![2012 ASME-ISPS /JSME-IIP Joint International Conference on
Micromechatronics for Information and Precision Equipment
MIPE2012
June 18-20, 2012, Santa Clara, California, USA
*Corresponding author: V. Kartik
#
These authors have contributed equally to this work
A ROBUST AND LOW-COST HYBRID LASER GUIDANCE TECHNIQUE FOR AUTONOMOUS
VEHICLES OPERATING IN PRE-DEFINED ENVIRONMENTS
Pushkar Limaye
#+
, Nimish Mehta
#+
, Chaitanya Talnikar
#^
, Prathamesh Joshi
#+
and V. Kartik
+
+
Department of Mechanical Engineering ^
Department of Chemical Engineering
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India.
E-mail: {pushkar_limaye, nimish_mehta, chaitanya.talnikar, prathamesh.joshi and vkartik}@iitb.ac.in
Introduction
This paper presents a guidance scheme that enables
autonomous vehicles to navigate in enclosed
indoor/outdoor environments where an approximate map
of the area is a priori known, but where the conventional
techniques that involve placement of legends/markers
have considerable limitations. Autonomous vehicles have
extensive applications in manufacturing shop-floors,
supermarkets, smart warehouses and similar
environments, where the map of the terrain is largely
known in advance, and vehicle operation is repetitive and
over extended time periods. The typical navigation
method for such applications involves the placement of
continuous or distinct markers at stationary points in the
environment itself, from which information on the terrain
and the vehicle’s position within it can be obtained.
However, for several such applications, the common
solutions based on this principle – line-following or
magnetic strip-following – are highly intrusive, difficult
to re-configure once placed, prone to damage/degradation
with repeated and extended use, and unsuitable in the
presence of temporary obstacles. A review of existing
literature [1-2] reveals that a major barrier towards
enabling completely-automated indoor systems is the
achievement of reliable point-to-point navigation of its
component vehicles, but with (a) minimally-intrusive
modifications due to legends, (b) versatility in
reconfiguring the terrain map, and (c) allowance for
obstacle avoidance. On the other hand, for fully
autonomous vehicles that operate without prior terrain
information, navigation typically involves the use of
vision systems, and/or inertial sensors such as
accelerometers and gyroscopes. From the standpoint of
achieving low cost and high reliability in repetitive and
extended operation, the main limitation of the computer
vision method or with the use of inertial sensors is the
high computational overhead. The position-estimating
algorithms have low accuracy when these are, for reasons
of cost and/or reliability, required to run on a single or
low-end microcontroller [3]. We present here a scheme
that addresses the challenge of achieving reliable
navigation in pre-defined environments, by combining
inputs from low-resolution onboard sensors with those
from external legends that are not only low-cost, non-
obstructive, and robust in harsh operating conditions and
with extended use, but also entail minimal alterations to
the operating area, and are amenable to rapid
reconfiguration of the map. The proposed solution for
autonomous vehicles is implemented and demonstrated in
the example application of a low-cost book deposition
robot for a library. The navigation technique and
algorithm – that runs on a single, low computing-power
microcontroller – has been verified both in simulation as
well as in test runs over example obstacle courses.
Operating Principle
In our hybrid guidance scheme, we create a coarsely-
spaced laser grid, and combine position inputs from it
with onboard sensors such as an encoder and
magnetometer. The use of multiple laser transmitters as
sparsely-spaced passive markers divides the terrain map
into a grid that provides waypoints for navigation, which
are then detected through onboard receivers. The laser
grid acts as a periodic correction to the position estimates
determined by using the (lower resolution) encoder and
magnetometer that are prone to noise and drift [4].
Combining position estimates from both sources ensures
that even in the event of any or some of the laser markers
becoming unavailable due to failure or blocking of the
line-of-sight, or in the presence of a temporary obstacle
that blocks a waypoint or the vehicle’s path, the vehicle
can still navigate the terrain using the simpler onboard
sensors, albeit with lower accuracy.
The example vehicle on which we have implemented our
technique has a two wheel differential drive, comprising
one motor for each wheel, and with castor wheels for
support. The algorithm uses three states to completely
describe the vehicle’s position. These states are the (a) X
position coordinate, (b) Y position coordinate, and (c)](https://image.slidesharecdn.com/hybridautonomousnavigationplimaye-et-al3pgabstract-150322133218-conversion-gate01/85/Hybrid-autonomousnavigation-p_limaye-et-al_3pgabstract-1-320.jpg)
![angle of heading Φ. The vehicle is equipped with two
types of sensors, a motor position encoder for each wheel,
and a magnetometer that is used to determine Φ. This
angle, along with the extent of rotation of the wheels
obtained from the encoders, is used to estimate the spatial
coordinates of the vehicle at the nth
time instant,
(X , Y ), using simple kinematical equations. (Here,
the notation ()est
denotes an estimated quantity, which is
calculated onboard, and which can differ from the actual
state ()act
due to the measurement error ()err
.) Such
errors are further compounded with the use of low
resolution sensors, and with the use of encoders where
wheel slip is not accounted for. The kinematical
equations [2] of motion relating the states are
X = X + V cos Φ ∆t
Y = Y + V sin Φ ∆t
where X , Y are the estimated X- and Y-coordinates,
∆t is the time step of the vehicle's microcontroller, and
the subscript n denotes quantities at the nth
time step.
With input speeds V , V provided to the left and
right wheels respectively, the estimated linear speed is
V = (V + V )/2. The heading angle Φ
measured by the vehicle differs from the actual heading
by the error term Φ , i.e., Φ = Φ + Φ .
While following the reference trajectory, the vehicle
deviates from its ideal path due to errors in estimating the
speed and heading. In order to correct this deviation,
position inputs from the laser grid are used to reset the
estimated position of the vehicle, whenever these become
available. Whenever the vehicle encounters a laser grid
point or beam, it updates the position parameter(s) in the
kinematic and control equations which govern the
motion, and recalculates its position. The controller then
calculates the necessary input to the wheels. Figure 1
depicts this control scheme in schematic form1
.
Vehicle and Path Modeling
To verify that the proposed scheme with periodic external
corrections improves the path tracking performance of the
vehicle, we modeled the vehicle’s motion by considering
the following three errors. (a) Motor speed error, V :
This is modeled as a fixed error which can be calibrated
from an initial characterization of the encoder; here, this
value is experimentally determined to be 1% of speed.
(b) Wheel slip error, V : This is a random error which
can, again, be calibrated from an initial characterization
1
The notation ()inp
refers to an input quantity, ()corr
to a
correction received from the grid, and ()meas
and ()ref
refer to a
measured and reference state, respectively.
of the encoder; here this error is taken to have mean 0 and
variance 4%. (c) Magnetometer heading error: The
orientation provided by the magnetometer has a random
error with mean 0 and variance 0.1 radians, obtained from
the manufacturer’s specifications [4].
Fig. 1: Schematic diagram of the control scheme
The above errors will lead to a deviation of the actual
position of the vehicle from the reference trajectory, as
well as from the estimated position. For the purposes of
this simulation, the scheme first discretizes the reference
trajectory into multiple straight segments, in order to
simplify the control algorithm for vehicle speed. The
shortest length within this discretized set of straight lines
depends on factors such as the desired spatial resolution
for following the trajectory, and the actual accuracy of the
vehicle in following each straight segment. At the end of
each segment, the vehicle is assumed to reorient itself in
the direction of the next segment using its differential
drive [5-7]. The random errors are assumed to follow a
Gaussian distribution, with the simulation results being
averaged over a 100 runs. The actual wheel speeds for
the right and left wheels, accounting for the above errors,
are V = V + V + V , and
V = V + V . The linear and angular
velocities can, then, be calculated to be V = (V +
V )/2 and Ω = ([V ] − [V ] )/ , where D
is the distance between the wheels. The governing
equations for the actual position taking these errors into
account are
X = X + V cos Φ ∆t
Y = Y + V sinΦ ∆t
Φ = Φ + Ω ∆t
Simulation Results
In the simulation results that follow, the lasers in the grid
are positioned at equal intervals along both the X- and Y-](https://image.slidesharecdn.com/hybridautonomousnavigationplimaye-et-al3pgabstract-150322133218-conversion-gate01/85/Hybrid-autonomousnavigation-p_limaye-et-al_3pgabstract-2-320.jpg)
![axes. Whenever the vehicle detects an X- and/or Y-axis
laser, the estimator corrects the corresponding position
estimate(s). Since the vehicle largely knows the path a
priori, its heading Φ is reset using the onboard
magnetometer. The vehicle, thus, corrects its estimated
position using information from the external laser grid.
Fig. 2: Normalized position error vs. number of lasers per axis.
Figure 2 shows the error in the vehicle’s position from the
desired path versus the number of lasers per axis. The
total error is the perpendicular distance between the
actual position and the tangent to the trajectory, summed
over all time steps. The plot clearly demonstrates that the
average and maximum error decrease as the number of
lasers are increased. The average position error also
plateaus after a certain number of lasers is reached; this
factor can be used to design the laser grid.
Fig. 3: Normalized position error vs. vehicle speed.
Figure 3 shows the simulated error when the linear speed
of the vehicle is varied. Since the model considers errors
(a) and (b) to be proportional to the linear speed of the
vehicle, the average error expectedly increases with the
vehicle speed. Figure 4 shows simulated trajectories of
the vehicle for different combinations of the resolution of
the onboard magnetometer, and with or without external
corrections from the grid. Table 1 summarizes the
position error for each of these cases; clearly, the
developed navigation technique using external corrections
can enable performance improvements by a factor of two
over the one with only onboard sensors.
Fig. 4: Simulated trajectories for different cases of
magnetometer resolution, and with or without grid correction.
Magnetometer
Resolution
Grid Correction
Available
Normalized Average
Error
Low No 0.00348
High No 0.00027
Low Yes 0.00172
High Yes 0.00014
Table 2: Normalized average error for the cases of Fig. 4.
References
[1] Mark Ollis, 1997, “Vision-Based Perception for an Automated
Harvester,” Proceedings of the 1997 IEEE/RSJ International
Conference on Intelligent Robots and Systems, Grenoble, France.
[2] R.R. Murphy, 1990, “Autonomous Navigation in a Manufacturing
Environment,” IEEE Transactions on Robotics and Automation,
6(4), pp.445-454.
[3] Atmega2560 based Arduino Mega microcontroller (URL:
www.arduino.cc/en/Main/ArduinoBoardMega; retrieved on 27
April, 2012).
[4] Honeywell Two-Axis Compass with Algorithms, Model HMC6352
(URL:http://www51.honeywell.com/aero/common/documents/my
aerospacecatalog-documents/Missiles-Munitions/HMC6352.pdf;
retrieved on 27 April, 2012).
[5] Misel Brezak, 2009, “Experimental Comparison of
Trajectory Tracking Algorithms For Nonholonomic Mobile
Robots,” 5th Annual Conference of the IEEE Industrial Electronics
Society, Porto, Portugal, pp.2229-2234.
[6] Julio V. Mendez., 2011, “Controller Design and
Implementation for a Differential Drive Wheeled Mobile Robot,”
Chinese Control and Decision Conference (CCDC), Mianyang,
China, pp.4038-4043.
[7] Hamidreza Chitsaz, 2007, “Minimum Wheel-Rotation Paths For
Differential Drive Mobile Robots Among Piecewise Smooth
Obstacles,” Proceedings of the IEEE Conference on Robotics and
Automation (ICRA), Roma, Italy.](https://image.slidesharecdn.com/hybridautonomousnavigationplimaye-et-al3pgabstract-150322133218-conversion-gate01/85/Hybrid-autonomousnavigation-p_limaye-et-al_3pgabstract-3-320.jpg)
Hybrid autonomousnavigation p_limaye-et-al_3pgabstract
- 1. 2012 ASME-ISPS /JSME-IIP Joint International Conference on Micromechatronics for Information and Precision Equipment MIPE2012 June 18-20, 2012, Santa Clara, California, USA *Corresponding author: V. Kartik # These authors have contributed equally to this work A ROBUST AND LOW-COST HYBRID LASER GUIDANCE TECHNIQUE FOR AUTONOMOUS VEHICLES OPERATING IN PRE-DEFINED ENVIRONMENTS Pushkar Limaye #+ , Nimish Mehta #+ , Chaitanya Talnikar #^ , Prathamesh Joshi #+ and V. Kartik + + Department of Mechanical Engineering ^ Department of Chemical Engineering Indian Institute of Technology Bombay Powai, Mumbai 400076, India. E-mail: {pushkar_limaye, nimish_mehta, chaitanya.talnikar, prathamesh.joshi and vkartik}@iitb.ac.in Introduction This paper presents a guidance scheme that enables autonomous vehicles to navigate in enclosed indoor/outdoor environments where an approximate map of the area is a priori known, but where the conventional techniques that involve placement of legends/markers have considerable limitations. Autonomous vehicles have extensive applications in manufacturing shop-floors, supermarkets, smart warehouses and similar environments, where the map of the terrain is largely known in advance, and vehicle operation is repetitive and over extended time periods. The typical navigation method for such applications involves the placement of continuous or distinct markers at stationary points in the environment itself, from which information on the terrain and the vehicle’s position within it can be obtained. However, for several such applications, the common solutions based on this principle – line-following or magnetic strip-following – are highly intrusive, difficult to re-configure once placed, prone to damage/degradation with repeated and extended use, and unsuitable in the presence of temporary obstacles. A review of existing literature [1-2] reveals that a major barrier towards enabling completely-automated indoor systems is the achievement of reliable point-to-point navigation of its component vehicles, but with (a) minimally-intrusive modifications due to legends, (b) versatility in reconfiguring the terrain map, and (c) allowance for obstacle avoidance. On the other hand, for fully autonomous vehicles that operate without prior terrain information, navigation typically involves the use of vision systems, and/or inertial sensors such as accelerometers and gyroscopes. From the standpoint of achieving low cost and high reliability in repetitive and extended operation, the main limitation of the computer vision method or with the use of inertial sensors is the high computational overhead. The position-estimating algorithms have low accuracy when these are, for reasons of cost and/or reliability, required to run on a single or low-end microcontroller [3]. We present here a scheme that addresses the challenge of achieving reliable navigation in pre-defined environments, by combining inputs from low-resolution onboard sensors with those from external legends that are not only low-cost, non- obstructive, and robust in harsh operating conditions and with extended use, but also entail minimal alterations to the operating area, and are amenable to rapid reconfiguration of the map. The proposed solution for autonomous vehicles is implemented and demonstrated in the example application of a low-cost book deposition robot for a library. The navigation technique and algorithm – that runs on a single, low computing-power microcontroller – has been verified both in simulation as well as in test runs over example obstacle courses. Operating Principle In our hybrid guidance scheme, we create a coarsely- spaced laser grid, and combine position inputs from it with onboard sensors such as an encoder and magnetometer. The use of multiple laser transmitters as sparsely-spaced passive markers divides the terrain map into a grid that provides waypoints for navigation, which are then detected through onboard receivers. The laser grid acts as a periodic correction to the position estimates determined by using the (lower resolution) encoder and magnetometer that are prone to noise and drift [4]. Combining position estimates from both sources ensures that even in the event of any or some of the laser markers becoming unavailable due to failure or blocking of the line-of-sight, or in the presence of a temporary obstacle that blocks a waypoint or the vehicle’s path, the vehicle can still navigate the terrain using the simpler onboard sensors, albeit with lower accuracy. The example vehicle on which we have implemented our technique has a two wheel differential drive, comprising one motor for each wheel, and with castor wheels for support. The algorithm uses three states to completely describe the vehicle’s position. These states are the (a) X position coordinate, (b) Y position coordinate, and (c)
- 2. angle of heading Φ. The vehicle is equipped with two types of sensors, a motor position encoder for each wheel, and a magnetometer that is used to determine Φ. This angle, along with the extent of rotation of the wheels obtained from the encoders, is used to estimate the spatial coordinates of the vehicle at the nth time instant, (X , Y ), using simple kinematical equations. (Here, the notation ()est denotes an estimated quantity, which is calculated onboard, and which can differ from the actual state ()act due to the measurement error ()err .) Such errors are further compounded with the use of low resolution sensors, and with the use of encoders where wheel slip is not accounted for. The kinematical equations [2] of motion relating the states are X = X + V cos Φ ∆t Y = Y + V sin Φ ∆t where X , Y are the estimated X- and Y-coordinates, ∆t is the time step of the vehicle's microcontroller, and the subscript n denotes quantities at the nth time step. With input speeds V , V provided to the left and right wheels respectively, the estimated linear speed is V = (V + V )/2. The heading angle Φ measured by the vehicle differs from the actual heading by the error term Φ , i.e., Φ = Φ + Φ . While following the reference trajectory, the vehicle deviates from its ideal path due to errors in estimating the speed and heading. In order to correct this deviation, position inputs from the laser grid are used to reset the estimated position of the vehicle, whenever these become available. Whenever the vehicle encounters a laser grid point or beam, it updates the position parameter(s) in the kinematic and control equations which govern the motion, and recalculates its position. The controller then calculates the necessary input to the wheels. Figure 1 depicts this control scheme in schematic form1 . Vehicle and Path Modeling To verify that the proposed scheme with periodic external corrections improves the path tracking performance of the vehicle, we modeled the vehicle’s motion by considering the following three errors. (a) Motor speed error, V : This is modeled as a fixed error which can be calibrated from an initial characterization of the encoder; here, this value is experimentally determined to be 1% of speed. (b) Wheel slip error, V : This is a random error which can, again, be calibrated from an initial characterization 1 The notation ()inp refers to an input quantity, ()corr to a correction received from the grid, and ()meas and ()ref refer to a measured and reference state, respectively. of the encoder; here this error is taken to have mean 0 and variance 4%. (c) Magnetometer heading error: The orientation provided by the magnetometer has a random error with mean 0 and variance 0.1 radians, obtained from the manufacturer’s specifications [4]. Fig. 1: Schematic diagram of the control scheme The above errors will lead to a deviation of the actual position of the vehicle from the reference trajectory, as well as from the estimated position. For the purposes of this simulation, the scheme first discretizes the reference trajectory into multiple straight segments, in order to simplify the control algorithm for vehicle speed. The shortest length within this discretized set of straight lines depends on factors such as the desired spatial resolution for following the trajectory, and the actual accuracy of the vehicle in following each straight segment. At the end of each segment, the vehicle is assumed to reorient itself in the direction of the next segment using its differential drive [5-7]. The random errors are assumed to follow a Gaussian distribution, with the simulation results being averaged over a 100 runs. The actual wheel speeds for the right and left wheels, accounting for the above errors, are V = V + V + V , and V = V + V . The linear and angular velocities can, then, be calculated to be V = (V + V )/2 and Ω = ([V ] − [V ] )/ , where D is the distance between the wheels. The governing equations for the actual position taking these errors into account are X = X + V cos Φ ∆t Y = Y + V sinΦ ∆t Φ = Φ + Ω ∆t Simulation Results In the simulation results that follow, the lasers in the grid are positioned at equal intervals along both the X- and Y-
- 3. axes. Whenever the vehicle detects an X- and/or Y-axis laser, the estimator corrects the corresponding position estimate(s). Since the vehicle largely knows the path a priori, its heading Φ is reset using the onboard magnetometer. The vehicle, thus, corrects its estimated position using information from the external laser grid. Fig. 2: Normalized position error vs. number of lasers per axis. Figure 2 shows the error in the vehicle’s position from the desired path versus the number of lasers per axis. The total error is the perpendicular distance between the actual position and the tangent to the trajectory, summed over all time steps. The plot clearly demonstrates that the average and maximum error decrease as the number of lasers are increased. The average position error also plateaus after a certain number of lasers is reached; this factor can be used to design the laser grid. Fig. 3: Normalized position error vs. vehicle speed. Figure 3 shows the simulated error when the linear speed of the vehicle is varied. Since the model considers errors (a) and (b) to be proportional to the linear speed of the vehicle, the average error expectedly increases with the vehicle speed. Figure 4 shows simulated trajectories of the vehicle for different combinations of the resolution of the onboard magnetometer, and with or without external corrections from the grid. Table 1 summarizes the position error for each of these cases; clearly, the developed navigation technique using external corrections can enable performance improvements by a factor of two over the one with only onboard sensors. Fig. 4: Simulated trajectories for different cases of magnetometer resolution, and with or without grid correction. Magnetometer Resolution Grid Correction Available Normalized Average Error Low No 0.00348 High No 0.00027 Low Yes 0.00172 High Yes 0.00014 Table 2: Normalized average error for the cases of Fig. 4. References [1] Mark Ollis, 1997, “Vision-Based Perception for an Automated Harvester,” Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robots and Systems, Grenoble, France. [2] R.R. Murphy, 1990, “Autonomous Navigation in a Manufacturing Environment,” IEEE Transactions on Robotics and Automation, 6(4), pp.445-454. [3] Atmega2560 based Arduino Mega microcontroller (URL: www.arduino.cc/en/Main/ArduinoBoardMega; retrieved on 27 April, 2012). [4] Honeywell Two-Axis Compass with Algorithms, Model HMC6352 (URL:http://www51.honeywell.com/aero/common/documents/my aerospacecatalog-documents/Missiles-Munitions/HMC6352.pdf; retrieved on 27 April, 2012). [5] Misel Brezak, 2009, “Experimental Comparison of Trajectory Tracking Algorithms For Nonholonomic Mobile Robots,” 5th Annual Conference of the IEEE Industrial Electronics Society, Porto, Portugal, pp.2229-2234. [6] Julio V. Mendez., 2011, “Controller Design and Implementation for a Differential Drive Wheeled Mobile Robot,” Chinese Control and Decision Conference (CCDC), Mianyang, China, pp.4038-4043. [7] Hamidreza Chitsaz, 2007, “Minimum Wheel-Rotation Paths For Differential Drive Mobile Robots Among Piecewise Smooth Obstacles,” Proceedings of the IEEE Conference on Robotics and Automation (ICRA), Roma, Italy.