding about on it in Lanká, rested there for some time, being hospitably entertained by Vibhíshaṇa. One day he asked the king of the Rákshasas, feeling curiosity on the point, why the whole ground of Lanká was made of wood; and Vibhíshaṇa when he heard that, explained the circumstance to him, saying, “Bráhman, if you take any interest in this matter, listen, I will explain it to you. Long ago Garuḍa the son of Kaśyapa, wishing to redeem his mother from her slavery to the snakes, to whom she had been subjected in accordance with an agreement,13 and preparing to obtain from the gods the nectar which was the price of her ransom, wanted to eat something which would increase his strength, and so he went to his father, who being importuned said to him, “My son, in the sea there is a huge elephant, and a huge tortoise. They have assumed their present forms in consequence of a curse: go and eat them.” Then Garuḍa went and brought them both to eat, and then perched on a
- 62. bough of the great wishing-tree of paradise. And when that bough suddenly broke with his weight, he held it up with his beak, out of regard to the Bálakhilyas14 who were engaged in austerities underneath it. Then Garuḍa, afraid that the bough would crush mankind, if he let it fall at random, by the advice of his father brought the bough to this uninhabited part of the earth, and let it drop. Lanká was built on the top of that bough, therefore the ground here is of wood.” When he heard this from Vibhíshaṇa, Lohajangha was perfectly satisfied. Then Vibhíshaṇa gave to Lohajangha many valuable jewels, as he desired to set out for Mathurá. And out of his devotion to the god Vishṇu, who dwells at Mathurá, he entrusted to the care of Lohajangha a lotus, a club, a shell, and a discus all of gold, to be offered to the god; Lohajangha took all these, and mounted the bird given to him by Vibhíshaṇa, that could accomplish a hundred thousand yojanas,15 and rising up into the air in Lanká, he crossed the sea and without any difficulty arrived at Mathurá. And there he descended from the air in an empty convent outside the town, and deposited there his abundant treasure, and tied up that bird. And then he went into the market and sold one of his jewels, and bought garments and scented unguents, and also food. And he ate the food in that convent where he was, and gave some to his bird; and he adorned himself with the garments, unguents, flowers and other decorations. And when night came, he mounted that same bird and went to the house of Rúpiṇiká, bearing in his hand the shell, discus and mace; then he hovered over it in the air, knowing the place well, and made a low deep sound, to attract the attention of his beloved, who was alone. But Rúpiṇiká, as soon as she heard that sound, came out, and saw hovering in the air by night a being like Náráyaṇa, gleaming with jewels. He said to her, “I am Hari come hither for thy sake;” whereupon she bowed with her face to the earth and said—“May the god have mercy upon me!” Then Lohajangha descended and tied up his bird, and entered the private apartments of his beloved hand in hand with her. And after remaining there a short time, he came out, and mounting the bird as before, went off through the air.16 In the morning Rúpiṇiká remained observing an obstinate silence, thinking to herself—“I am the wife of the god Vishṇu, I must cease to converse with mortals.” And then her mother Makaradanshṭrá
- 63. said to her,—“Why do you behave in this way, my daughter?” And after she had been perseveringly questioned by her mother, she caused to be put up a curtain between herself and her parent, and told her what had taken place in the night, which was the cause of her silence. When the kuṭṭiní heard that, she felt doubt on the subject, but soon after at night she saw that very Lohajangha mounted on the bird, and in the morning Makaradanshṭrá came secretly to Rúpiṇiká, who still remained behind the curtain, and inclining herself humbly, preferred to her this request; “Through the favour of the god, thou, my daughter, hast obtained here on earth the rank of a goddess, and I am thy mother in this world, therefore grant me a reward for giving thee birth; entreat the god that, old as I am, with this very body I may enter Paradise; do me this favour.” Rúpiṇiká consented and requested that very boon from Lohajangha, who came again at night disguised as Vishṇu. Then Lohajangha, who was personating the god, said to that beloved of his —“Thy mother is a wicked woman, it would not be fitting to take her openly to Paradise, but on the morning of the eleventh day the door of heaven is opened, and many of the Gaṇas, Śiva’s companions, enter into it before any one else is admitted. Among them I will introduce this mother of thine, if she assume their appearance. So, shave her head with a razor, in such a manner that five locks shall be left, put a necklace of sculls round her neck, and stripping off her clothes, paint one side of her body with lamp-black, and the other with red lead,17 for when she has in this way been made to resemble a Gaṇa, I shall find it an easy matter to get her into heaven.” When he had said this, Lohajangha remained a short time, and then departed. And in the morning Rúpiṇiká attired her mother as he had directed; and then she remained with her mind entirely fixed on Paradise. So, when night came, Lohajangha appeared again, and Rúpiṇiká handed over her mother to him. Then he mounted on the bird, and took the kuṭṭiní with him naked, and transformed as he had directed, and he flew up rapidly with her into the air. While he was in the air, he beheld a lofty stone pillar in front of a temple, with a discus on its summit. So he placed her on the top of the pillar, with the discus as her only support,18 and there she hung like a banner to blazon forth his revenge for his ill-usage. He said to her —“Remain here a moment while I bless the earth with my approach,” and vanished from her sight. Then beholding a number of people in front of the
- 64. temple, who had come there to spend the night in devout vigils before the festive procession, he called aloud from the air—“Hear, ye people, this very day there shall fall upon you here the all-destroying goddess of Pestilence, therefore fly to Hari for protection.” When they heard this voice from the air, all the inhabitants of Mathurá who were there, being terrified, implored the protection of the god, and remained devoutly muttering prayers to ward off calamity. Lohajangha, for his part, descended from the air, and encouraged them to pray, and after changing that dress of his, came and stood among the people, without being observed. The kuṭṭiní thought, as she sat upon the top of the pillar,—“the god has not come as yet, and I have not reached heaven.” At last feeling it impossible to remain up there any longer, she cried out in her fear, so that the people below heard; “Alas! I am falling, I am falling.” Hearing that, the people in front of the god’s temple were beside themselves, fearing that the destroying goddess was falling upon them, even as had been foretold, and said, “O goddess, do not fall, do not fall.” So those people of Mathurá, young and old, spent that night in perpetual dread that the destroying goddess would fall upon them, but at last it came to an end; and then beholding that kuṭṭiní upon the pillar in the state described,19 the citizens and the king recognized her at once; all the people thereupon forgot their alarm, and burst out laughing, and Rúpiṇiká herself at last arrived having heard of the occurrence. And when she saw it, she was abashed, and with the help of the people, who were there, she managed to get that mother of hers down from the top of the pillar immediately: then that kuṭṭiní was asked by all the people there, who were filled with curiosity, to tell them the whole story, and she did so. Thereupon the king, the Bráhmans, and the merchants, thinking that that laughable incident must have been brought about by a sorcerer or some person of that description, made a proclamation, that whoever had made a fool of the kuṭṭiní, who had deceived innumerable lovers, was to shew himself, and he would receive a turban of honour on the spot. When he heard that, Lohajangha made himself known to those present, and being questioned, he related the whole story from its commencement. And he offered to the god the discus, shell, club, and lotus of gold, the present which Vibhíshaṇa had sent, and which aroused the astonishment of the people. Then all the people of Mathurá, being pleased, immediately invested him with a turban of
- 65. 1 2 3 4 5 6 7 8 honour, and by the command of the king, made that Rúpiṇiká a free woman. And then Lohajangha, having wreaked upon the kuṭṭiní his wrath caused by her ill-usage of him, lived in great comfort in Mathurá with that beloved of his, being very well off by means of the large stock of jewels which he brought from Lanká. Hearing this tale from the mouth of the transformed Vasantaka, Vásavadattá who was sitting at the side of the fettered king of Vatsa, felt extreme delight in her heart. They would not go near for fear of disturbing it. Wild elephants are timid, so there is more probability in this story, than in that of the Trojan horse. Even now scouts who mark down a wild beast in India, almost lose their heads with excitement. I. e., they sat in Dharna outside the door of the palace. Perhaps we should read samantataḥ one word. Sattva, when applied to the forest, means animal, when applied to wisdom, it means excellence. Vetála is especially used of a goblin that tenants dead bodies. See Colonel R. Burton’s Tales of Vikramáditya and the Vampire. They will be found in the 12th book of this work. In the Vth Chapter of Ralston’s Russian Folk-Tales will be found much interesting information with regard to the Slavonic superstitions about Vampires. They resemble very closely those of the Hindus. See especially p. 311. “At cross-roads, or in the neighbourhood of cemeteries, an animated corpse of this description often lurks, watching for some unwary traveller whom it may be able to slay and eat.” Cp. the way in which the Ritter Malegis transmutes Reinold in the story of Die Heimonskinder (Simrock’s Deutsche Volksbücher, Vol. II, p. 86). “He changed him into an old man, a hundred years of age, with a decrepit and misshapen body, and long hair.” See also p. 114. So Merlin assumes the form of an old man and disguises Uther and Ulfin, Dunlop’s History of Fiction, translated by Liebrecht, p. 66. Such people dance in temples I believe. Mr. Growse writes to me with reference to the name Lohajangha—“This name still exists on the spot, though probably not to be found elsewhere. The original bearer of the title is said to have been one of the demons whom Kṛishṇa slew, and a village is called
- 66. 9 10 11 12 13 14 15 16 Lohaban after him, where an ancient red sandstone image is supposed to represent him, and has offerings of iron made to it at the annual festival. Ráginí means affectionate and also red. Ataví is generally translated “forest.” I believe the English word “forest” does not necessarily imply trees, but it is perhaps better to avoid it here. For the vṛitam of the text I read kṛitam. Cp. this incident with Joseph’s adventure in the 6th story of the Sicilianische Märchen. He is sewn up in a horse’s skin, and carried by ravens to the top of a high mountain. There he stamps and finds a wooden trap-door under his feet. In the notes Dr. Köhler refers to this passage, Campbell No. 44, the Story of Sindbad and other parallels. Cp. also Veckenstedt’s Wendische Sagen, p. 124. See also the story of Heinrich der Löwe, Simrock’s Deutsche Volksbücher, Vol. I, p. 8. Dr. Köhler refers to the story of Herzog Ernst. The incident will be found in Simrock’s version of the story, at page 308 of the IIIrd Volume of his Deutsche Volksbücher. Names of Vishṇu, who became incarnate in the hero Kṛishṇa. See Chapter 22 śl. 181 and ff. Kaśyapa’s two wives disputed about the colour of the sun’s horses. They agreed that whichever was in the wrong should become a slave to the other. Kadrú, the mother of the snakes, won by getting her children to darken the horses. So Garuḍa’s mother Vinatá became a slave. Divine personages of the size of a thumb; sixty thousand were produced from Brahmá’s body and surrounded the chariot of the sun. The legend of Garuḍa and the Bálakhilyas is found in the Mahábhárata, see De Gubernatis, Zoological Mythology, p. 95. A yojana is probably 9 miles, some say 2–1/2, some 4 or 5. See Monier Williams s. v. Compare the 5th story in the first book of the Panchatantra, in Benfey’s translation. Benfey shows that this story found its way into Mahometan collections, such as the Thousand and one Nights, and the Thousand and one Days, as also into the Decamerone of Boccaccio, and other European story-books, Vol. I, p. 159, and ff. The story, as given in the Panchatantra, reminds us of the Squire’s Tale in Chaucer, but Josephus in Ant. Jud. XVIII, 3, tells it of a Roman knight named Mundus, who fell in love with Paulina the wife of Saturninus, and by corrupting the priestess of Isis was enabled to pass himself off as Anubis. On the matter coming to the ears of Tiberius, he had the temple of Isis destroyed, and the priests crucified. (Dunlop’s History of Fiction, Vol. II, p. 27. Liebrecht’s German translation, p. 232). A similar story is told by the Pseudo-Callisthenes
- 67. 17 18 19 of Nectanebos and Olympias. Cp. Coelho’s Contos Populares Portuguezes, No. LXXI, p. 155. Thus she represented the Arddhanáríśvara, or Śiva half male, and half female, which compound figure is to be painted in this manner. She held on to it by her hands. Wilson remarks that this presents some analogy to the story in the Decamerone (Nov. 7 Gior. 8) of the scholar and the widow “la quale egli poi, con un suo consiglio, di mezzo Luglio, ignuda, tutto un dì fa stare in su una torre.” It also bears some resemblance to the story of the Master Thief in Thorpe’s Yule-tide Stories, page 272. The Master thief persuades the priest that he will take him to heaven. He thus induces him to get into a sack, and then he throws him into the goose-house, and when the geese peck him, tells him that he is in purgatory. The story is Norwegian. See also Sir G. W. Cox’s Mythology of the Aryan Nations, Vol. 1. p. 127.
- 68. Chapter XIII. As time went on, Vásavadattá began to feel a great affection for the king of Vatsa, and to take part with him against her father. Then Yaugandharáyaṇa again came in to see the king of Vatsa, making himself invisible to all the others, who were there. And he gave him the following information in private in the presence of Vasantaka only; “King, you were made captive by king Chaṇḍamahásena by means of an artifice. And he wishes to give you his daughter, and set you at liberty, treating you with all honour; so let us carry off his daughter and escape. For in this way we shall have revenged ourselves upon the haughty monarch, and we shall not be thought lightly of in the world for want of prowess. Now the king has given that daughter of his, Vásavadattá, a female elephant called Bhadravatí. And no other elephant but Naḍágiri is swift enough to catch her up, and he will not fight when he sees her. The driver of this elephant is a man here called Ásháḍhaka, and him I have won over to our side by giving him much wealth. So you must mount that elephant with Vásavadattá, fully armed, and start from this place secretly by night. And you must have the superintendent of the royal elephants here made drunk with wine, in order that he may not perceive what is about to take place,1 for he understands every sign that elephants give. I, for my part, will first repair to your ally Pulindaka in order that he may be prepared to guard the road by which you escape.” When he had said this, Yaugandharáyaṇa departed. So the king of Vatsa stored up all his instructions in his heart; and soon Vásavadattá came to him. Then he made all kinds of confidential speeches to her, and at last told her what Yaugandharáyaṇa had said to him. She consented to the proposal, and made up her mind to start, and causing the elephant driver Ásháḍhaka to be summoned, she prepared his mind for the attempt, and on the pretext of worshipping the gods, she gave the superintendent of the elephants, with all the elephant drivers, a supply of spirits, and made them drunk. Then in the evening, which was disturbed with the echoing roar of clouds,2 Ásháḍhaka brought that female elephant ready harnessed, but she, while she was being harnessed, uttered a cry, which was heard by the
- 69. superintendent of the elephants, who was skilled in elephants’ language; and he faltered out in a voice indistinct from excessive intoxication,—“the female elephant says, she is going sixty-three yojanas to-day.” But his mind in his drunken state was not capable of reasoning, and the elephant-drivers, who were also intoxicated, did not even hear what he said. Then the king of Vatsa broke his chains by means of the charms, which Yaugandharáyaṇa had given him, and took that lute of his, and Vásavadattá of her own accord brought him his weapons, and then he mounted the female elephant with Vasantaka. And then Vásavadattá mounted the same elephant with her friend and confidante Kánchanamálá; then the king of Vatsa went out from Ujjayiní with five persons in all, including himself and the elephant-driver, by a path which the infuriated elephant clove through the rampart. And the king attacked and slew the two warriors who guarded that point, the Rájpúts Vírabáhu and Tálabhaṭa. Then the monarch set out rapidly on his journey in high spirits, mounted on the female elephant, together with his beloved, Ásháḍhaka holding the elephant-hook; in the meanwhile in Ujjayiní the city-patrol beheld those guards of the rampart lying dead, and in consternation reported the news to the king at night. Chaṇḍamahásena enquired into the matter, and found out at last that the king of Vatsa had escaped, taking Vásavadattá with him. Then the alarm spread through the city, and one of his sons named Pálaka mounted Naḍágiri and pursued the king of Vatsa. The king of Vatsa for his part, combated him with arrows as he advanced, and Naḍágiri, seeing that female elephant, would not attack her. Then Pálaka, who was ready to listen to reason, was induced to desist from the pursuit by his brother Gopálaka, who had his father’s interests at heart; then the king of Vatsa boldly continued his journey, and as he journeyed, the night gradually came to an end. So by the middle of the day the king had reached the Vindhya forest, and his elephant having journeyed sixty-three yojanas, was thirsty. So the king and his wife dismounted, and the female elephant having drunk water, owing to its being bad, fell dead on the spot. Then the king of Vatsa and Vásavadattá, in their despair, heard this voice coming from the air—“I, O king, am a female Vidyádhara named Máyávatí, and for this long time I have been a female elephant in consequence of a curse; and to-day, O lord of Vatsa, I have done you a good turn, and I will do another to your son that is to be: and this queen of yours
- 70. Vásavadattá is not a mere mortal; she is a goddess for a certain cause incarnate on the earth.” Then the king regained his spirits, and sent on Vasantaka to the plateau of the Vindhya hills to announce his arrival to his ally Pulindaka; and as he was himself journeying along slowly on foot with his beloved, he was surrounded by brigands, who sprang out from an ambuscade. And the king, with only his bow to help him, slew one hundred and five of them before the eyes of Vásavadattá. And immediately the king’s ally Pulindaka came up, together with Yaugandharáyaṇa, Vasantaka shewing them the way. The king of the Bheels ordered the surviving brigands3 to desist, and after prostrating himself before the king of Vatsa, conducted him with his beloved to his own village. The king rested there that night with Vásavadattá, whose foot had been cut with a blade of forest grass, and early in the morning the general Rumaṇvat reached him, who had before been summoned by Yaugandharáyaṇa, who sent a messenger to him. And the whole army came with him, filling the land as far as the eye could reach, so that the Vindhya forest appeared to be besieged. So that king of Vatsa entered into the encampment of his army, and remained in that wild region to wait for news from Ujjayiní. And, while he was there, a merchant came from Ujjayiní, a friend of Yaugandharáyaṇa’s, and when he had arrived reported these tidings, “The king Chaṇḍamahásena is pleased to have thee for a son-in-law, and he has sent his warder to thee. The warder is on the way, but he has stopped short of this place, however, I came secretly on in front of him, as fast as I could, to bring your Highness information.” When he heard this, the king of Vatsa rejoiced, and told it all to Vásavadattá, and she was exceedingly delighted. Then Vásavadattá, having abandoned her own relations, and being anxious for the ceremony of marriage, was at the same time bashful and impatient: then she said, in order to divert her thoughts, to Vasantaka who was in attendance—“Tell me some story.” Then the sagacious Vasantaka told that fair-eyed one the following tale in order to increase her affection for her husband.
- 71. Story of Devasmitá. There is a city in the world famous under the name of Támraliptá, and in that city there was a very rich merchant named Dhanadatta. And he, being childless, assembled many Bráhmans and said to them with due respect; “Take such steps as will procure me a son soon.” Then those Bráhmans said to him: “This is not at all difficult, for Bráhmans can accomplish all things in this world by means of ceremonies in accordance with the scriptures. To give you an instance there was in old time a king who had no sons, and he had a hundred and five wives in his harem. And by means of a sacrifice to procure a son, there was born to him a son named Jantu, who was like the rising of the new moon to the eyes of his wives. Once on a time an ant bit the boy on the thigh as he was crawling about on his knees, so that he was very unhappy and sobbed loudly. Thereupon the whole harem was full of confused lamentation, and the king himself shrieked out ‘My son! my son!’ like a common man. The boy was soon comforted, the ant having been removed, and the king blamed the misfortune of his only having one son as the cause of all his grief. And he asked the Bráhmans in his affliction if there was any expedient by which he might obtain a large number of children. They answered him,—‘O king, there is one expedient open to you; you must slay this son and offer up all his flesh in the fire. By smelling the smell of that sacrifice all thy wives will obtain sons.’ When he heard that, the king had the whole ceremony performed as they directed; and he obtained as many sons as he had wives. So we can obtain a son for you also by a burnt-offering.” When they had said this to Dhanadatta, the Bráhmans, after a sacrificial fee had been promised them, performed a sacrifice: then a son was born to that merchant. That son was called Guhasena, and he gradually grew up to man’s estate. Then his father Dhanadatta began to look out for a wife for him. Then his father went with that son of his to another country, on the pretence of traffic, but really to get a daughter-in-law, there he asked an excellent merchant of the name of Dharmagupta to give him his daughter named Devasmitá for his son Guhasena. But Dharmagupta, who was tenderly attached to his daughter, did not approve of that connexion, reflecting that
- 72. the city of Támraliptá was very far off. But when Devasmitá beheld that Guhasena, her mind was immediately attracted by his virtues, and she was set on abandoning her relations, and so she made an assignation with him by means of a confidante, and went away from that country at night with her beloved and his father. When they reached Támraliptá they were married, and the minds of the young couple were firmly knit together by the bond of mutual love. Then Guhasena’s father died, and he himself was urged by his relations to go to the country of Kaṭáha4 for the purpose of trafficking; but his wife Devasmitá was too jealous to approve of that expedition, fearing exceedingly that he would be attracted by some other lady. Then, as his wife did not approve of it, and his relations kept inciting him to it, Guhasena, whose mind was firmly set on doing his duty, was bewildered. Then he went and performed a vow in the temple of the god, observing a rigid fast, trusting that the god would shew him some way out of his difficulty. And his wife Devasmiṭá also performed a vow with him; then Śiva was pleased to appear to that couple in a dream; and giving them two red lotuses the god said to them,—“take each, of you one of these lotuses in your hand. And if either of you shall be unfaithful during your separation, the lotus in the hand of the other shall fade, but not otherwise5.” After hearing this, the two woke up, and each beheld in the hand of the other a red lotus, and it seemed as if they had got one another’s hearts. Then Guhasena set out, lotus in hand, but Devasmitá remained in the house with her eyes fixed upon her flower. Guhasena for his part quickly reached the country of Kaṭáha, and began to buy and sell jewels there. And four young merchants in that country, seeing that that unfading lotus was ever in his hand, were greatly astonished. Accordingly they got him to their house by an artifice, and made him drink a great deal of wine, and then asked him the history of the lotus, and he being intoxicated told them the whole story. Then those four young merchants, knowing that Guhasena would take a long time to complete his sales and purchases of jewels and other wares, planned together, like rascals as they were, the seduction of his wife out of curiosity, and eager to accomplish it set out quickly for Támraliptá without their departure being noticed. There they cast about for some instrument, and at last had recourse to a female ascetic of the name of Yogakaraṇḍiká, who lived in a sanctuary of Buddha; and they said to her in an affectionate
- 73. manner, “Reverend madam, if our object is accomplished by your help, we will give you much wealth.” She answered them; “No doubt, you young men desire some woman in this city, so tell me all about it, I will procure you the object of your desire, but I have no wish for money; I have a pupil of distinguished ability named Siddhikarí; owing to her kindness I have obtained untold wealth.” The young merchants asked—“How have you obtained untold wealth by the assistance of a pupil?” Being asked this question, the female ascetic said,—“If you feel any curiosity about the matter, listen, my sons, I will tell you the whole story.” Story of the cunning Siddhikarí. Long ago a certain merchant came here from the north; while he was dwelling here, my pupil went and obtained, with a treacherous object, the position of a serving-maid in his house, having first altered her appearance, and after she had gained the confidence of that merchant, she stole all his hoard of gold from his house, and went off secretly in the morning twilight. And as she went out from the city moving rapidly through fear, a certain Ḍomba6 with his drum in his hand, saw her, and pursued her at full speed with the intention of robbing her. When she had reached the foot of a Nyagrodha tree, she saw that he had come up with her, and so the cunning Siddhikarí said this to him in a plaintive manner, “I have had a jealous quarrel with my husband, and I have left his house to die, therefore my good man, make a noose for me to hang myself with.” Then the Ḍomba thought, “Let her hang herself, why should I be guilty of her death, especially as she is a woman,” and so he fastened a noose for her to the tree. Then Siddhikarí, feigning ignorance, said to the Ḍomba, “How is the noose slipped round the neck? shew me, I entreat you.” Then the Ḍomba placed the drum under his feet, and saying,—“This is the way we do the trick”—he fastened the noose round his own throat; Siddhikarí for her part smashed the drum to atoms with a kick, and that Ḍomba hung till he was dead.7 At that moment the merchant arrived in search of her, and beheld from a
- 74. distance Siddhikarí, who had stolen from him untold treasures, at the foot of the tree. She too saw him coming, and climbed up the tree without being noticed, and remained there on a bough, having her body concealed by the dense foliage. When the merchant came up with his servants, he saw the Ḍomba hanging by his neck, but Siddhikarí was nowhere to be seen. Immediately one of his servants said “I wonder whether she has got up this tree,” and proceeded to ascend it himself. Then Siddhikarí said—“I have always loved you, and now you have climbed up where I am, so all this wealth is at your disposal, handsome man, come and embrace me.” So she embraced the merchant’s servant, and as she was kissing his mouth, she bit off the fool’s tongue. He, overcome with the pain, fell from that tree, spitting blood from his mouth, uttering some indistinct syllables, which sounded like Lalalla. When he saw that, the merchant was terrified, and supposing that his servant had been seized by a demon, he fled from that place, and went to his own house with his attendants. Then Siddhikarí the female ascetic, equally frightened, descended from the top of the tree, and brought home with her all that wealth. Such a person is my pupil, distinguished for her great discernment, and it is in this way, my sons, that I have obtained wealth by her kindness. When she had said this to the young merchants, the female ascetic shewed to them her pupil who happened to come in at that moment; and said to them, “Now, my sons, tell me the real state of affairs—what woman do you desire? I will quickly procure her for you.” When they heard that they said, “procure us an interview with the wife of the merchant Guhasena named Devasmitá.” When she heard that, the ascetic undertook to manage that business for them, and she gave those young merchants her own house to reside in. Then she gratified the servants at Guhasena’s house with gifts of sweetmeats and other things, and afterwards entered it with her pupil. Then, as she approached the private rooms of Devasmitá, a bitch, that was fastened there with a chain, would not let her come near, but opposed her entrance in the most determined way. Then Devasmitá seeing her, of her own accord sent a maid, and had her brought in, thinking to herself, “What can this person be come for?” After she had entered, the wicked ascetic gave Devasmitá her blessing, and, treating the virtuous woman with affected respect, said to her—“I have always had a desire to see you, but to-
- 75. day I saw you in a dream, therefore I have come to visit you with impatient eagerness; and my mind is afflicted at beholding you separated from your husband, for beauty and youth are wasted when one is deprived of the society of one’s beloved.” With this and many other speeches of the same kind she tried to gain the confidence of the virtuous woman in a short interview, and then taking leave of her she returned to her own house. On the second day she took with her a piece of meat full of pepper dust, and went again to the house of Devasmitá, and there she gave that piece of meat to the bitch at the door, and the bitch gobbled it up, pepper and all. Then owing to the pepper dust, the tears flowed in profusion from the animal’s eyes, and her nose began to run. And the cunning ascetic immediately went into the apartment of Devasmitá, who received her hospitably, and began to cry. When Devasmitá asked her why she shed tears, she said with affected reluctance: “My friend, look at this bitch weeping outside here. This creature recognized me to-day as having been its companion in a former birth, and began to weep; for that reason my tears gushed through pity.” When she heard that, and saw that bitch outside apparently weeping, Devasmitá thought for a moment to herself, “What can be the meaning of this wonderful sight?” Then the ascetic said to her, “My daughter, in a former birth, I and that bitch were the two wives of a certain Bráhman. And our husband frequently went about to other countries on embassies by order of the king. Now while he was away from home, I lived with other men at my pleasure, and so did not cheat the elements, of which I was composed, and my senses, of their lawful enjoyment. For considerate treatment of the elements and senses is held to be the highest duty. Therefore I have been born in this birth with a recollection of my former existence. But she, in her former life, through ignorance, confined all her attention to the preservation of her character, therefore she has been degraded and born again as one of the canine race, however, she too remembers her former birth.” The wise Devasmitá said to herself, “This is a novel conception of duty; no doubt this woman has laid a treacherous snare for me”; and so she said to her, “Reverend lady, for this long time I have been ignorant of this duty, so procure me an interview with some charming man.”—Then the ascetic said —“There are residing here some young merchants that have come from another country, so I will bring them to you.” When she had said this, the ascetic returned home delighted, and Devasmitá of her own accord said to
- 76. her maids: “No doubt those scoundrelly young merchants, whoever they may be, have seen that unfading lotus in the hand of my husband, and have on some occasion or other, when he was drinking wine, asked him out of curiosity to tell the whole story of it, and have now come here from that island to seduce me, and this wicked ascetic is employed by them. So bring quickly some wine mixed with Datura,8 and when you have brought it, have a dog’s foot of iron made as quickly as possible.” When Devasmitá had given these orders, the maids executed them faithfully, and one of the maids, by her orders, dressed herself up to resemble her mistress. The ascetic for her part chose out of the party of four merchants, (each of whom in his eagerness said—“let me go first”—) one individual, and brought him with her. And concealing him in the dress of her pupil, she introduced him in the evening into the house of Devasmitá, and coming out, disappeared. Then that maid, who was disguised as Devasmitá, courteously persuaded the young merchant to drink some of that wine drugged with Datura. That liquor,9 like his own immodesty, robbed him of his senses, and then the maids took away his clothes and other equipments and left him stark naked; then they branded him on the forehead with the mark of a dog’s foot, and during the night took him and pushed him into a ditch full of filth. Then he recovered consciousness in the last watch of the night, and found himself plunged in a ditch, as it were the hell Avíchi assigned to him by his sins. Then he got up and washed himself and went to the house of the female ascetic, in a state of nature, feeling with his fingers the mark on his forehead. And when he got there, he told his friends that he had been robbed on the way, in order that he might not be the only person made ridiculous. And the next morning he sat with a cloth wrapped round his branded forehead, giving as an excuse that he had a headache from keeping awake so long, and drinking too much. In the same way the next young merchant was maltreated, when he got to the house of Devasmitá, and when he returned home naked, he said, “I put on my ornaments there, and as I was coming out I was plundered by robbers.” In the morning he also, on the plea of a headache, put a wrapper on to cover his branded forehead. In the same way all the four young merchants suffered in turns branding and other humiliating treatment, though they concealed the fact. And they
- 77. went away from the place, without revealing to the female Buddhist ascetic the ill-treatment they had experienced, hoping that she would suffer in a similar way. On the next day the ascetic went with her disciple to the house of Devasmitá, much delighted at having accomplished what she undertook to do. Then Devasmitá received her courteously, and made her drink wine drugged with Datura, offered as a sign of gratitude. When she and her disciple were intoxicated with it, that chaste wife cut off their ears and noses, and flung them also into a filthy pool. And being distressed by the thought that perhaps these young merchants might go and slay her husband, she told the whole circumstance to her mother-in-law. Then her mother-in- law said to her,—“My daughter, you have acted nobly, but possibly some misfortune may happen to my son in consequence of what you have done.” Then Devasmitá said—I will deliver him even as Śaktimatí in old time delivered her husband by her wisdom. Her mother-in-law asked; “How did Śaktimatí deliver her husband? tell me, my daughter.” Then Devasmitá related the following story: Story of Śaktimatí. In our country, within the city, there is the shrine of a powerful Yaksha named Maṇibhadra, established by our ancestors. The people there come and make petitions at this shrine, offering various gifts, in order to obtain various blessings. Whenever a man is found at night with another man’s wife, he is placed with her within the inner chamber of the Yaksha’s temple. And in the morning he is taken away from thence with the woman to the king’s court, and his behaviour being made known, he is punished; such is the custom. Once on a time in that city a merchant, of the name of Samudradatta, was found by a city-guard in the company of another man’s wife. So he took him and placed him with the woman in that temple of the Yaksha, fastening the door firmly. And immediately the wise and devoted wife of that merchant, whose name was Śaktimatí, came to hear of the occurrence; then that resolute woman, disguising herself, went confidently
- 78. at night to the temple of the Yaksha, accompanied by her friends, taking with her offerings for the god. When she arrived there, the priest whose business it was to eat the offerings, through desire for a fee, opened the door and let her enter, informing the magistrate of what he had done. And she, when she got inside, saw her husband looking sheepish, with a woman, and she made the woman put on her own dress, and told her to go out. So that woman went out in her dress by night, and got off, but Śaktimatí remained in the temple with her husband. And when the king’s officers came in the morning to examine the merchant, he was seen by all to be in the company of his own wife.10 When he heard that, the king dismissed the merchant from the temple of the Yaksha, as it were from the mouth of death, and punished the chief magistrate. So Śaktimatí in old time delivered her husband by her wisdom, and in the same way I will go and save my husband by my discretion. So the wise Devasmitá said in secret to her mother-in-law, and, in company with her maids, she put on the dress of a merchant. Then she embarked on a ship, on the pretence of a mercantile expedition, and came to the country of Kaṭáha where her husband was. And when she arrived there, she saw that husband of hers, Guhasena, in the midst of a circle of merchants, like consolation in external bodily form. He seeing her afar off in the dress of a man,11 as it were, drank her in with his eyes, and thought to himself, “Who may this merchant be that looks so like my beloved wife”? So Devasmitá went and represented to the king that she had a petition to make, and asked him to assemble all his subjects. Then the king full of curiosity assembled all the citizens, and said to that lady disguised as a merchant, “What is your petition?” Then Devasmitá said—There are residing here in your midst four slaves of mine who have escaped, let the king make them over to me. Then the king said to her, “All the citizens are present here, so look at every one in order to recognise him, and take those slaves of yours.” Then she seized upon the four young merchants, whom she had before treated in such a humiliating way in her house, and who had wrappers bound round their heads. Then the merchants, who were there, flew in a passion, and said to her, “These are the sons of distinguished merchants, how then can they be your slaves?” Then she answered them, “If you do not believe what I say,
- 79. examine their foreheads which I marked with a dog’s foot.” They consented, and removing the head-wrappers of these four, they all beheld the dog’s foot on their foreheads. Then all the merchants were abashed, and the king, being astonished, himself asked Devasmitá what all this meant. She told the whole story, and all the people burst out laughing, and the king said to the lady,—“They are your slaves by the best of titles.” Then the other merchants paid a large sum of money to that chaste wife, to redeem those four from slavery, and a fine to the king’s treasury. Devasmitá received that money, and recovered her husband, and being honoured by all good men, returned then to her own city Támraliptá, and she was never afterwards separated from her beloved. “Thus, O queen, women of good family ever worship their husbands with chaste and resolute behaviour,12 and never think of any other man, for to virtuous wives the husband is the highest deity.” When Vásavadattá on the journey heard this noble story from the mouth of Vasantaka, she got over the feeling of shame at having recently left her father’s house, and her mind, which was previously attached by strong affection to her husband, became so fixed upon him as to be entirely devoted to his service. Note on Chapter XIII. With regard to the incident of the bitch and the pepper in the story of Devasmitá see the note in the 1st volume of Wilson’s Essays on Sanskrit Literature. He says: “This incident with a very different and much less moral dénouement is one of the stories in the Disciplina Clericalis, a collection of stories professedly derived from the Arabian fabulists and compiled by Petrus Alfonsus a converted Jew, who flourished about 1106 and was godson to Alfonso I, king of Arragon. In the Analysis prepared by Mr. Douce, this story is the 12th, and is entitled “Stratagem of an old woman in favour of a young gallant.” She persuades his mistress who had rejected his addresses that her little dog was formerly a woman, and so
- 80. 1 2 transformed in consequence of her cruelty to her lover. (Ellis’s Metrical Romances, I, 130.) This story was introduced into Europe, therefore, much about the time at which it was enrolled among the contents of the Vṛihat Kathá in Cashmir. The metempsychosis is so much more obvious an explanation of the change of forms, that it renders it probable the story was originally Hindu. It was soon copied in Europe, and occurs in Le Grand as La vieille qui séduisit la jeune fille. III. 148 [ed. III. Vol. IV. 50]. The parallel is very close and the old woman gives “une chienne à manger des choses fortement saupoudrèes de senève qui lai picotait le palais et les narines et l’animal larmoyait beaucoup.” She then shows her to the young woman and tells her the bitch was her daughter. “Son malheur fut d’avoir le cœur dur; un jeune homme l’aimait, elle le rebuta. Le malheureux après avoir tout tenté pour l’attendrir, désespéré de sa dureté en prit tant de chagrin qu’il tomba malade et mourut. Dieu l’a bien vengè; voyez en quel état pour la punir il a reduit ma pauvre fille, et comment elle pleure sa faute.” The lesson was not thrown away. The story occurs also in the Gesta Romanorum as “The Old Woman and her Dog” [in Bohn’s edition it is Tale XXVIII], and it also finds a place where we should little have expected to find it, in the Promptuarium of John Herolt of Basil, an ample repository of examples for composing sermons: the compiler a Dominican friar, professing to imitate his patron saint, who always abundabat exemplis in his discourses.” [In Bohn’s edition we are told that it appears in an English garb amongst a translation of Æsop’s Fables published in 1658.] Dr. Rost refers us to Th. Wright, Latin Stories, London, 1842, p. 218. Loiseleur Deslongchamps Essai sur les Fables Indiennes, Paris, 1838, p. 106 ff. F. H. Von der Hagen, Gesammtabenteuer, 1850 I, cxii. ff and Grässe, I. 1, 374 ff. In Gonzenbach’a Sicilianische Märchen, No. 55, Vol. I, p. 359, Epomata plays some young men much the same trick as Devasmitá, and they try in much the same way to conceal their disgrace. The story is the second in my copy of the Śuka Saptati. Cp. the way in which Rüdiger carries off the daughter of king Osantrix, Hagen’s Helden-Sagen, Vol. I, p. 227. τηρήσαντες νύκτα χειμέριον ὕδατι καὶ ἀνέμῳ καὶ ἅμ’ ἀσέληνον ἐξῇσαν. Thucyd. III. 22.
- 81. 3 4 5 The word dasyu here means savage, barbarian. These wild mountain tribes called indiscriminately Śavaras, Pulindas, Bhillas c., seem to have been addicted to cattle-lifting and brigandage. So the word dasyu comes to mean robber. Even the virtuous Śavara prince described in the story of Jímútaváhana plunders a caravan. Cathay? Compare the rose garland in the story of the Wright’s Chaste Wife; edited for the early English Text Society by Frederick J. Furnivall, especially lines 58 and ff. “Wete thou wele withowtyn fable “Alle the whyle thy wife is stable “The chaplett wolle holde hewe; “And yf thy wyfe use putry “Or telle eny man to lye her by Then welle yt change hewe, And by the garland thou may see, Fekylle or fals yf that sche be, Or elles yf she be true. See also note in Wilson’s Essays on Sanskrit Literature, Vol. I, p. 218. He tells us that in Perce Forest the lily of the Kathá Sarit Ságara is represented by a rose. In Amadis de Gaul it is a garland which blooms on the head of her that is faithful, and fades on the brow of the inconstant. In Les Contes à rire, it is also a flower. In Ariosto, the test applied to both male and female is a cup, the wine of which is spilled by the unfaithful lover. This fiction also occurs in the romances of Tristan, Perceval and La Morte d’Arthur, and is well known by La Fontaine’s version, La Coupe Enchantée. In La Lai du Corn, it is a drinking-horn. Spenser has derived his girdle of Florimel from these sources or more immediately from the Fabliau, Le Manteau mal taillé or Le Court Mantel, an English version of which is published in Percy’s Reliques, the Boy and the Mantel (Vol. III.) In the Gesta Romanorum (c. 69) the test is the whimsical one of a shirt, which will neither require washing nor mending as long as the wearer is constant. (Not the wearer only but the wearer and his wife). Davenant has substituted an emerald for a flower. The bridal stone, And much renowned, because it chasteness loves, And will, when worn by the neglected wife, Shew when her absent lord disloyal proves By faintness and a pale decay of life.
- 82. 6 7 8 9 10 11 12 I may remark that there is a certain resemblance in this story to that of Shakespeare’s Cymbeline, which is founded on the 9th Story of the 2nd day in the Decamerone, and to the 7th Story in Gonzenbach’s Sicilianische Märchen. See also “The king of Spain and his queen” in Thorpe’s Yule-tide Stories, pp. 452–455. Thorpe remarks that the tale agrees in substance with the ballad of the “Graf Von Rom” in Uhland, II, 784; and with the Flemish story of “Ritter Alexander aus Metz und Seine Frau Florentina.” In the 21st of Bandello’s novels the test is a mirror (Liebrecht’s Dunlop, p. 287). See also pp. 85 and 86 of Liebrecht’s Dunlop, with the notes at the end of the volume. A man of low caste now called Ḍom. They officiate as executioners. Compare the way in which the widow’s son, the shifty lad, treats Black Rogue in Campbell’s Tales of the Western Highlands (Tale XVII d. Orient und Occident, Vol. II, p. 303.) Datura is still employed, I believe, to stupefy people whom it is thought desirable to rob. I read iva for the eva of Dr. Brockhaus’s text. A precisely similar story occurs in the Bahár Dánish. The turn of the chief incident, although not the same, is similar to that of Nov VII, Part 4 of Bandello’s Novelle, or the Accorto Avvedimento di una Fantesca à liberare la padrona e l’innamorato di quella de la morte. (Wilson’s Essays, Vol. I, p. 224.) Cp. also the Mongolian version of the story in Sagas from the Far East, p. 320. The story of Śaktimatí is the 19th in the Śuka Saptati. I have been presented by Professor Nílmani Mukhopádhyáya with a copy of a MS. of this work made by Babu Umeśa Chandra Gupta. Cp. the story of the Chest in Campbell’s Stories from the Western Highlands. It is the first story in the 2nd volume and contains one or two incidents which remind us of this story. I read mahâkulodgatáḥ.
- 83. Chapter XIV. Accordingly while the king of Vatsa was remaining in that Vindhya forest, the warder of king Chaṇḍamahásena came to him. And when he arrived, he did obeisance to the king and spoke as follows: The king Chaṇḍamahásena sends you this message. You did rightly in carrying off Vásavadattá yourself, for I had brought you to my court with this very object; and the reason I did not myself give her to you, while you were a prisoner, was, that I feared, if I did so, you might not be well disposed towards me. Now, O king, I ask you to wait a little, in order that the marriage of my daughter may not be performed without due ceremonies. For my son Gopálaka will soon arrive in your court, and he will celebrate with appropriate ceremonies the marriage of that sister of his. This message the warder brought to the king of Vatsa, and said various things to Vásavadattá. Then the king of Vatsa, being pleased, determined on going to Kauśámbí with Vásavadattá, who was also in high spirits. He told his ally Pulindaka, and that warder in the service of his father-in-law to await, where they were, the arrival of Gopálaka, and then to come with him to Kauśámbí. Then the great king set out early the next day for his own city with the queen Vásavadattá, followed by huge elephants raining streams of ichor, that seemed like moving peaks of the Vindhya range accompanying him out of affection; he was, as it were, praised by the earth, that outdid the compositions of his minstrels, while it rang with the hoofs of his horses and the tramplings of his soldiers; and by means of the towering clouds of dust from his army, that ascended to heaven, he made Indra fear that the mountains were sporting with unshorn wings.1 Then the king reached his country in two or three days, and rested one night in a palace belonging to Rumaṇvat; and on the next day, accompanied by his beloved, he enjoyed after a long absence the great delight of entering Kauśámbí, the people of which were eagerly looking with uplifted faces for his approach. And then that city was resplendent as a wife, her lord having returned after a long absence, beginning her adornment and auspicious bathing vicariously by means of her women; and there the citizens, their sorrow now at an end, beheld the king of Vatsa
- 84. accompanied by his bride, as peacocks behold a cloud accompanied by lightning;2 and the wives of the citizens standing on the tops of the palaces, filled the heaven with their faces, that had the appearance of golden lotuses blooming in the heavenly Ganges. Then the king of Vatsa entered his royal palace with Vásavadattá, who seemed like a second goddess of royal fortune; and that palace then shone as if it had just awaked from sleep, full of kings who had come to shew their devotion, festive with songs of minstrels.3 Not long after came Gopálaka the brother of Vásavadattá, bringing with him the warder and Pulindaka; the king went to meet him, and Vásavadattá received him with her eyes expanded with delight, as if he were a second spirit of joy. While she was looking at this brother, a tear dimmed her eyes lest she should be ashamed; and then she, being encouraged by him with the words of her father’s message, considered that her object in life was attained, now that she was reunited to her own relations. Then, on the next day, Gopálaka, with the utmost eagerness, set about the high festival of her marriage with the king of Vatsa, carefully observing all prescribed ceremonies. Then the king of Vatsa received the hand of Vásavadattá, like a beautiful shoot lately budded on the creeper of love. She too, with her eyes closed through the great joy of touching her beloved’s hand, having her limbs bathed in perspiration accompanied with trembling, covered all over with extreme horripilation, appeared at that moment as if struck by the god of the flowery bow with the arrow of bewilderment, the weapon of wind, and the water weapon in quick succession;4 when she walked round the fire keeping it to the right, her eyes being red with the smoke, she had her first taste, so to speak, of the sweetness of wine and honey.5 Then by means of the jewels brought by Gopálaka, and the gifts of the kings, the monarch of Vatsa became a real king of kings.6 That bride and bridegroom, after their marriage had been celebrated, first exhibited themselves to the eyes of the people, and then entered their private apartments. Then the king of Vatsa, on the day so auspicious to himself invested Gopálaka and Pulindaka with turbans of honour and other distinctions, and he commissioned Yaugandharáyaṇa and Rumaṇvat to confer appropriate distinctions on the kings who had come to visit him, and on the citizens. Then Yaugandharáyaṇa said to Rumaṇvat; “The king has given us a difficult commission, for men’s feelings are hard
- 85. to discover. And even a child will certainly do mischief if not pleased; to illustrate this point listen to the tale of the child Vinashṭaka, my friend.” Story of the clever deformed child. Once on a time there was a certain Bráhman named Rudraśarman, and he, when he became a householder, had two wives, and one of his wives gave birth to a son and died; and then the Bráhman entrusted that son to the care of his step-mother; and when he grew to a tolerable stature, she gave him coarse food; the consequence was, the boy became pale, and got a swollen stomach. Then Rudraśarman said to that second wife, “How comes it that you have neglected this child of mine that has lost its mother?” She said to her husband, “Though I take affectionate care of him, he is nevertheless the strange object you see; what am I to do with him?” Whereupon the Bráhman thought, “No doubt it is the child’s nature to be like this.” For who sees through the deceitfulness of the speeches of women uttered with affected simplicity? Then that child began to go by the name of Bálavinashṭaka7 in his father’s house, because they said this child (bála) is deformed (vinashṭa.) Then Bálavinashṭaka thought to himself—“This step- mother of mine is always ill-treating me, therefore I had better be revenged on her in some way”—for though the boy was only a little more than five years old, he was clever enough. Then he said secretly to his father when he returned from the king’s court, with half suppressed voice—“Papa, I have two Papas.” So the boy said every day, and his father suspecting that his wife had a paramour, would not even touch her. She for her part thought —“Why is my husband angry without my being guilty; I wonder whether Bálavinashṭaka has been at any tricks?” So she washed Bálavinashṭaka with careful kindness, and gave him dainty food, and taking him on her lap, asked him the following question: “My son why have you incensed your father Rudraśarman against me?” When he heard that, the boy said to his step-mother, “I will do more harm to you than that, if you do not
- 86. immediately cease ill-treating me. You take good care of your own children; why do you perpetually torment me?” When she heard that, she bowed before him, and said with a solemn oath, “I will not do so any more; so reconcile my husband to me.” Then the child said to her—“Well, when my father comes home, let one of your maids shew him a mirror, and leave the rest to me.” She said, “Very well,” and by her orders a maid shewed a mirror to her husband as soon as he returned home. Thereupon the child pointing out the reflection of his father in the mirror, said, “There is my second father.” When he heard that, Rudraśarman dismissed his suspicions and was immediately reconciled to his wife, whom he had blamed without cause. “Thus even a child may do mischief if it is annoyed, and therefore we must carefully conciliate all this retinue.” Saying this, Yaugandharáyaṇa with the help of Rumaṇvat, carefully honoured all the people on this the king of Vatsa’s great day of rejoicing.8 And they gratified all the kings so successfully that each one of them thought, “These two men are devoted to me alone.” And the king honoured those two ministers and Vasantaka with garments, unguents, and ornaments bestowed with his own hand, and he also gave them grants of villages. Then the king of Vatsa, having celebrated the great festival of his marriage, considered all his wishes gratified, now that he was linked to Vásavadattá. Their mutual love, having blossomed after a long time of expectation, was so great, owing to the strength of their passion, that their hearts continually resembled those of the sorrowing Chakravákas, when the night, during which they are separated, comes to an end. And as the familiarity of the couple increased, their love seemed to be ever renewed. Then Gopálaka, being ordered by his father to return to get married himself, went away, after having been entreated by the king of Vatsa to return quickly. In course of time the king of Vatsa became faithless, and secretly loved an attendant of the harem named Virachitá, with whom he had previously had an intrigue. One day he made a mistake and addressed the queen by her name, thereupon he had to conciliate her by clinging to her feet, and bathed in her tears he was anointed9 a fortunate king. Moreover he married a princess of the name of Bandhumatí, whom Gopálaka had captured by the
- 87. might of his arm, and sent as a present to the queen; and whom she concealed, changing her name to Manjuliká; who seemed like another Lakshmí issuing from the sea of beauty. Her the king saw, when he was in the company of Vasantaka, and secretly married her by the Gándharva ceremony in a summer-house. And that proceeding of his was beheld by Vásavadattá, who was in concealment, and she was angry, and had Vasantaka put in fetters. Then the king had recourse to the good offices of a female ascetic, a friend of the queen’s, who had come with her from her father’s court, of the name of Sánkrityánaní. She appeased the queen’s anger, and got Bandhumatí presented to the king by the obedient queen, for tender is the heart of virtuous wives. Then the queen released Vasantaka from imprisonment; he came into the presence of the queen and said to her with a laugh, “Bandhumatí did you an injury, but what did I do to you? You are angry with adders10 and you kill water-snakes.” Then the queen, out of curiosity, asked him to explain that metaphor, and he continued as follows: Story of Ruru. Once on a time a hermit’s son of the name of Ruru, wandering about at will, saw a maiden of wonderful beauty, the daughter of a heavenly nymph named Menaká by a Vidyádhara, and brought up by a hermit of the name of Sthúlakeśa in his hermitage. That lady, whose name was Prishaḍvará, so captivated the mind of that Ruru when he saw her, that he went and begged the hermit to give her to him in marriage. Sthúlakeśa for his part betrothed the maiden to him, and when the wedding was nigh at hand, suddenly an adder bit her. Then the heart of Ruru was full of despair, but he heard this voice in the heaven—“O Bráhman raise to life with the gift of half thy own life,11 this maiden, whose allotted term is at an end.” When he heard that, Ruru gave her the half of his own life, as he had been directed; by means of that she revived, and Ruru married her. Thenceforward he was incensed with the whole race of serpents, and whenever he saw a serpent he killed it, thinking to himself as he killed each one—“This may have bitten my wife.”
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