TCatarino_Dissertation_Final

Tiago Filipe Rodrigues Catarino
Development of a Hand-Tracker:
Wireless Solution based on Inertial Sensors
September 2016

UNIVERSITY OF COIMBRA
FACULTY OF SCIENCES AND TECHNOLOGY
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
Development of a Hand-Tracker
Wireless Solution based on Inertial Sensors
Tiago Filipe Rodrigues Catarino
Jury:
Prof. João Pedro de Almeida Barreto
Prof. João Filipe de Castro Cardoso Ferreira
Prof. Paulo Jorge Carvalho Menezes
Advisors:
Prof. Paulo Jorge Carvalho Menezes
Master Bruno André Santos Patrão
Dissertation submitted to the Electrical and Computer Engineering Department of the
Faculty of Science and Technology of the University of Coimbra in partial fulfilment of the
requirements for the Degree of Master of Science.
Coimbra, September of 2016

Acknowledgements
The accomplishment of this work would not have been possible without the contribution
of a group of people who have been beside me along the way. First and foremost, I would
like to express my gratitude to my advisers Professor Paulo Jorge Carvalho Menezes and
Bruno André Santos Patrão for their permanent teaching and scientific rigor. I would also
like to acknowledge my colleagues at the Mobile Robotics Laboratory in ISR, particularly
Samuel Pedro and José Francisco, for their constant contributions and involvement in every
step throughout the process.
Getting through my dissertation required not only academic support but also a great deal
of friendship and companionship, in this way for many memorable evenings out and in, I
must thank all my colleagues and friends at the Department of Electrical and Computer
Engineering. Furthermore, a big thanks to two special friends, with his own brand of humor,
to my long term friend and already a brother in life João Cascalho, and to Marta Barroqueiro
for all the encouragement and constant understanding.
Most importantly, none of this could have happened without my family, my deepest
gratitude to my parents, brother, aunt Odete Costa and uncle João Catarino for their endless
love and support.

Abstract
The success of virtual reality comes from the sense of immersion it offers, providing sensory
experiences that replicate the real world. This feeling is further extended when we are able
to simulate a user’s physical presence by providing intuitive ways of interaction. Our hands
being a natural tool for real world interaction, interest in solutions that explore the tracking
and recognition of hand motions grows. Using a hand tracking solution as an interactive
tool can provide a multitude of advantages, not only on virtual reality but on any kind of
human-computer interaction system.
However, most of the existing systems are high-cost solutions or exhibit limitations that
either hinder the natural hand movements or have limited range of action, constraining the
set of possible interactions.
This dissertation proposes a low-cost, ergonomic and wireless solution based on MEMS
inertial sensors. This system fuses orientation data from gyroscopes, accelerometers and
magnetometers in a developed low-complexity filter, known as Complementary Filter. To
guarantee the performance of the low-cost sensors, a study was performed describing the
motion sensors disturbances and calibration solutions to mitigate these effects. On our
approach, the sensors are placed on specific places of the hand, to obtain hand and finger
pose tracking relative to a reference frame on the wrist. This solution aims to be used
in conjunction with Microsoft’s Kinect in order to complement its skeleton pose tracking
capabilities.
The proposed filter is compared to classical algorithms and the performance evaluation
compared to a well-known commercial solution. The results demonstrate that the implemen-
tation provides an acceptable accuracy and is even comparable to more complex filters. This
implementation is kept with low computational requirements, making it possible to develop
a battery-operated/wearable device where computational power is limited.
With a fully working sensor fusion solution, the developed work during this dissertation
culminated in a comfortable-to-use prototype solution and intends to provide a supportive
tool extending the set of possible interactions within a virtual reality scenario. This way, we
expect to improve a user’s experience in a virtual experience by adding the feeling of full
virtual hand ownership.

vi
Keywords: Virtual Reality, Hand-tracker, Inertial Sensors, Complementary Filter, Wear-
able Device, Virtual Hand.

Resumo
O sucesso da realidade virtual advém da sensação de realidade que esta nos proporciona,
oferecendo experiências inovadoras e imersivas. Esta sensação de imersão é ampliada quando
somos capazes de simular a presença física de um utilizador, oferecendo formas intuitivas de
interacção. Uma vez que as mãos são a nossa ferramenta natural para interagir com o mundo
exterior, o seguimento e reconhecimento de movimentos das mãos oferece uma solução de
interacção que nos é intuitiva e natural. A utilização de uma ferramenta que permita replicar
fielmente os movimentos das mãos apresenta vantagens notórias, não só em realidade virtual
mas em qualquer sistema de interacção homem-computador.
Contudo, os sistemas existentes de seguimento de mãos têm um preço elevado ou ap-
resentam restrições que limitam a quantidade de possíveis interacções no ambiente virtual.
Normalmente estes sistemas, se forem dispositivos vestíveis, apresentam formatos pouco
ergonómicos que acabam por constringir movimentos naturais das mãos, ou se forem dis-
positivos que façam o seguimento à distância, acabam por estar limitados no alcance do
seguimento.
Neste trabalho propomos uma solução de baixo custo, ergonómica e sem fios utilizando
sensores inerciais baseados em sistemas Microelectromecânicos. A nossa solução obtém da-
dos de orientação de sensores como giroscópios, acelerómetros e magnetómetros, utilizando
um filtro de fusão sensorial de baixa complexidade, conhecido como Filtro Complementar.
Para garantir o desempenho de sensores inerciais de baixo custo, é feito um estudo sobre o
ruído associado a estes sensores, de forma a compor métodos de calibração que reduzam estes
efeitos. Na nossa abordagem colocamos estes sensores em pontos específicos da mão, de
forma a obter informação da sua pose relativo a um sistema de referência local no pulso. Esta
solução tem o intuito de ser utilizada juntamente com o sensor de movimentos da Microsoft,
Kinect, e complementar as suas capacidades de seguimento do corpo.
O filtro de baixa complexidade desenvolvido é comparado com algoritmos clássicos
de fusão sensorial e o seu desempenho avaliado em relação a um produto comercial de
referência na área. Os resultados obtidos demonstram um bom comportamento por parte do
filtro, sendo até equiparáveis a filtros de maior complexidade. Com a nossa implementação é

viii
possível o desenvolvimento de plataformas onde o poder computacional é limitado, devido
aos requisitos computacionais baixos exigidos pelo filtro.
Sendo o objectivo desta solução melhorar as formas de interacção num cenário virtual,
com trabalho produzido ao longo desta dissertação, foi desenvolvido um protótipo de segui-
mento da mão confortável de usar. Com esta nova ferramenta é esperado um aumento da
sensação de imersão atingido num ambiente de realidade virtual.
Palavras-Chave: Realidade Virtual, Seguimento da Mão, Sensores Inerciais, Filtro
Complementar, Dispositivo Vestível.

Table of contents
List of figures xi
List of symbols xiii
List of acronyms xv
1 Introduction 1
1.1 Motivation and Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 State-of-the-art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Hand Tracking Devices for Consumer Electronics . . . . . . . . . . 2
1.2.2 Inertial Sensing and Related Estimation Techniques . . . . . . . . . 6
1.3 Approach and IMU Technology Pricing Inquiry . . . . . . . . . . . . . . . 8
1.4 Contributions and Dissertation structure . . . . . . . . . . . . . . . . . . . 9
2 Supporting Technologies and Background 10
2.1 Motion Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 MEMS Gyroscope . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1.1 Minimal usage calibration . . . . . . . . . . . . . . . . . 11
2.1.1.2 Extended Calibration . . . . . . . . . . . . . . . . . . . 12
2.1.2 MEMS Accelerometer . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 Robust Calibration using both Gyroscope and Accelerometer . . . . 17
2.1.4 MEMS Magnetometer . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1.4.1 Calibration - Magnetic Distortions Compensation . . . . 20
2.2 Quaternions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Orientation Estimation Techniques . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Estimating Orientation in an Inertial Navigation System . . . . . . 25
2.3.1.1 Strapdown Inertial Navigation . . . . . . . . . . . . . . . 25
2.3.1.2 Orientation from Angular Rate . . . . . . . . . . . . . . 25

x Table of contents
2.3.2 Complementary Filter . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.2.1 Explicit Complementary Filter . . . . . . . . . . . . . . 27
2.3.2.2 Explicit Complementary Filter with magnetometer . . . . 28
3 Filter Results and Discussion 31
3.1 Orientation Tracking Experiments . . . . . . . . . . . . . . . . . . . . . . 31
3.1.1 Strapdown Inertial Navigation . . . . . . . . . . . . . . . . . . . . 32
3.1.2 Complementary Filter without magnetometer . . . . . . . . . . . . 34
3.1.3 Complementary Filter with magnetometer . . . . . . . . . . . . . . 37
3.1.4 Evaluation of the Estimator Quality . . . . . . . . . . . . . . . . . 38
4 Development of a Prototype for the Hand Tracking System 41
4.1 Human Hand Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.1 MATLAB Based Animation . . . . . . . . . . . . . . . . . . . . . 44
4.2 Hardware Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.1 Proof-of-Concept Prototypes . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 Hand-Tracker Prototype . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Software Implementation - OpenAR Animation . . . . . . . . . . . . . . . 49
5 Conclusion and Future Work 51
References 52
Appendix A Mathematical Background 57
A.1 Matrix Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
A.2 Euler Angles Representation . . . . . . . . . . . . . . . . . . . . . . . . . 58
A.3 Orientation Representations Assessment . . . . . . . . . . . . . . . . . . . 59

List of figures
2.1 Gyroscope calibration comparison example. . . . . . . . . . . . . . . . . . 12
2.2 Gyroscope calibration setup. . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Accelerometer calibration comparison example. . . . . . . . . . . . . . . . 17
2.4 Calibration protocol flowchart. . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Disturbances to Earth’s magnetic field readings. . . . . . . . . . . . . . . . 21
2.6 Magnetometer calibration example. . . . . . . . . . . . . . . . . . . . . . 23
2.7 Strapdown Inertial Navigation algorithm. . . . . . . . . . . . . . . . . . . 25
2.8 INS orientation estimation block diagram. . . . . . . . . . . . . . . . . . . 26
2.9 Explicit complementary filter block diagram. . . . . . . . . . . . . . . . . 28
2.10 Complementary filter with magnetometer block diagram. . . . . . . . . . . 30
3.1 Standard INS algorithm vs. DMP output. . . . . . . . . . . . . . . . . . . 32
3.2 INS algorithm stationary drift (quaternion representation). . . . . . . . . . 33
3.3 INS algorithm stationary drift (Euler angles representation). . . . . . . . . 34
3.4 Complementary filter algorithm vs. DMP output. . . . . . . . . . . . . . . 35
3.5 Complementary filter stationary drift (quaternion representation). . . . . . . 36
3.6 Complementary filter stationary drift (Euler angles representation). . . . . . 36
3.7 Complementary Filter with and without magnetometer data (quaternion
representation). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.8 Complementary Filter with and without magnetometer data (Euler angles
representation). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.9 Complementary Filter vs. Xsens Kalman Filter. . . . . . . . . . . . . . . . 39
3.10 Performance of Complementary Filter as function of Kp. . . . . . . . . . . 40
4.1 Human hand bone structure and joints layout. . . . . . . . . . . . . . . . . 42
4.2 Hand model with virtual bone structure. . . . . . . . . . . . . . . . . . . . 43
4.3 Hand in default 3D view of the toolbox. . . . . . . . . . . . . . . . . . . . 45
4.4 Examples of impossible to perform hand configurations. . . . . . . . . . . 45

xii List of figures
4.5 Proof-of-concept Prototype. . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.6 Hand-Tracker prototype. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.7 Prototype primary board (left) and ESP8266 ESP-01 board example (right) 48
4.8 Prototype finger board. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.9 Final Hand-Tracker demonstration. . . . . . . . . . . . . . . . . . . . . . . 49
4.10 Intended tracking examples, considering a secured arm. . . . . . . . . . . . 50
4.11 Tracking examples with a different kinematic approach. . . . . . . . . . . . 50
A.1 Euler angles as described in aeronautical conventional. . . . . . . . . . . . 58

List of symbols
Cartesian Coordinate Frames
A, B Generic coordinate frames
E Earth Frame (Reference Frame)
S Sensor Frame (Body Frame)
Scalars
Ki Mahony gyroscope bias drift control gain (Integral gain)
Kp Mahony filter cutoff frequency gain (Proportional gain)
qs Quaternion scalar component
qx, qy, qz Quaternion vector components
t Step
ς Static detector operator
Vectors
a Measured acceleration
b Ideal Earth’s magnetic field
g Gravity acceleration
h Earth’s magnetic field from orientation estimate
l Generic vector
m Measured magnetic field

xiv List of symbols
q Orientation quaternion
v Noise measures
ω Measured angular velocity
ωe Angular error
Ω Data Fusion
Matrices
A Accelerometer calibration parameters
E Transformation Matrix representing an end factor
G Gyroscope calibration parameters
K Scale factor
R Rotation matrix
T Transformation Matrix
Ta, Tg Accelerometer and Gyroscope Misalignment correction
X Calibration parameters
W Average of collected data
Y Known data
Other symbols
⊗ Quaternion product
× Cross product
ˆ Normalized quantity
˜ Estimated quantity
· Derivative
¯ Average

List of acronyms
2D Two-dimensional
3D Three-dimensional
AHRS Attitude and Heading Reference System
CMC Carpometacarpal
CMOS Complementary Metal–Oxide Semiconductor
DIP Distal Interphalanges
DMP Digital Motion Processing
DoF Degrees of Freedom
DP Distal Phalanges
ECF Explicit Complementary Filter
FFC Flexible flat cable
FPS Frames per Second
GDCF Gradient Descent Complementary Filter
HMD Head-Mounted Display
HU Hardware Units
IMC Intermetacarpal
IDE Integrated development environment
IMU Inertial Measurement Unit

xvi List of acronyms
INS Inertial Navigation System
IP Interphalangeal
IR Infrared
LiPo Lithium Polymer
LED Light-Emitting Diode
LSB Least significant bit
MC Metacarpal
MCP Metacarpophalangeal
MEMS Microelectromechanical System
MP Medial Phalanges
OpenCV Open Source Computer Vision
OpenGL Open Graphics Library
PCB Printed Circuit Board
PI Proportional-Integral
PIP Proximal Interphalangeal
PP Proximal Phalanges
SDK Software Development Kit
SMT Surface-Mount Technology
TV Television
UDP User Datagram Protocol
VR Virtual Reality

Chapter 1
Introduction
1.1 Motivation and Goals
Nowadays, with the constant development and improvement in technology, new ways for
people to interact with virtual environments have been proposed. Even though virtual reality
has been around since the 1960s, it regained popularity after the release of the Oculus
Rift1 Head-Mounted Display (HMD), receiving recently a large focus from researchers and
developers alike.
Virtual reality is the term used to describe a 3D (three-dimensional), computer generated
environment which can be explored by a person, using realistic sensations to replicate the real
world. In this way, virtual reality can be defined as a realistic simulation which artificially
creates sensory experiences (including sight, touch, hearing, and, less commonly, smell)
and simulate a user’s physical presence to enable interactions with this space, resulting in
a sense of immersion that feels authentic. This sense of authenticity is further extended
when the actions made by a user are faithfully replicated in this virtual world, specially hand
movements and interactions.
Humans are skilful users of their hands, being our primary tactile sensory organ, they
are our natural tools to explore the world around us. Analogously, we use them to grasp
and manipulate objects to complete daily tasks, making them perfect candidates to use as
interfaces between the real and virtual world. The tracking and recognition of detailed hand
motions offer the possibility of building a natural and intuitive controller solution that target
not only virtual reality but any kind of human-computer interaction system.
Theoretically, hand tracking solutions can get to a point where the accuracy is such that a
user can start to feel like the avatar hand is their real hand. This illusion of body ownership
1Product details available on: www.oculus.com

2 Introduction
was studied by Ehrsson et al. [1] on the "rubber hand illusion", their experiments showed that,
by manipulating the visual perspective of a subject and also supplying visual and sensory
signals which correlate to the subject’s hand, the subject would begin to perceive the rubber
hand as their own.
With this in mind, the aim of this work is to develop a hand tracking solution to enable a
new way of interaction with 3D content (targeting virtual reality) and improve user experience.
More specifically, we intend to develop an ergonomic solution, that does not hinder the natural
hand movements, with finger motion tracking capabilities and as inexpensive as possible.
1.2 State-of-the-art
In virtual reality HMDs, the 3D environment is displayed to a user in a stereoscopic display.
The perspective which the software shows the user depends on the direction of his/her gaze,
obtained by tracking the HMD orientation. This need to know the user’s head position
resulted in the research and development of different tracker technologies. The first HMD
which included tracking capabilities was "The Sword of Democles", created in 1968 [2]. This
was still a primitive and mechanical device, to track the head movements the HMD needed
to be attached to a mechanical arm suspended from the ceiling of the laboratory, using servo
or stepping motors to acquire the measurements.
Since then many tracking devices emerged in different areas, using various technologies.
Nowadays, there are technologies such as the Vicon Motion Capture Systems2, generally used
in film-making and video game development, these make use of optical-passive techniques
where retro-reflective markers are tracked by infrared cameras, recording the movement of
objects or people. On the other hand, systems like the Optotrak Certus3 use optical-active
techniques that triangulate positions using markers that emit their own light instead, widely
used by researchers in the fields of medicine and biomechanic sciences. Another reference
example are the Xsens products, which allow for motion capture using miniature MEMS
(microelectromechanical system) based motion trackers.
1.2.1 Hand Tracking Devices for Consumer Electronics
Even though these technologies provide body motion capture, they are not really suitable to
be used for hand and finger tracking. However, there are already some available technologies
2Further details available on: www.vicon.com
3Available on: certus.ndigital.com

1.2 State-of-the-art 3
for consumers that are relevant in the context of this dissertation, providing solutions similar
to the one intended in this work:
Glove-Based Systems
Numerous glove designs were proposed over the past 30 years, typically these systems are
composed of a cloth glove made of Lycra with sensors sewn into it. A survey of glove-based
systems is presented by Dipietro et al. [3], these glove designs use various technologies but
all present the same basic concepts, to measure the finger joints bending and all use a cloth for
supporting the sensors. Earlier gloves used mechanical trackers to measure the joint bending,
whereas more recent models include non-contact position measurement devices (typically
magnetic, ultrasonic, or optical). Some typical examples of these technologies include:
hall-effect sensors in the Humanglove, commercialized by Humanware Srl; optical-fiber
flex sensors in the 5DT Data Glove, commercialized by Fifth Dimension Technologies; flex
and flexi-force sensors like the Smart Glove present in [4]; goniometric sensors like in the
PERCRO data-glove [5]; 9-DoF (degrees of freedom) orientation sensors (inertial sensors
with magnetometers) and vibro-tactile actuators like VMG data gloves4, commercialized
by Virtual Motion Labs. Besides commercial glove solutions various research gloves, that
never reached consumers, were also developed along the years. The InerTouchHand system,
which explored the use of distributed inertial sensors and vibro-tactile stimulators on the
hand, presented by J.Lobo and P.Trindade in [6] is an example of a previous research work in
Human Machine Interaction applications.
Major limitations for these gloves originated from the cloth support, which not only acts
as a constraint on the user’s hand, but also affect measurements repeatability. Not only that,
but these devices usually need tedious user-specific calibration procedures and the overall
measurement performance is influenced by the sensor support and the quality of its fit to the
user’s hand.
Game Controllers
Game controllers were not developed with the intention to replicate the human hand in a
virtual environment but they were the first kind of controllers that offered the possibility of
motion tracking and gesture identification presented to common consumers. Game controllers
like the Nintendo Wii remote, PlayStation Move or Razer Hydra allow position tracking and
navigation through multimedia content, presenting technology that can easily be used for
hand tracking.
4Available on: www.virtualmotionlabs.com

4 Introduction
The Nintendo Wii remote is equipped with a 3-axes accelerometer (providing the tilt of
the remote and the amount of force applied to it in respect to gravity) and an Infrared (IR)
camera sensor that, using a sensor bar (with 4 IR light sources) as reference point, allows to
obtain position tracking through triangulation, as well as a rough orientation estimate. An
extension was released, the Wii Remote Plus, adding 3 gyroscopes which further increased
the precision of the orientation tracking.
The PlayStation Move, developed by Sony, contains a 3-axes accelerometer, two gy-
roscopes (one with 2 axes and one with a single axis), a temperature sensor and a 3-axes
magnetometer. In combination with the PlayStation 3 Eye (a 2.0 USB camera allowing
position tracking of the controller) this system allowed for an even more precise tracking
than the Nintendo Wii remote.
The Razer Hydra5 uses a base station which emits a weak magnetic field, the motion
tracking is executed by reading this field allowing to detect the absolute position and orienta-
tion of the controllers. With a declared resolution of 1 millimetre and 1 degree when closer
than 0.5 meters from the base station, this tracker works extremely well in good conditions,
however outside this range the tracking becomes unstable.
Microsoft’s Kinect
The Kinect sensor incorporates a depth camera, a colour camera and a four-microphone
array that provide full-body 3D motion capture, facial recognition, and voice recognition
capabilities. The depth sensor consists of an IR laser projector combined with a monochrome
CMOS (complementary metal–oxide semiconductor) sensor, which captures video data in
3D. Together with the RGB camera and skeletal tracking software, the Kinect performs
formidably well in human body tracking and body gesture recognition [7]. Compared to the
entire human body, the hand is a smaller object with more complex articulations and more
easily affected by segmentation and occlusion errors, nevertheless many researches have
demonstrated the capabilities of this technology as a hand tracking solution. Particularly the
Microsoft’s Handpose system presents an algorithm that can accurately reconstruct complex
hand poses and allows for robust tracking. The system still presents some limitations and
failed cases due to the previously mentions errors, but also presents solutions where the
tracking rapidly recovers from these temporary failures [8].
5Product details available on: www.razerzone.com

Leap Motion
The leap motion controller is a small peripheral device which is designed to be placed, facing
upward, on a physical desktop or mounted onto a virtual reality headset. Leap supports hand
and finger motions as input, delivering positions in Cartesian space of predefined objects
like finger tips, pen tip, etc. It uses IR optics and cameras instead of depth sensors, and
does not cover as large an area as Microsoft’s Kinect sensor (the device only observes a
roughly hemispherical area, to a distance of about 1 meter). Leap does its motion sensing at
a fidelity unmatched by any depth camera currently available, tracking all 10 of your fingers
simultaneously to within a hundredth of a millimetre [9].
Virtual Reality Controllers
With the recent release of virtual reality (VR) HMDs for consumers, VR specific controllers
are emerging on the market. The two most relevant system at the moment are the HTC Vive
controllers, which are the official input devices for the HTC Vive HMD, and the unreleased
Oculus Touch for the Oculus Rift.
HTC Vive controllers use the same tracking system as the Vive HMD6, this system is
called Lighthouse. Lighthouse is defined as a laser-based inside-out positional tracking
system, the rotational tracking is achieved with Inertial Measurement Units (IMUs), while
positional tracking is accomplish with two lighthouse Base Stations. These Base Stations
work as reference points, constantly flooding the room with IR light, the controllers are
covered with photo-sensors that recognize this IR light and calculate the appropriate position.
This system allows freedom of movement in spaces up to 4.6 meters by 4.6 meters and is
optimized for sub-millimetre positional tracking with latency counted in single milliseconds.
The main limitation of this technology is that, since the controllers require their users to
firmly grip them the whole time they are using them, it is not possible to perform any gestures
that involve fingers and thumbs.
Oculus Touch7 achieves high precision, low latency and 6 DoF tracking through the same
Constellation tracking system as the Rift headset, defined as an optical-based outside-in
positional tracking system. Similar to Lighthouse, rotational tracking is achieved with IMUs,
whereas positional tracking is accomplish with an external camera sensor. Tiny LED (light-
emitting diode) markers are placed on the controllers bodies and the camera sensor is able to
recognize these markers, tracking their positions. Additionally, this system claims to have
hand presence and gesture sensing, the grip of the controller feels natural (similar to shaking
6HTC and Valve virtual reality systems available at: www.htcvive.com/eu/
7Product details available at: www3.oculus.com/en-us/touch/

6 Introduction
someone’s hand) and with a matrix of sensors mounted onto the device, it allows to keep
track of some fingers and detect hand gestures.
1.2.2 Inertial Sensing and Related Estimation Techniques
Having taken into consideration all these technologies, as well as their advantages and
handicaps, in this work we use inertial and magnetic field sensors as the main tracking
technology. This choice was taken in order to maintain the balance between the requirements
of the hand tracker functionalities and the need for it to be a comfortable-to-use device.
Nowadays, these types of sensors are embedded in very small packages (IMUs) allowing
for very simplistic and ergonomic designs for any kind of product. Also, taking a look at
the state of the art literature in section 1.2, technologies like the ones used for the gloves
systems (for example, flex sensors or goniometric sensors) restrain the user’s movement
and technologies that rely on line of sight (for example, depth cameras or IR laser) present
limitations in their range of action and possible occlusion between the fingers.
This approach does not come without its drawbacks, IMUs offer a precise orientation
tracking but lack the stability to provide accurate position tracking for more than a few
seconds [10]. Given the context of research in which this dissertation is integrated, many
of our interactive scenarios already use the Kinect sensor in order to track the users body.
In this way, we propose to use the body tracking capabilities of the Kinect as an external
auxiliary system to obtain the position estimation of the hand, specifically the kinematic
joint8 associated with the wrist.
In order to mitigate sensor errors and obtain a correct orientation estimate, the sensors
data has to be fused through an algorithm, usually referred as a filter. In this regard, we
discuss three major approaches developed in the last years, Stochastic Filters (commonly
Kalman Filters), Particle Filters and Complementary Filters.
Kalman Filters
The Kalman filter is one of the most celebrated and popular data fusion algorithms in the
field of information processing. Due to its applicability to a wide range of fields, extensions
and generalizations to the method have also been developed allowing its usage for non-linear
problems. Since orientation determination is intrinsically a non-linear problem, Kalman
filtering based estimation techniques are usually employed in this regard and are considered
a de-facto standard. Most common implementations are the Extended Kalman Filter [11]
and Unscented Kalman Filter [12].
8Further details on Kinematics presented is in section 4.1)

The problem associated with Kalman based algorithms is the demand for the computa-
tional complexity, due to intensive matrix operations and Jacobian matrices computation,
which may be computationally expensive for some applications [13]. Still, few filters can
accomplish the same levels of accuracy, making these implementations the preferred solution
for professional use in motion tracking applications. In the context of this work, the MTi
AHRS (Attitude and Heading Reference System)9, employing a proprietary XSens Kalman
filter, was used as reference for results validation.
Particle Filters
Particle Filters are recursive implementations of Monte Carlo based statistical signal pro-
cessing [14]. Its methodology consists in estimating the internal states in dynamical systems
when partial observations are made, and random perturbations are present in the sensors as
well as in the dynamical system. The particle filters are seen as a serious alternative for real-
time applications classically approached by model-based Kalman filter techniques. These
methods have the great advantage of not being subject to any linear or Gaussian constrains on
the model, and they also have engaging convergence properties. Some works that use these
filters can be easily found in the literature, for instance [15][16] present experiments that
show a clear improvement in performance compared to the conventional Extended Kalman
Filter. However, these filters employed in the regard of orientation estimation are associated
with an even more demanding computational burden than the Kalman Filter[17].
Complementary Filters
Complementary Filters work in the frequency domain, where some signals pass through
a low-pass filter and others signals through its complementary high-pass filter, combining
both signals in the end. The search for simple and still effective filtering algorithm lead to
the development of these constant gain based complimentary algorithms. These techniques
have been shown to offer efficient performance with little computational cost, the drawback
is that, complementary filters do not contemplate adaptability, making parameters like the
sensor error lost during the filter process. However, filters such as the explicit complementary
filter (ECF) suggested by Mahony et al. [18] and gradient descent based complementary
filter (GDCF) authored by Madgwick et al. [19] have been shown to implement ways to
dynamically adapt the filter, to estimate sensors bias, and respond to readings deviations.
Both ECF and GDCF are effective and novel approaches in this regard, with the power of
adjustable gain, these techniques find places in most of the real world applications. Research
9Commercialized by Xsens, further details on: www.xsens.com

8 Introduction
studies [20] have demonstrated that the evaluation of these filter results in identical outcome,
however, ECF has a bit edge over GDCF with slightly higher accuracy and partly because
of the two adjustable gains resulting in extra choices (GDCF only has a single adjustable
parameter). Moreover, ECF is less sensitive to variation in filter gain in comparison to GDCF.
1.3 Approach and IMU Technology Pricing Inquiry
Even though the Extended Kalman filter has become the accepted basis for the majority of
orientation algorithms, being its widespread use a testament to its accuracy and effectiveness,
it can be complicated to implement and may demand a large computational load. In embedded
systems where portability is critical, the challenges presented by Kalman-based solutions
provide a clear motivation for alternative approaches. Particle filters do not provide a
viable solution and can in fact be even more demanding. In order to keep computational
requirements as low as possible while maximizing available resources, in this work an
adaptation of the ECF is implemented and tested.
Concerning existing IMU hardware solutions, their cost varies significantly between
manufacturers, this includes solutions with price range close to 4000C and others not
surpassing 10C. This discrepancy is mostly associated to the IMU performance each
manufacture guarantees, besides the obvious additional features each individual IMU solution
has. Whereas some IMU solutions arrive at the consumer directly after leaving the assembly
procedure, others go through rigorous calibration and performance assessment procedures.
As such, several hardware IMU solutions were considered in the context of this work, the
following table 1.1 presents some of these IMU technologies and their associated price range.
Model Manufacturer Price Range (C)
UM7 CH Robotics 116 - 134
AHRS-I/II Inertial Labs 2676 - 3122
VN-100 Vectonav Technologies 446 - 713
MTi 1/10/100 series Xsens 129 - 3980
STM32F3DISCOVERY ST Semiconductors 10 - 13
x-IMU x-io 285 - 320
Razor IMU Sparkfun 57 - 67
MPU-9250 Invensense 4 - 6
Table 1.1 IMU models price range comparison.

1.4 Contributions and Dissertation structure 9
All the aforementioned IMU models are solutions based on MEMS technologies that
have at least a 3-axis gyroscope, a 3-axis accelerometer and a 3-axis magnetometer.
The UM7, presented by CH Robotics [21], the AHRS-I/II, developed by Inertial Labs
[22], the VN-100, produced by Vectonav Technologies [23], and the MTi 1/10/100 series,
developed by Xsens [24], are AHRS enclosed motion tracking solutions directed at industrial
use, allowing easy integration for applications that suffer from board stresses and hazards
due to harsh environmental conditions. The STM32F3DISCOVERY developed by ST
Semiconductors [25] and the x-IMU, designed by x-io [26], are embedded board solutions
containing on-board microcontrollers, sensors, algorithms, debug tools and configurable
communication ports making these models ideal standalone solutions. There also exist small
evaluation/breakout boards for individual IC sensors, the Razor IMU, distributed by Sparkfun
[27], is such an example. Considering the application at hand, these IC sensor solutions
bring various advantages, being very low cost and small in size. The MPU-9250 IC, by
Invensense [28] combines all the intended sensors into only one component and presents an
unrivalled price. The choice of such an inexpensive sensor provides the overall hand tracking
solution discussed in this work with a very promising economical potential when compared
to available commercial solutions.
1.4 Contributions and Dissertation structure
The Mobile Robotics Laboratory, present in Institute of Systems and Robotics—University of
Coimbra, promotes constant research and development in multidisciplinary areas, including
virtual reality. More recently, research in the use of virtual reality as an immersive interface
exploring this technology potential in many contexts. The Hand-Tracker developed in this
dissertation intends to provide a supportive tool to further extend the available experimental
scenarios for this research and the sense of immersion these offer. In this way, contributing
to previous research in various virtual reality scenarios: training simulators [29]; remote
operation of robots [30][31]; support in psychological therapies [32][33].
The outline of this dissertation is organized as follows: Chapter 2 includes a characteriza-
tion of the motion sensors used, their associated disturbances and calibration solutions to
mitigate these effects, introduces quaternion representation and presents the implemented
sensor fusion filter for orientation estimation; Chapter 3 evaluates the performance of the
implemented fusion filter algorithm (ECF); Chapter 4 describes an overview of the kine-
matic constrains, depicts the developed Hand-Tracker hardware and illustrates the software
implementation that validates the overall system; finally, in Chapter 5 we reflect upon the
completion of our objectives and on possible future work.

Chapter 2
Supporting Technologies and
Background
This chapter presents the relevant supporting technologies, as well as the appropriate back-
ground about the implemented orientation filter. In the first section the inertial and magnetic
field sensors technologies are introduced together with their respective calibration require-
ments. The following section presents a brief review of the orientation representation using
quaternions, in order to allow a better understanding of the topics ahead. The final sec-
tion analyses orientation estimation techniques, emphasizing the studied low-complexity
complementary filter.
2.1 Motion Sensors
Motion tracking sensors have had a wide range of applications, mostly industrial such as
in the automotive or aircraft industry, however, in recent years these sensors received a
high miniaturization and are rapidly becoming a common technology in many consumer
electronic devices. Consumers are now able to interact in intuitive ways using motions
as input commands with their smartphones, gaming consoles, tablets and even smart TVs
(television). This was made possible due to the introduction of MEMS technology: we
now have small chips that combine a 3-axis gyroscope, a 3-axis accelerometer and 3-axis
magnetometer all in the same package. These chips, referred to as IMUs, are extremely
low-cost, lightweight and compact (reaching sizes of 3x3x1mm), but have some flaws, the
measurements they give are relatively noisy, can have offset bias, different scale factors,
non-orthogonality between axes and, due to the fabrication process, the characteristics of
individual sensors may be altered if not properly handled in the soldering process. These

2.1 Motion Sensors 11
problems led to the development of highly rigorous calibration and assembly procedures by
manufacturers, providing IMU solutions which are extremely accurate but suffer from a huge
cost increase. According to the application and precision needed, simple calibration methods
may suffice providing an affordable and reliable solution. In this section we analyse these
three types of sensors as well as their respective calibration procedures.
2.1.1 MEMS Gyroscope
MEMS gyroscopes are sensors capable of measuring the rate of rotation of a body. Based
upon simple mechanical principles, these sensors exploit the Coriolis effect [34] of a vibrating
structure. When a vibrating structure is rotated, a secondary vibration is induced from which
the angular velocity can be calculated [35].
The disadvantage of using MEMS technology in gyroscopes is that it is far less accurate
than mechanical gyroscopes, when handling these sensors there is a need to examine their
error characteristics and the effect they have on the integrated orientation signal, in order to
apply a proper calibration procedure. Typically, they present a non-zero offset at rest, in other
words, a constant bias is present when the gyroscope is not undergoing any rotation. When
integrated, this error causes an angular error which grows linearly with time. Additionally
there occurs an offset drift over time, which is caused collectively by non accurate scaling,
sensor axis misalignments, cross-axis sensitivities and even temperature effects. Although
fusion algorithms (using gyroscopes and other sensors) could estimate this drift and correct
it in real-time, these errors should be minimized to obtain higher accuracy. An appropriate
calibration provides all the parameters needed to estimate and correct these errors.
2.1.1.1 Minimal usage calibration
In order to obtain meaningful information from inexpensive MEMS gyroscopes we assume a
model for the gyroscope in its own reference frame, where the true angular rate one wants to
measure, Sω, is given by [36]:
S
ω = Kg.(S
ωraw −S
ω0) (2.1)
• Sω - Real angular velocity given in ◦/s;
• Kg - Scale factor (or sensitivity) given in (◦/s)/HU (hardware units);
• Sωraw - Raw readings of the gyroscope given in HU;
• Sω0 - Average raw readings at rest given in HU.

12 Supporting Technologies and Background
This simple calibration procedure allows to compensate for bias instability, using the first
few readings of the gyroscope, at least 50 to 100 samples, to subtract from the subsequent
data. This has to be done with the sensor at rest, readings with the gyroscope in motion
must be discarded. ω0 is obtained by calculating the readings average for each gyroscope
axis. The gyroscope scale factor, which converts hardware units into angular velocity units,
differs with each sensor, is given by the manufacturer and should be applied accordingly.
This procedure takes little time (varies with chosen sampling rate for the sensor) and should
occur after the gyroscope is powered on, so that the subsequent data becomes calibrated. The
following figure represents an example of the effect of correction due to calibration with the
available sensor board, for comparison purposes the scale factor Kg was included with the
raw data.
Fig. 2.1 Gyroscope calibration comparison example.
2.1.1.2 Extended Calibration
Further extending the previous calibration, after installing the sensor on the PCB (printed
circuit board) and the PCB on the actual body of the device we want, there may exist axes

misalignment between the device body axes, the PCB and the actual sensor axes. If any
misalignment is present, the angular velocity that is applied to one axis of the device will
have projection on the other two axes of the device axes. Therefore, to correct misalignment
an extended calibration is required to use, but it is more difficult to implement, requiring the
use of an external setup while knowing the real angular velocity during calibration. To find
the misalignment matrix to compensate the gyroscope measurements, the model presented in
equation (2.1) is extended, becoming,
S
ω = TgKg(S
ωraw −S
ω0) (2.2)
where Tg is the matrix that defines the misalignment between the sensor axes and the
body axes of the device. Unfolding equation (2.2) to equation (2.3):



ωx
ωy
ωz


 =



G11 G12 G13
G21 G22 G23
G31 G32 G33


·



ωrx −G10
ωry −G20
ωrz −G30


 (2.3)
The values of Gmm correspond to the calibration parameters needed to adjust the output
data from the gyroscope. G10, G20 and G30 are calculated, as in the previous method, by
averaging samples with the sensor at rest. The remaining parameters may be determined by
using a single-axis rate table or a step-motor spin table as shown in figure 2.2 [36].
Fig. 2.2 Gyroscope calibration setup.
The objective of this setup is to know and control the real angular velocity while reading
the angular velocity values from the gyroscope. Measurements should be done for each
axis independently at two different speeds and in opposite directions. In order to apply a
least squares method to determine the calibration parameters, we can construct the known

applied angular velocity data into a matrix and the average angular velocity obtained from
the gyroscops’s raw data into another matrix. This way we are able to construct the following
equation 2.4:
Yω = Wω ·Xω (2.4)
• Yω - Known angular rate data in a 12x3 matrix;
• Wω - Average of the collected data from the gyroscope;
• Xω - Calibration matrix that needs to be determined.
Considering for example 50 °/s and 100 °/s as our two speeds, we can represent the same
equation (2.4) as:

























50 0 0
−50 0 0
100 0 0
−100 0 0
0 50 0
0 −50 0
0 100 0
0 −100 0
0 0 50
0 0 −50
0 0 100
0 0 −100

























=

























ωrx1 ωry1 ωrz1
ωrx2 ωry2 ωrz2
ωrx3 ωry3 ωrz3
ωrx4 ωry4 ωrz4
ωrx5 ωry5 ωrz5
ωrx6 ωrz6 ωrz6
ωrx7 ωry7 ωrz8
ωrx8 ωry8 ωrz8
ωrx9 ωry9 ωrz9
ωrx10 ωry10 ωrz10
ωrx11 ωry11 ωrz11
ωrx12 ωrz12 ωrz12

























·



G11 G12 G13
G21 G22 G23
G31 G32 G33


 (2.5)
Using the pseudo-inverse we can obtain the intended parameters for calibration.
Xω = WT
ω .Wω
−1
.W−1
ω .Yω (2.6)

2.1.2 MEMS Accelerometer
An accelerometer is an electromechanical device that measures acceleration. These devices
are able to sense constant accelerations, like the force of gravity, as well as dynamic accelera-
tions, caused by moving or vibrating the accelerometer. A typical MEMS accelerometer is
composed of a movable proof mass with plates that is attached through a mechanical suspen-
sion system to a reference frame. These fixed and movable plates form various capacitors,
when the geometry of a capacitor changes the variation in capacitance is detected. By using
the capacitance difference we are able to measure the deflection of proof mass and therefore,
with proper signal conditioning, translate it to acceleration [37].
These sensors are characterized by very accurate measurements (considering the pertur-
bations associated with MEMS technology on other sensors), still for certain applications,
calibration is needed to remove systematic measurement bias, which vary both with tempera-
ture and in time.
2.1.2.1 Calibration
Similarly to the gyroscope sensor there are calibrations for the accelerometer that can be
done with minimal human intervention, simply by ensuring a rest position of the sensor (no
external acceleration besides gravity). Like in the gyroscope calibration, assuming a model
for the accelerometer in its own reference frame, the acceleration, Sa, one wants to measure,
is given by the equation [38]:
S
a = TaKa(S
araw −S
a0) (2.7)
• Sa - Acceleration given in g (1g = 9.81m/s2);
• Ta - Misalignment matrix;
• Ka - Scale factor (or sensitivity) given in g/HU;
• Saraw - Raw readings of the accelerometer given in HU;
• Sa0 - Average raw readings at rest given in HU.
Unfolding equation 2.7 results in:



ax
ay
az


 =



A11 A12 A13
A21 A22 A23
A31 A32 A33


.



arx −A10
ary −A20
arz −A30


 (2.8)
The values of Amm correspond to the estimated system model parameters, resulting
from calibration, needed to adjust the output data from the accelerometer. The method

used for calibration consists in placing the sensor at six stationary positions, in all three
orthogonal directions, while collecting the raw values in order to calculate the calibration
matrix. Equation 2.8 can be written as:
ax ay az = arx ary arz −1 .





A11 A12 A13
A21 A22 A23
A31 A32 A33
A10 A20 A30





(2.9)
Labelling the above matrices:
Ya = Wa.Xa (2.10)
• Ya - Known normalized gravity vector;
• Wa - Collected data from the 6 stationary positions;
• Xa - Calibration matrix that needs to be determined.
Considering the ideal output values for the 6 calibration positions the following equation
system is obtained:










0 0 1
0 0 −1
0 1 0
0 −1 0
1 0 0
−1 0 0










=










arx1 ary1 arz1 −1
arx2 ary2 arz2 −1
arx3 ary3 arz3 −1
arx4 ary4 arz4 −1
arx5 ary5 arz5 −1
arx6 arz6 arz6 −1










.





A11 A12 A13
A21 A22 A23
A31 A32 A33
A10 A20 A30





(2.11)
Where arxn,aryn and arzn, (n = 1, 2, 3, 4, 5, 6), correspond to the readings average of each
axis, in each of the six positions.
To obtain the intended calibration matrix, the calibration parameter Xa, can be determined
by the least square method as:
Xa = WT
a .Wa
−1
.W−1
a .Ya (2.12)

The following figure represents an example of calibration with the available sensor board,
for comparison purposes the scale factor Ka was included with the raw data.
Fig. 2.3 Accelerometer calibration comparison example.
2.1.3 Robust Calibration using both Gyroscope and Accelerometer
Alberto Pretto and Giorgio Grisetti [39] propose a calibration method for IMUs without the
use of any external equipment, providing calibration parameters for both the gyroscope and
accelerometer. Using features from both sensors they are able to minimize existing errors
and estimate calibration parameters between the sensors, such as misalignment and scaling
factors as well as sensor biases.
Their procedure for data acquisition employs placing the IMU in multiple static positions
with small intervals of time in-between. Starting with a relatively short period of time with
the sensor at rest (for example 30 seconds), the user should move the IMU in different
positions (maintaining the sensor still in those positions for a fixed time, between 1 to 4

seconds) as many times as needed in order to obtain at least 36 distinct static orientations.
This protocol can be executed by hand and is described in figure 2.4.
Fig. 2.4 Calibration protocol flowchart.
This calibration explores previous studies on accelerometers calibrations[40] which
consider that, in a static position, the norms of the measured accelerations is equal to the
magnitudes of the gravity plus multiple error factors and, with a set of multiple static attitudes,
these factors can be estimated through minimization.
For this calibration, misalignments between the accelerometer and gyroscope frames
(due to assembly inaccuracy) are considered and compensated by means of two matrices, Ta
and Tg respectively. The accelerometer frame is used as frame of reference for the gyroscope
misalignment matrix. As in previous calibration methods the scaling matrices Ka and Kg, and
the bias vectors Sa0 and Sω0 are estimated. The complete error models for the sensors are:
S
a = TaKa(S
araw −S
a0 −S
va) (2.13)
S
ω = TgKg(S
ωraw −S
ω0 −S
vg) (2.14)
where Sva and Svg are the accelerometer measurement noise and the gyroscope measure-
ment noise, respectively.

Classifying correctly static and motion intervals heavily influences the accuracy of this
calibration, since the accelerometer only considers static intervals for calibration whereas, for
the gyroscope, motion intervals are also included. A variance based static detector operator
using the accelerometer signals is proposed. For each accelerometer sample (ax,ay,az) at
time t, the magnitude of the variance is computed as:
ςt = [vartw(ax)]2 +[vartw(ay)]2 +[vartw(az)]2 (2.15)
where vartw(a) is an operator that computes the variance of the accelerometer signal in a
time interval of length tw seconds centered in time t. Using this operator, a static interval is
considered if the variance magnitude is lower than a certain threshold (computed during the
initialization period).
To estimate the accelerometers parameters a cost function is used:
L(θa) =
M
∑
k=1
(||g||2
−||h(S
ak,θa)||2
)2
(2.16)
where M is the number of static intervals, θa is the vector containing the unknown
parameters, ||g|| is the actual magnitude of the local gravity vector (can easily be recovered
from specific public tables) and h is a function that corrects the readings applying the
current parameter vector. To minimize equation 2.16 the Levenberg-Marquardt algorithm is
employed [41].
With the accelerometer calibrated in this way, and using the same set of multiple at-
titudes, the gyroscope is calibrated using the corrected gravity vector (obtained from the
accelerometer) as a reference between the different orientations. The angular velocities from
the gyroscope are integrated to estimate the gravity vector orientation, and by minimizing
the errors between the two gravity estimates it is possible to estimate the wanted calibration
parameters, θg. In this case, the cost function becomes:
L(θg) =
M
∑
k=2
||ua,k −ug,k||2
(2.17)
where ua,k is the acceleration versor measured averaging in a temporal window the
calibrated accelerometer readings in the k-th static interval and ug,k is the acceleration versor
computed integrating the angular velocities between the k −1-th and the k-th static intervals,
as described in [42]. Once again the minimization algorithm is employed to minimize
equation 2.17.
This calibration procedure takes advantage of the combination of gyroscopes and ac-
celerometers on IMUs, providing a reliable and more robust calibration solution.

2.1.4 MEMS Magnetometer
The most common MEMS magnetometers are Hall-effect transducers with a magnetic
concentrator. Ideally, a magnetometer would provide information about the vector pointing
North, nevertheless the earth magnetic field does not point North, as a matter of fact it is not
even constant over time (changing over the years). Depending on where we are on the planet,
the magnitude of the field over the surface of the Earth varies as well as the declination angle
between the magnetic North and the geographic North. Be that as it may, these characteristics
of the Earth’s magnetic field do not represent a problem for indoor navigation, as the objective
of using a magnetometer is to support and prevent deviations on the navigation provided by
other sensors. Problems in indoor navigation arise on the measurements of the local magnetic
field, which is usually composed by the sum of multiple magnetic fields, that exist on the
local frame of the sensor, plus the Earth’s magnetic field.
Furthermore, the measurements of the magnetic field obtained with low cost sensors are
corrupted by several errors including sensor fabrication issues and the magnetic deviations
induced by the host platform.
2.1.4.1 Calibration - Magnetic Distortions Compensation
Proper calibration of the magnetometers is required to achieve high accuracy measurements,
generally performed by means of experimentation and calibration parameters estimation
techniques. Several procedures and algorithms have been proposed to perform the calibration
[43]. However their performances often rely on assumptions that constrain the type of the
errors in the measurements and ignore some critical components.
We propose a simplified model of calibration to deal only with unwanted or interfering
magnetic fields. This way we do not take into consideration some characteristic on the error
modeling of magnetometer readings, a characteristic that should be factory calibrated, such
as the corruption of the output of magnetometers by wideband measurement noise, stochastic
biases due to sensor imperfections or installation errors.
The unwanted or interfering magnetic fields [44] can be classified into two distinct groups.
The first group consists of constant or slowly time-varying fields generated by ferromagnetic
structural materials in the proximity of the magnetometers. The field measurement errors
resulting from such interferences are referred to as hard iron biases. The second group of
interfering magnetic fields result from materials that generate their own magnetic field in
response to an externally applied field. This generated field is affected by both the magnitude
and direction of the externally applied magnetic field. Such materials are called soft irons
and the error they generate is referred to as a soft iron bias. In summary, although these

disturbances are not completely decoupled, it is possible to somewhat relate the hard iron
distortions with the device and the soft iron distortions with the environment where the device
is located.
The calibration procedure implies the rotation of the sensor platform in complete circles
around it self, in a way that allows us to gather many points of an ellipsoid. Figure 2.5 shows
a three-dimensional (3D) representation of the effects in the magnetic field measurements,
for these types of distortions. The combination of both distortions in 3D cause the expected
perfect and origin-located sphere to be distorted into a displaced ellipsoid.
Fig. 2.5 Disturbances to Earth’s magnetic field readings.
Soft and hard-iron distortions are compensated using a simple method, taking into
consideration the following model of the sensor:
S
m = RmKm(S
mraw −S
m0) (2.18)
• Sm - Corrected measurement of the magnetic field;
• Smraw - Raw data from magnetometer;
• Rm - Orientation of axes correction;
• Km - Parameters that compensate soft-iron effects.
• Sm0 - Parameters that compensate hard-iron effects.
Where Rm is a rotation matrix used to align the axes of the magnetometer regarding the
axes of both the gyroscope and accelerometer, most IMUs contain different orientation for
the sensitivity axes of the magnetometer.
Compensating for hard-iron distortion is straightforward, recording some of the magne-
tometer data as the sensor is moved (for example in a figure eight pattern) and keep track of

the minimum and maximum field measured in each of the six principal directions. Once the
minimum and maximum values along the three axes are known, the average can be subtracted
from the subsequent data which amounts to re-centering the response surface on the origin.
S
m0 =



max(mx)+min(mx)
2
max(my)+min(my)
2
max(mz)+min(mz)
2


 (2.19)
Compensating for soft-iron distortion is more computationally intensive than compen-
sating for hard-iron distortion, and it may be more effective from a cost and efficiency
perspective, particularly if designing or implementing an embedded system, to eliminate the
soft-iron material(s) from the proximity of the sensor.
Still, taking the minimum and maximum values already computed it is possible to use
them to rescale the magnetometer data to equalize the response along the three measurement
axes. A scale factor can be calculated by taking the ratio of the average (max−min) along
each axis and the average of all three axes. This means that an axis where the (max−min) is
large has its magnetic field reduced and an axis that under-measures the field with respect
to the other axes has its magnetic field values increased. This is just a simple orthogonal
rescaling allowing some additional correction for scale bias.
α =



max(mx)−min(mx)
2
max(my)−min(my)
2
max(mz)−min(mz)
2


 (2.20)
Km =
¯α
α
(2.21)
Figure 2.6 shows an example of the calibration of the magnetometer. As explained
previously, the data is collected with rotational movements of the magnetometer in such a
way, that it allows covering a large number of points on a sphere. The values of the raw sensor
are 3D plotted and approximated to an ellipsoid (red in the figure). The expected perfect
and origin-located sphere is also plotted to use as reference (green in figure), following the
procedure described previously, the calibrated data readings (blue in figure) will tend to that
sphere.

2.2 Quaternions 23
Fig. 2.6 Magnetometer calibration example.
2.2 Quaternions
There are various mathematical formulations to represent the orientation of a rigid body. In
this work the quaternion representation is used. A quaternion, generally represented by q,
is a four-element vector composed of one real element and three complex elements. When
normalized, ˆq = 1, a quaternion can be used to encode any rotation in a 3D coordinate system.
Considering a rigid body in a coordinate frame (B) relatively to any other generic coordinate
frame (A), a quaternion B
Aq can be used to represent the orientation of the body as in equation
2.22.
B
Aq = qs qx qy qz (2.22)
The elements qx, qy and qz of the quaternion can be thought of as a vector about which
rotation should be performed. The element qs represents a scalar component that specifies
the amount of rotation that should be performed about the vector part. Specifically, if θ is
the angle of rotation and the vector l = [lx ly lz] is a unit vector representing the axes of

rotation, equation 2.22 can be written as:
B
Aq = cos θ
2 lx ·sin θ
2 ly ·sin θ
2 lz ·sin θ
2
(2.23)
This definition does not need to be used explicitly, but it is included here to provide an
intuitive description of the quaternion representation.
The quaternions also have important properties that simplify calculation. As mentioned
previously a quaternion only represents a rotation if it is normalized, the normalization
procedure is presented in equation 2.24.
ˆq =
q
||q||
=
q
q2
s +q2
x +q2
y +q2
z
(2.24)
As long as ||q|| = 1, the inverse quaternion is equivalent to the quaternion conjugate, a
property which can be used to reverse rotations or swap between frames.
q∗
= qs −qx −qy −qz (2.25)
B
A ˆq−1
= B
A ˆq∗
= A
B ˆq (2.26)
Another important property, that can be used to compute successive rotations, is the
quaternion multiplication, presented as ⊗ in equation 2.27. This is a non-commutative
operation, that is q⊗ p ̸= p⊗q.
q⊗ p =





qs ps −qx px −qy py −qz pz
qs px +qx ps +qy pz −qz py
qs py −qx pz +qy ps +qz px
qs pz +qx py −qy px +qz ps





(2.27)
Also, a vector can be rotated, as in equation 2.28, where Al and Bl are the same vector
represented in two different frames.
A
l = B
A ˆq⊗B
l ⊗B
A ˆq∗
(2.28)
The choice of orientation representation depends on the application in question [45],
additional information regarding the other representations, as well as advantages and disad-
vantages of each one that lead to the choice of quaternion representation over the others can
be found in Appendix A.

2.3 Orientation Estimation Techniques 25
2.3 Orientation Estimation Techniques
2.3.1 Estimating Orientation in an Inertial Navigation System
2.3.1.1 Strapdown Inertial Navigation
Inertial navigation is a self-contained navigation technique in which measurements provided
by accelerometers and gyroscopes are used to estimate the position and orientation of an
object relative to a known starting point, orientation and velocity. IMUs used in this kind of
systems typically use sensors capable of obtaining measurements in a single direction and
are mounted with their sensitive axes mutually perpendicular, respectively containing three
orthogonal rate-gyroscopes and three orthogonal accelerometers.
In strapdown systems the inertial sensors are mounted rigidly onto the device, and
therefore output quantities measured in the body frame rather than the global frame. To
keep track of orientation, the signals from the rate-gyroscopes are integrated. To estimate
position the three accelerometer signals are resolved into global coordinates using the
known orientation, as determined by the integration of the gyroscopes signals. The global
acceleration signals are then integrated as in the stable platform algorithm. This procedure is
shown in figure 2.7 [46].
Fig. 2.7 Strapdown Inertial Navigation algorithm.
2.3.1.2 Orientation from Angular Rate
In an Inertial Navigation System (INS) the orientation, or attitude, is tracked by integrating
the angular velocity signal Sω = [ωx ωy ωz] obtained from the system’s rate-gyroscopes.
An IMU provides samples of the angular velocity at a fixed frequency rather than providing
a continuous signal. An integration scheme is needed to integrate the sampled signal, for this

application which has a short timespan and low accuracy, the rectangular rule is presented as
a sufficient solution.
Using the quaternion attitude representation, for a single period [t −1,t] the solution to
obtain the quaternion derivative that describes the orientation change rate of the sensor frame
(S) relative to the Earth frame (E), S
E ˙qω,t, can be written as [47]:
S
E ˙qω,t =
1
2
S
E ˜qt−1 ⊗S
pt (2.29)
where:
S
p = [0 ωx ωy ωz] (2.30)
Let the period between successive angular velocity samples be δt. The orientation
estimation S
E ˜qω,t is yielded by integrating the quaternion derivative.
S
E ˜qt = S
E ˜qt−1 +S
E ˙qω,t ·δt (2.31)
Equation 2.31 represents the attitude update equation used to update S
E ˜qt as each new sam-
ple becomes available. This orientation estimate is always relative to the starting orientation.
The block diagram for this algorithm is depicted in figure 2.8.
Fig. 2.8 INS orientation estimation block diagram.
Since the angular velocity signals obtained from the gyroscopes are integrated by the INS
attitude algorithm, errors in the gyroscope signal will propagate through to the calculated
orientation. Such errors lead to the accumulation of an additional drift in the integrated signal.
This drift is observable while the device is turning, with its magnitude being proportional to
the rate and duration of the motions. This issue leads to the development of a more robust
solution to keep track of the appropriate orientation signal.

2.3.2 Complementary Filter
This sensor fusion algorithm combines the best attributes of each sensor type, and tries to
mitigate the characteristics that introduce error in the estimates. Basically, it provides a
robust trade-off between a good short term precision given by the gyroscopic integration
and reliable long term accuracy provided by other sensors. Taking into consideration the
use of a PI (proportional-integral) controller to provide the feedback of the angular error
together with the quaternion representation of the data, this algorithm manages to have low
computational needs without compromising efficiency.
2.3.2.1 Explicit Complementary Filter
This complementary filter fuses accelerometer and gyroscope data for orientation estimation
such that low-pass filtering is applied on accelerometer data and high-pass filtering on
gyroscope output [18]. On this filter we still want to compute the quaternion derivative, S
E ˙qω,t,
in equation 2.29:
S
E ˙qω,t =
1
2
S
E ˜qt−1 ⊗S
pt (2.29 revisited)
But this time considering S pt as:
S
pt = [0,S
Ωt] (2.32)
where, SΩt represents the data fusion, here the gyroscope data is debiased by applying
the feedback error. The first step for implementing the explicit complementary algorithm is
to measure inertial direction S ˆat (by normalizing the accelerometer data). Then, estimate the
direction of gravity from the quaternion output using
S
ˆgt = S
E ˜q∗
t−1 ⊗E
ˆg⊗S
E ˜qt−1 (2.33)
This way we can estimate the angular error, being computed by cross multiplying the
normalized accelerometer data and estimated direction of gravity as
S
ωe,t = S
ˆat ×S
ˆgt (2.34)
From here we apply the data fusion in equation 2.35 through the use of a PI controller
(this way we account not only, for the error at each time t, but also consider the history of the
error).

S
Ωt = S
ωt +Kp ·S
ωe,t +Ki · S
ωe,t (2.35)
for suitable values of KP and Ki [48]. To compute the rate of change of quaternion
the same principal from the INS orientation tracking algorithm is used. Following the
same development, for a single period [t −1,t], we can obtain S
E ˙qω,t in equation 2.29. The
quaternion output is once again obtained by integrating the quaternion derivative:
S
E ˜qt = S
E ˜qt−1 +S
E ˙qω,t ·δt (2.31 revisited)
Finally, for the quaternion to represent rotation correctly it needs to be normalized before
the next iteration in the algorithm:
S
E ˆqt =
S
E ˜qt
||S
E ˜qt||
(2.36)
The block diagram for this algorithm is depicted in figure 2.9.
Fig. 2.9 Explicit complementary filter block diagram.
2.3.2.2 Explicit Complementary Filter with magnetometer
This implementation adds the data of the magnetometer, meaning that the complementary
filter will combine the low frequency signals from accelerometer and magnetometer with the
high frequency signals from the gyroscope [49].
The angular error, Sωe,t, is relative to the difference between the measured orientation
and the predicted one. It is obtained with the cross product between the orientation given by
magnetometer measures,S ˆmt and the predicted one, S ˆbt, plus the gravitational field direction
measured by the accelerometer, S ˆbt, and the predicted one, S ˆgt.

S
ωe,t = S
ˆat ×S
ˆgt +S
ˆmt ×S ˆbt (2.37)
S
ˆgt = S
E ˜q∗
t−1 ⊗E
ˆg⊗S
E ˜qt−1 (2.33 revisited)
Obtaining the predicted reference direction of the earth’s magnetic field is achieved by
computing E ˆbt as E ˆht (measured direction of the earth’s magnetic field) normalised to have
only components in the earth frame x and z axes. Compensating for magnetic distortions in
this way ensures that magnetic disturbances are limited to only affect the estimated heading
component of orientation [50].
E ˆht = 0 hx hy hz = S
E ˜qt−1 ⊗S
ˆmt⊗S
E ˜q∗
t−1 (2.38)
E ˆbt = 0 h2
x +h2
y 0 hz (2.39)
S ˆbt = S
E ˜q∗
t−1 ⊗E ˆb⊗S
E ˜qt−1 (2.40)
The equation for the orientation of the sensor, SΩt, is obtained through a PI gain of
the angular error. The gains Kp and Ki correspond to the proportional and integral gains,
respectively. The proportional gain controls the frequency value that delimits the importance
of the gyroscope sensor information versus the accelerometer and the magnetometer sensors
data. The integral gain is adjusted to correct the gyroscope offset drift.
S
Ωt = S
ωt +Kp ·S
ωe,t +Ki · S
ωe,t (2.41)
To obtain the estimated orientation, it is necessary to compute the rate of change of the
quaternion as follows:
S
pt = [0,S
Ωt] (2.32 revisited)
S
E ˙qω,t =
1
2
S
E ˜qt−1 ⊗S
pt (2.29 revisited)

To maintain a proper estimation, the quaternion is integrated (equation 2.31) and normal-
ized (equation 2.36) at the end of each iteration.
The implementation of this filter can be easily understood on the following high level
block diagram:
Fig. 2.10 Complementary filter with magnetometer block diagram.

Chapter 3
Filter Results and Discussion
3.1 Orientation Tracking Experiments
In order to access the implemented algorithms on inexpensive sensors, a motion device
from Invensense1 was used for testing, the 9-axis MPU-9250. This sensor combines a
3-axis gyroscope, a 3-axis accelerometer and a 3-axis magnetometer on the same package.
Experiments were performed on the MPU-9250 breakout board. This breakout board expands
the integrated circuit pins onto a PCB that has its own pins that are spaced perfectly for
a solderless breadboard, giving you easy access to use the sensor. This way, real time
experiments are performed using an Arduino micro-controller board2, whereas offline data
processing and simulation is done using Matlab3 programming IDE (Integrated development
environment). Although the prototype contains MPU-9150 sensors, due to the immediate
availability and similar performance, for testing purposes the MPU-9250 also contains an
onboard Digital Motion Processor (DMP) capable of processing data fusion on the IMU
chip itself. The downside of using the DMP is that the manufacturer did not provide much
information on its proprietary inner workings. It acquires raw data from the sensors, processes
the data using proprietary algorithms and outputs directly calculated orientation information.
Since this solution is already integrated in the IC, we use this output for comparison in the
initial experiments.
Although the DMP provides a reliable source to approve the algorithms capabilities
during short periods of time, the MTi sensor from XSens is used as ground-truth for this
work. The Xsens has become an industry standard in the production of MEMS AHRSs,
their products are often used as replacements for high-grade IMUs, providing high quality
1Invensense Motion Technologies details present at: www.invensense.com/technology/motion/
2Further details: www.arduino.cc
3Additional details: https://www.mathworks.com/products/matlab/

32 Filter Results and Discussion
components with proven and robust filter design. They use a proprietary Kalman filtering
solution that copes with transient accelerations, magnetic disturbances and even vibrations.
3.1.1 Strapdown Inertial Navigation
Tests were performed using an Arduino board, raw data from the sensor and both the INS
algorithm and DMP outputs were recorded and processed at 50 Hz for comparison. No
specific experimental procedure was used for testing, the tests included rotations along the
threes sensor axes with multiple accelerations and durations. As supplementary work, we
also present an output of an implementation of the algorithm in Matlab, using the obtain raw
data values. An example of such experiments is shown in figure 3.1, which demonstrate a
graphical comparison between the orientation estimates, using quaternion representation.
The four graphics represent the four components that compose a quaternion. The results
were as expected, the INS algorithm follows the same estimation as the DMP with minimal
differences during small periods of time.
Fig. 3.1 Standard INS algorithm vs. DMP output.

3.1 Orientation Tracking Experiments 33
As it was already mentioned in chapter 2.3.1.1, the angular velocity signals obtained
from the gyroscopes are integrated, therefore errors in the gyroscope signals propagate
through to the calculated orientation causing a drift over time on the calculated quaternion.
To confirm this error in orientation, a test was performed where the sensor was left in a
stationary position while using the algorithm during a longer period of time (15 minutes).
The experiment was made with two independent sensors left at rest, the resulting drift can be
seen in figure 3.2 (each column of graphics represent the four components of the estimated
quaternion, respectively per sensor).
Fig. 3.2 INS algorithm stationary drift (quaternion representation).
As predicted the drift occurs and its magnitude varies differently between sensors. To
have a better perception of the amount of drift the quaternion representation was converted
to Euler angles (figure 3.3).

Fig. 3.3 INS algorithm stationary drift (Euler angles representation).
If we compare the initial and final orientation, on sensor 1 (which represents the worst
case scenario) we can observe an error up to 247° on the yaw angle, whereas on sensor 2 we
observe a maximum difference of 43° on the pitch angle.
These results make the standard INS algorithm unsuitable for our application, only giving
a precise orientation tracking during a very small period of time.
3.1.2 Complementary Filter without magnetometer
Following the same experimental procedure as with the INS algorithm, raw data was obtained
to simulate on Matlab, as well as the quaternions from both the DMP and the complementary
filter directly implemented on Arduino. The parameters used for the filter were Kp = 0.9 and
Ki = 0.02 as suggested in literature [48].

Again as expected, the complementary filter algorithm follows the same estimation with
minimal differences for short periods of time. The following figure 3.4 presents these results.
Fig. 3.4 Complementary filter algorithm vs. DMP output.
This filter, besides using the gyroscope axis output as velocity reference, it also uses
the angle between the accelerometer output and the body-fixed-frame as attitude reference
to obtain a zero bias estimate of the gravitational direction. This results in a much better
estimation and a smaller orientation drift over time.
Repeating the same experiment as before, leaving the sensors at rest during 15 minutes,
we can observe in figure 3.5 and figure 3.6 that the drift is almost removed, or at least it
takes much more time to be significant enough to disrupt the intended output. Comparing the
initial and final orientation, on sensor 1 we can observe a maximum final drift of only 6° on
the yaw angle, whereas on sensor 2 we observe a maximum error of 26° on the pitch angle.

Fig. 3.5 Complementary filter stationary drift (quaternion representation).
Fig. 3.6 Complementary filter stationary drift (Euler angles representation).

3.1.3 Complementary Filter with magnetometer
Without the heading provided by the magnetometer, with the addition of motion the previous
algorithm still has a drift over time on the initial orientation. This drift can be identified on
the z and scalar components of the quaternion (or the yaw angle of the Euler angles) since the
gravity correction only takes into account drifts that occur on the XY plane (perpendicular
plane to gravity).
Some long-term experiments were made in order to access if this is true and that the new
implementation corrects this drift. Figure 3.7 and figure 3.8 shows the results of one of these
experiments, a ten minutes experiment maintaining the sensor at rest and moving it after a
couple of minutes, in arbitrary orientations and magnitude, to consider not only the time of
experiment but also perturbations in the orientation estimate. Both implementations were
tested and the obtain results were overlapped on the same graphics to have a better perception
of the differences.
Fig. 3.7 Complementary Filter with and without magnetometer data (quaternion representa-
tion).

The results are as expected, the previous algorithm has a small drift over time, it can be
seen clearly on the scalar component of the quaternion and slightly on the z component of
the quaternion. Keeping the sensor with the same orientation throughout the experiment,
with the new implementation the obtained quaternion is the approximately the same, both
at the start and ending of the experiment. Without the magnetometer, the orientation has a
drift of 30° on the yaw angle, while, using the magnetometer, a 3° drift is observed and only
0.0066° and 0.5022° drifts for the roll and pitch angles, respectively.
Fig. 3.8 Complementary Filter with and without magnetometer data (Euler angles representa-
tion).
3.1.4 Evaluation of the Estimator Quality
The final algorithm was tested using the Xsens MTi sensor. Raw sensor data was logged
to a PC at 100 Hz and imported through Xsens software to provide calibrated sensor mea-
surements which were then processed by the proposed orientation estimation algorithm. As
both the Kalman-based algorithm and Complementary filter estimates of orientation were
computed using identical sensor data, the performance of each algorithm could be evaluated
relative to one-another.
Various experiments were conducted and both algorithms compared, figure 3.9 shows a
variable scenario with rotations in different velocities on all three axes and a period with the
sensor stationary.

Fig. 3.9 Complementary Filter vs. Xsens Kalman Filter.
It is common [19][51][52] to quantify orientation sensor performance using the Root-
Mean-Square Error (RMSE) which measures the differences between values predicted by an
estimator and the values actually observed. In order to obtain the best performance possible,
the Complementary filter was evaluated for different values of the tunable parameters Kp
and Ki. As described in chapter 2.3.2.2 the gain Ki is associated with the bias estimation
process of the complementary filter. For such short datasets the slow dynamics associated
with the bias estimate do not influence greatly the estimated outputs. Consequently, in the
experimental studies undertaken the bias gain is set to a very low value, Ki = 0.02. This
way by tuning Kp we were able to obtain RMSE values of 0.0586 (in quaternion units) and

0.9585° (Euler angles). Figure 3.10 evaluates this performance of the Complementary filter
by showing the RMSE as function of Kp, for constant Ki = 0.02.
Fig. 3.10 Performance of Complementary Filter as function of Kp.

Chapter 4
Development of a Prototype for the Hand
Tracking System
In this chapter we present the prototype produced as a result of this dissertation. We start
by giving an overview of the human hand model and the corresponding kinematic approach,
as well as the considerations and simplifications implemented in order to provide a simpler
analytical solution. The second section describes the hardware implementation detailing
the modules and devices used. Finally, the third section show the implemented animation
developed in the OpenAR platform.
4.1 Human Hand Kinematics
Kinematics is the branch of classical mechanics which studies the motion of bodies without
considering neither the masses nor the forces which cause the motion. In the context of hand
modelling, it defines the set of possible motions a hand can do. A kinematic model of a hand
is comprised of links that imitate the human bones and joints, which determine the constrains
of motion between the links. Taking a look at the human hand bone structure as presented by
Gustus et al.[53] in figure 4.1 we are able to realize that an accurate modelling may prove
difficult due to the complexity of the human hand.
The bones of a human hand consist of the carpal bones, the metacarpal (MC) bones,
the proximal phalanges (PP), medial phalanges (MP) and distal phalanges (DP). They are
connected by the carpometacarpal (CMC) joints, the intermetacarpal (IMC) joints, the
metacarpophalangeal (MCP) joints, the proximal interphalangeal (PIP) joints, the distal
interphalanges (DIP) joints and the interphalangeal (IP) joint of the thumb. The fingers are
numbered as follows: 1 thumb, 2 index, 3 middle, 4 ring, 5 little.

42 Development of a Prototype for the Hand Tracking System
Fig. 4.1 Human hand bone structure and joints layout.
In this work we arrived at a kinematic model where many simplifications are made while
preserving the kinematic information for the hand manipulation. This way we provide a
suitable solution to ease implementation and improve computational speed for applications
in real time. In our implementation we consider three joints for each finger and one joint for
the wrist. Comparing with the bone structure in figure 4.1, we maintain the DIP2-5, PIP2-5,
MCP2-5, IP1, MCP1 joints while defining one joint for the base of the thumb and one for the
wrist, this way we simplify the remaining joints without decreasing the range of motion. Our
hand model with the implemented virtual bone structure is depicted in figure 4.2.
All the joints in the hand kinematic model are defined by pure rotations, meaning that
they have a maximum of 3 DoF, each describing a rotation around an axis of the attached
frame. We propose a hand model with 24 DoF: one DoF (extension/flexion) for DIP2-5,
PIP2-5, IP1 and MCP1, two DoF (extension/flexion and adduction/abduction) for MCP2-5
joints and three DoF on the joint on the base of the thumb (allowing the thumb to also rotate
longitudinally) and the wrist joint (simulating the twist of the forearm).

4.1 Human Hand Kinematics 43
Fig. 4.2 Hand model with virtual bone structure.
As with any model, it is important to understand its limitations to assure that the desired
behaviours are produced and that the assumptions of the model are not violated. This way
many geometrical restrictions supplement the kinematic chain in order to define correct
finger configuration according to the model structure and the space of possible postures.
Direct kinematic equations are used to provide the position and orientation of each finger tip.
Equation 4.1 show the direct kinematics of each finger.
Ei = wrist
base T ·wrist
tip Ti (4.1)
• Ei represents a matrix that contains position and orientation of the finger tip (i =
1,2,3,4,5; fingers numbered as in figure 4.2);
• wrist
base T represents the distance between wrist and the base reference frame that connects
the hand to the forearm;
• wrist
tip Ti is a matrix that contains the geometrical transformation between the i-finger
reference frame and its corresponding finger tip. This matrix is composed by the
concatenation of more simple matrices that represents the contribution of each finger
joint.
By expanding equation 4.1 for the thumb we obtain equation 4.2. Anatomical terminology
is considered for the joints except for the two simplified joints (wrist and thumb).
E1 = wrist
base T ·wrist
thumbT ·thumb
MCP1T ·MCP1
IP1 T (4.2)
And for each of the remaining finger, where j = 2,3,4,5.

Ej = wrist
base T ·wrist
MCPjT ·
MCPj
PIPj T ·
PIPj
DIPjT (4.3)
With the proposed hand model, to obtain the orientation of each joint, in terms of
hardware, the ideal solution would be to place an IMU sensor in each joint and read the
corresponding orientation as the user moves his hands around. This would result in a solution
with 16 IMUs, making the final prototype relatively complex and not very comfortable to
use. Therefore, in order to decrease the amount of sensors placed on the hand, a study was
performed, based on literature [54][55][56][57], on the most common hand gestures and
motions that a user does (for example: grasping motions, okay sign or thumbs up, pointing
a finger to give directions and many others) and the impact these movements have on the
finger articulation. By assuming a constant relation between the joints of the fingers, we are
able to use only one sensor for each finger without losing enough gestures and motions that
would disrupt the immersion of a user. In this manner, we propose another simplification to
the kinematic model, where the orientation of the three joints of each finger are computed in
respect to only one joint. This results in a solution with only 6 IMUs, allowing the production
of an ergonomic hardware solution that does not disrupt the user and provides the similar
performance with subtle limitations.
4.1.1 MATLAB Based Animation
In order to validate the full kinematic model of the hand present in section 4.1 an experiment
was performed simulating a hand manipulator in Matlab environment. The toolbox presented
by Pajak in [58] was used as it provides the necessary tools and functions to simulate a
realistic model of a human upper limb. This toolbox allows to define any manipulator
described by Denavit-Hartenberg parameters (convention explained in [59]) and connect
the mechanisms created into one more complex mechanism, making it possible to simulate
any open kinematic chain. Furthermore, it contains default 3D representations for these
mechanisms to be shown in a realistic manner, as well as providing a set of basic blocks and
functions to manipulate position and orientation of those objects in the 3D space.
The toolbox was also modified to allow a real-time representation of the hand, while
reading the data from the sensors. Although this tweak granted an additional perception of
the tracking, it only allowed slow frame rates (between 10 to 15 frames per second), seeing
that the toolbox was never intended to have this feature and was not optimized for it.
An example of the hand manipulator used from the toolbox is depicted in figure 4.3.
The purpose of this simulation was to assess how the sensor placement affected the
behaviour of the hand, particularly the finger behaviour while only considering one sensor

4.1 Human Hand Kinematics 45
Fig. 4.3 Hand in default 3D view of the toolbox.
for the three joints. The Denavit-Hartenberg convention uses four parameters for attaching
reference frames to the links of the spatial kinematic chain, it assumes revolute joints and
allows to control the joint angle while the other parameters describe the constrains between
the link coordinate frames.
Taking into consideration the common active range of motion of the joints of the human
hand, as documented in [60], on our solution we calculate the kinematic chain with the finger
sensor on the first joint of the finger, the MCP joint, and assume a proportional relation for
the next two joints according to their range of motion (for example, for the finger joints
excluding the thumb, the MCP joint as a range of [0,100°], the PIP joint [0,105°] and the
DIP joint [0,85°]). With this approach, all expected hand configurations were faithfully
represented, although we lose independent joint motion, making less common configurations
like the ones in figure 4.4 impossible to perform.
Fig. 4.4 Examples of impossible to perform hand configurations.

Nevertheless, the prototype is not meant to be use for gesture recognition and most of
the gestures that result from independently moving these joints are not commonly used in
manipulation of objects or in interactions with an interface.
4.2 Hardware Implementation
4.2.1 Proof-of-Concept Prototypes
Before the development of the full prototype, to demonstrate the feasibility of this solution,
two simpler prototypes were developed. These first designs were never intended to be early
versions of the prototype, but merely proof-of-concept prototypes developed at an early stage
of the implementation. The first solution contained one sensor board and an ESP-01 on a
wrist band and the second one was extended containing an additional sensor board on one
finger, as is demonstrated on figure 4.5.
Fig. 4.5 Proof-of-concept Prototype.
In experiments using these prototypes the orientation data from the sensor on the wrist
was applied directly to the wrist joint and the data from the other sensor applied to all the
MCP joints of the fingers. These experiments only provided very limited finger motion and
allowed motions that did not respect the natural hand kinematic, however they proved the
capabilities of this approach with very precise tracking of the hand during small periods of
time (only using gyroscopes and accelerometers), giving the necessary enticement to further
extend and improve the technology.

4.2 Hardware Implementation 47
4.2.2 Hand-Tracker Prototype
To make the Hand-Tracker prototype as comfortable to use as possible two types of boards
were developed. The full design consists of six PCBs, a primary board containing the main
components of the prototype and placed on the back of the hand and five identical boards
containing one IMU sensor each, positioned on each respective finger. The five boards are
connected to the primary board using FFCs (flexible flat cables). These boards were designed
to occupy minimal space and fit easily on the dorsal part of the hand. Figure 4.6 shows the
complete Hand-Tracker prototype.
Fig. 4.6 Hand-Tracker prototype.
All these boards were designed and the components assembled at the laboratory with
the only exception of the ESP-01 board, depicted in figure 4.7, which is already designed to
occupy minimal PCB area and no further miniaturization was needed.
The primary board works as the core unit of the the prototype containing the processing
and communication modules, as well as the power input. It incorporates a power regulator,
one MPU-9150 sensor, a shift register and an ESP8266 board.
To power the Hand-Tracker a small LiPo (lithium polymer) battery is used, with a nominal
voltage of 3.7V regulated down to 3.3V. The power regulator is a XC6206 positive voltage
regulator with low power consumption that provides more than enough output current for our
implementation (up to 200mA) and the appropriate output voltage (3.3V).
The board also contains one IMU, the MPU-9150 sensor, which provides the data
corresponding to the wrist joint of the kinematic model. Even tough an MPU-9250 breakout
board was used for testing the algorithms, the MPU-9150 sensor was already available at the

Fig. 4.7 Prototype primary board (left) and ESP8266 ESP-01 board example (right)
laboratory in the appropriate SMT (surface-mount technology) case, ready to be mounted on
the PCB. Since these two sensors have very similar characteristics and identical performances,
there was no need to wait for the acquisition of new MPU-9250 sensors to assemble the
boards.
To be able to read multiple sensors we use the SN74HC595 8-Bit Shift Register. We use
this device due to a limitation in the I2C communication interface of the MPU-9150 sensor.
As described in [61], in a generalized I2C interface implementation, attached devices can
be a master or a slave. The master device puts the slave address on the bus, and the slave
device with the matching address acknowledges the master. In the case of the MPU-9150, it
always operates as a slave device when communicating to the system processor, which thus
acts as the master. The slave address of the MPU-9150 is 7 bits long with the LSB (least
significant bit) bit of the address determined by the logic level on pin AD0. This only allows
two MPU-9150s to be connected to the same I2C bus. For that reason we use a shift register
which is a device that allows to shift by one position the bit array stored in it. Basically we
only read from one slave address and keep all the remaining sensors with the other address,
in other words, every time we want to read a sensor, its AD0 pin has one logic level whereas
all remaining AD0 pins from other sensors have the opposite logic level. Using this strategy
the shift register allows to read each sensor successively.
To compute all the information provided by the sensors and transmit the data to a
computer a Wi-Fi module, the ESP8266 ESP-01, is used and connected to a stackable header
on the PCB. This module offers a self-contained Wi-Fi networking solution and capabilities
such as on-board processing and storage. Therefore, this module is used to store all the
calibration routines and sensor fusion algorithms. The module creates a wireless access point
and outputs the final orientation data of each sensor directly to the user’s computer.
The smaller boards placed on the fingers simply contain an MPU-9150 and its respective
operating circuit, depicted in figure 4.8.

4.3 Software Implementation - OpenAR Animation 49
Fig. 4.8 Prototype finger board.
With these board designs the final Hand-Tracker prototype is equipped with 6 IMU
sensors, it has an operating voltage of 3.3V and an operating current of 100mA, resulting in 3
hours of use with a 300mAh lithium battery. Currently containing wireless data transmission
(through Wi-Fi) and achieving a 59Hz sampling rate.
The electrical schematic diagram containing the operating circuit of each module and
appropriate connections between them, as well as the board design for the PCBs are presented
in the internal report [62].
4.3 Software Implementation - OpenAR Animation
The final prototype was tested directly in the OpenAR platform, by importing the hand model
proposed in section 4.1, an example of the demonstration is depicted in figure 4.9.
Fig. 4.9 Final Hand-Tracker demonstration.
The OpenAR is an in-house evolving development platform designed to implement
Augmented and Virtual Reality applications. It is written in C/C++ language, containing
various open source libraries, such as OpenCV and OpenGL, as well as interfaces with the
most common devices used in the context of these fields.

In terms of software, communication is established through network sockets, using UDP
(user datagram protocol), which allows a user to not only receive the orientation data but also
to send commands to access different implemented functions. Functions to stop or reset the
data stream, to acquire raw data and recalibrate the sensors if needed. The kinematics were
applied to the hand model by expanding and adapting the body kinematics implementation
provided by the Kinect SDK (software development kit), this way maintaining a consistent
approach for future applications (using also the Kinect sensor for body tracking).
This demonstration provided a constant and faithful tracking of the hand aside from some
model deformations due to the placement of the joints, resulting in some abnormal mesh
behaviours in specific positions (most noticeable on the thumb joints). The following figures
show examples of two types of control tested on the hand model. Figure 4.10 depicts the
intended behaviour of the hand, the model reference joint is placed in a fixed position and the
control of the hand starts at the wrist, this way considering that we have our forearm secured
(within a full body tracking this joint would be consistent with the far end of the forearm).
Fig. 4.10 Intended tracking examples, considering a secured arm.
Figure 4.11 depicts a control starting directly at the model reference joint, this approach
does not consider rotations on the wrist but provides additional range of motion within this
specific demonstration.
Fig. 4.11 Tracking examples with a different kinematic approach.

Chapter 5
Conclusion and Future Work
The ambition of this dissertation was to find a solution for adding hand-motion capture and
hand-interaction in a virtual reality environment. The existing solutions either hinder the hand
natural gestures or present limitations that would disrupt the sense of immersion of a user
during their virtual tours. In the compromises between the available functionalities and the
flexibility of the reached solution, we managed to use low-cost technology, obtaining a final
battery-operated prototype with wireless communication and an ergonomic design, which
feels comfortable to use and does not constrain the hand motion in any way. This was possible
because we analysed an orientation filter, that significantly ameliorates the computational load
and parameter tuning burdens associated with more conventional approaches. The algorithm
proved effective and even with a performance comparable to high quality commercial
Kalman-based systems. In summary, the initially proposed objectives for this dissertation
were completed with success, the developed Hand-Tracker prototype achieves a faithful
tracking of the hand and paves the way to a new form of interaction.
As future work, there are features that can be added to improve the proposed system.
Correctly estimating position using the accelerometers can really improve and support the
kinect tracking or even complement it in moments of hand occlusion during body motion
capture. Not only that, but with position tracking we can further extend the ways to interact
with the 3D virtual environments. Reflecting on the hardware, some features of the prototype
can also be improved. Incorporating a battery charger in the prototype or, if not suitable, just
adding a status indicator, would allow to check the battery level and help prolong its life.
To protect the components, we also recommend an encapsulation of the boards and the use
of shorter FFC cables. Last but not least , for the full experience of using our hands in an
interactive 3D environment a matching left hand prototype has yet to be assembled.

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Appendix A
Mathematical Background
This Appendix is a summary of representations of rotations by matrices, Euler angles, and
quaternions. Although the reader is assumed familiar with these topics, it intends to give a
brief description with some mathematical notions and their notations.
A.1 Matrix Representation
A 2D (two-dimensional) rotation is a transformation of the form:
x1
y1
=
cos(θ) −sin(θ)
sin(θ) cos(θ)
x0
y0
(A.1)
where θ is the angle of rotation. A 3D rotation is a 2D rotation that is applied within a
specified plane that contains the origin. Such a rotation can be represented by a 3×3 rotation
matrix R = [R0 R1 R2] whose columns R0, R1, and R2 correspond to the final rotated
values of the standard basis vectors (1,0,0), (0,1,0), and (0,0,1), in that order. These form
a right-handed orthonormal set, that is, |R0| = |R1| = |R2| = 1, R0 ·R1 = R0 ·R2 = R1 ·R2 = 0,
R0 ·R1 ×R2 = 1. Resulting in very important properties that allow to reduce some calculations,
RT = R−1 and det(R) = 1.
A rotation about one of the axis of a coordinate system by a given θ angle, usually called
elementary rotation, results in the following matrices:
Rx(θ) =



1 0 0
0 cos(θ) sin(θ)
0 −sin(θ) cos(θ)


 (A.2)

58 Mathematical Background
Ry(θ) =



cos(θ) 0 −sin(θ)
0 1 0
sin(θ) 0 cos(θ)


 (A.3)
Rz(θ) =



cos(θ) sin(θ) 0
−sin(θ) cos(θ) 0
0 0 1


 (A.4)
A.2 Euler Angles Representation
Euler angles provide a way to represent the 3D orientation of an object using a combination
of three sequential rotations about the axes a frame. These are given by the right hand rule,
following the aeronautical convention as in figure A.1, usually the roll (φ) angle is around
the x axis (normally this is the axis that points in the direction of the body), the pitch (θ)
angle is around the y axis (the other axis in the motion plane of the body), and the yaw angle
(ψ) around the z axis.
Fig. A.1 Euler angles as described in aeronautical conventional.
Considering that there are no consecutive rotations around the same axis, there are 12
different rotation sequences which can fully describe the final orientation of any body. By
multiplying the sequence of elementary rotations, the orientation between two generic frames,
A and B, can be described by a rotation matrix. Considering the successive rotations Rz(ψ),
Ry(θ) and Rx(φ), performing the multiplication, and letting c represent cos and s represent
sin, the complete rotation from a frame A to a frame B is given by:

A.3 Orientation Representations Assessment 59
B
AR(φ,θ,ψ) = Rx(φ)Ry(θ)Rz(ψ) (A.5)
B
AR(φ,θ,ψ) =



c(ψ)c(θ) c(θ)s(ψ) −s(θ)
c(ψ)s(φ)s(θ)−c(φ)s(ψ) c(φ)c(ψ)+s(φ)s(ψ)s(θ) c(θ)s(φ)
s(φ)s(ψ)+c(φ)c(ψ)s(θ) c(φ)s(ψ)s(θ)−c(ψ)s(φ) c(φ)c(θ)


 (A.6)
Euler angles suffer from singularities commonly know as gimbal lock, making sensors
unable to correctly represent orientation on specific cases. The exact orientation at which
gimbal lock occurs depends on the order of rotations used. In the sequence used previously,
the order of operations results in gimbal lock when the pitch angle is at 90 degrees. On
this situation, yaw and roll cause the sensor to move in exactly the same fashion. This is a
fundamental problem of Euler Angles and can only be solved by switching to a different
representation method [63].
A.3 Orientation Representations Assessment
As with most computer science topics, there is no answer to which is the best representation,
but depending on the application there may be trade-offs to consider.
Quaternions were chosen as the mathematical ground because, in the context of this work,
they deliver some advantages over the other representations. In terms of memory usage, a
rotation matrix yields a total of 9 parameters, resulting in 9 floats, a quaternion requires 4
floats and the Euler angles only 3 floats. Compared to quaternions and matrices, Euler Angles
provide the best choice, they are simple, intuitive and they lend themselves well to simple
analysis and control. On the other hand, Euler Angles are limited by the phenomenon known
as "gimbal lock", while the others have no problems with these singularities. Comparing
performances in terms of low level operation, as done by David Eberly in [64], when
composing two rotations the product of two rotation matrices requires 27 multiplications
and 18 additions, whereas the product of two quaternions requires only 16 multiplications
and 12 additions. Euler angles are not even used because it implies the use trigonometric
functions which are is quite expensive, so clearly quaternions present the best solution in an
application that requires computational efficiency.

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