'UBVERSITV OF MORATUWA. SRI I AN* 
D E V E L O P M E N T O F H O L O N O M I C M O B I L E 
P L A T F O R M F O R F I E L D R O B O T I C 
A P P L I C A T I O N S 
A Thesis submitted to the 
Department of Electronics and Telecommunications Engineering 
University of Moratuwa 
in partial fulfilment of the requirements for the 
degree of Master of Philosophy 
by 
W.R. D e Silva 
Supervised by: Dr Rohan Munasinghe G 2 . V 3 B ( P ^ 5 ) 
Department of Electronics and Telecommunications 
Engineering University of Moratuwa, Sri Lanka 
M a r c h 2011 (OOB€£ 
University of Moratuwa 
100855 
D E C L A R A T I O N 
The work submitted in this thesis is the result of my own investigation, expect 
otherwise stated. 
It has not already been accepted for any degree, and is not been concurrently 
submitted for any other degree. 
W. R. De Silva 
Date : 10 March 2011 
We/I endorse the declaration by the candidate. 
Dr. Rohan Munasinghe 
Senior Lecturer 
Dept. of Electronic and 
Telecommunication Engineering 
University of Moratuwa. 
i 
Abstract 
Most mobile platforms or vehicles used today are non holonomic. They only have 
one or two independent degrees of freedom. Due to that its maneuverability is lim­
ited and often requires much space to control functions like turning and parking. 
By improving degrees of freedom (improving the maneuverability) of a vehicle, it 
can follow many complex trajectories that are difficult or impossible by conven­
tional non holonomic vehicles. Any mobile platform tha t has three independent 
degrees of freedom in a plane is a holonomic platform. Independent degrees of free­
dom means that it can change its orientation or position without effecting other 
motions unlike in car type vehicles that require turning or changing its orientation 
when need to move. Holonomic motion is very useful to acquire abilities such as, 
avoid any obstacle while keeping its orientation the same, capability to move in 
constrained spaces and track a target while moving in an arbitrary trajectories etc. 
Because of these advantages and capabilities some of the scientific and industrial 
researches are targeting to develop holonomic mobile platforms. Already robotics 
community have managed to build some working models and used in applications 
like robot soccer games and mobile robot manipulators. Many different mecha­
nisms have been created to achieve the holonomic capability. These include various 
arrangements of Swedish wheels or omni wheels, chains of spherical or cylindrical 
wheels, ball wheels and powered caster wheels etc. While most of these designs are 
practical in indoor environments they are not suitable for outdoor operations in 
large scale versions. In this research project our goal was to develop a viable design 
to achieve holonomic capability that minimizes these problems and more suited 
to outdoor operations. The proposed design has a wheel arrangement similar to a 
car but with the capability of independent driving and steering capability of each 
of the four wheels. Car type rolling and steering mechanism avoid any uneven 
ii 
wear of the wheels and avoid lateral forces applied on the wheels. Wheel driving 
and steering mechanism was designed such a way that wheels can be steered 360 
degrees continuously without interfering with the wheel drive system. This en­
ables the platform to move in complex trajectories continuously without stopping 
for wheel resetting. The developed platform has increased ground clearance that 
is necessary for outdoor rough terrain operations like farming. Although these 
benefits exist, controlling the robot to acquire the desired motion is very complex 
and need innovative algorithm. Four independent wheels with eight degrees of 
freedoms to achieve three degree of freedom motion is a redundant control prob­
lem and require complex control system. Using inverse kinematics model of the 
platform and multiprocessor design with advance micro-controllers we have tried 
to solve these issues and were able to achieve successful performance. 
iii 
Dedicated to my parents Sujatha and Dayawansha 
and 
to my loving wife Nalika 
IV 
Acknowledgments 
I would like to take this opportunity to convey my sincere thanks to Dr Rohan 
Munasingha, my research supervisor in suggesting such a research project that 
invoked my design abilities. It has benefited immensely from his valuable advices, 
suggestions to fruitful the outcomes of the project. I also thank to Dr Palitha 
Dassanayake and senior lecturer Mr. Shiran Nanayakara for helping me for the 
control system design and implementation. 
Further more I would like to express my great appreciation to all academic staff 
members of the Department of Electronics and Telecommunication Engineering 
and workshop staff for their kind support. 
Finally I would like to thank to all my fellow researchers of the Intelligent 
Machines Laboratory for their enormous support throughout this period. 
W Rameesha De Silva 
Department of Electronics and Telecommunication Engineering 
University of Moratuwa 
v 
Contents 
Declaration i 
Abstract iii 
Dedication iv 
Acknowledgments v 
List of figures viii 
List of tables x 
1 Introduct ion 1 
1.1 Motivation 1 
1.2 The project goals and achievements 2 
1.3 Organization of the thesis 3 
2 Pre l iminary invest igat ions 4 
2.1 Literature Survey 4 
2.1.1 Swedish wheel (omni wheel) designs 4 
2.1.2 Power caster design 6 
2.1.3 Other state of the art outdoor holonomic designs 7 
2.1.4 Holonomic motion and non-holonomic motion 7 
3 Kinemat ic s of the holonomic mobi le platform 10 
3.1 Free body diagram of the mobile platform 10 
3.2 Inverse kinematics solution 11 
3.3 Possible robot motions 14 
4 M o d e l i n g and s imulat ion of mobi le manipulators 15 
4.1 Mathematical modeling 15 
vi 
I 
•J 
4.2 Simulation 15 
4.3 Newton Euler dynamics 16 
4.3.1 Newton Euler formulation for manipulators 16 
4.3.2 Newton Euler dynamics for mobile manipulators 17 
5 Mechanical des ign of ho lonomic mobi le platform 29 
5.1 Wheels mount arms with drive system 29 
5.2 Main body 29 
5.3 3D model of the mobile platform 31 
5.4 Mechanical power transmission system 32 
5.5 Steering power transmission 32 
5.6 Drive power transmission 32 
5.7 Mechanical system implementation 33 
6 M o t i o n planning and controller design 35 
6.1 Controller architecture 35 
6.2 Motion planner 35 
6.3 Servo controller 37 
6.4 Control system timing and flow 39 
6.5 Electronics and electrical system implementation 40 
7 Resu l t s and discuss ion 43 
7.1 PID parameter tunning results 43 
7.2 Holonomic robot in action 44 
8 Conclus ions and future research 47 
8.1 Future works 47 
Bibl iography 50 
A p p e n d i x 50 
A Master controller circuit 51 
B Servo controller circuit 55 
vn 
List of Figures 
2.1 Swedish wheel holonomic design . 
2.2 Typical omni wheel designs . . 
2.3 Power caster module used in XR4000 mobile Robot 
. . . 6 
2.4 Power caster holonomic design, XR4000 mobile Robot 
. . . 7 
2.5 Seekur holonomic robo t . . . 
2.6 Holonomic motion . . . 
2.7 Non-holonomic motion . 
3.1 Free body diagram of base and a single wheel 
3.2 Kinematics digram of body section . 
3.3 Kinematics digram of single wheel 
3.4 Kinematics digram of body section . 
3.5 Kinematics digram of body section . 
4.1 Simulation flow diagram . . 
4.2 Osculating circles for given trajectory y = f(x) 
4.3 f(x) = (x/l0)3-8(x/10)2 + x 
4.4 r(x) variation of f(x) = (x /10) 3 - 8 (z /10 ) 2 + x 22 
4.5 Virtual link concept . . . 
4.6 Simulated manipulator arm movements 
4.7 Force applied on the mobile base when it is stationary 
. . 26 
4.8 Force applied on the mobile base when it is moving 27 
4.9 Torques applied on the manipulator joints and mobile base 
. . 28 
5.1 Wheel mount arm . . . . 
viii 
5.2 Main body of mobile platform 31 
5.3 Mechanical power transmission system 32 
5.4 Cross section of the power transmission system 33 
5.5 Mobile platform mechanical construction 34 
6.1 Control system block diagram 36 
6.2 Master controller program flow 37 
6.3 Servo controller block diagram 38 
6.4 Prototype Servo controller 39 
6.5 Control loop timing diagram 40 
6.6 Dual servo card 41 
6.7 Servo card stack 41 
6.8 PIC32 starter kit with I /O expansion 42 
6.9 Electrical wiring block diagram 42 
7.1 Step response P = 20, D = 0, I = 0 Ts = 1.6 ms (Unstable) . . . . 43 
7.2 P = 10, D' = 0, I = 0, Ts = 1.6 ms (Settling time is high) 43 
7.3 P = 10, D = 200, I = 0, Ts = 1.6 ms (Stable with an offset) . . . . 44 
7.4 P = 10, Dl = 200, I = 1, Ts = 1.6 ms (Required step responce) . . . 44 
7.5 Holonomic type obstacle avoidance movement of the robot 45 
7.6 Robot trajectory for the obstacle avoidance movement 46 
7.7 Robot orientation error over the obstacle avoidance period 46 
8.1 Proposed holonomic mobile manipulator system 48 
A. l Master controller 51 
A.2 Master controller circuit diagram part 1 52 
A.3 Master controller circuit diagram part 2 53 
A.4 Master controller circuit diagram part 3 54 
B.l Servo controller prototype 55 
B.2 Servo controller circuit diagram part 1 56 
B.3 Servo controller circuit diagram part 2 57 
B.4 Servo controller circuit diagram part 3 58 
ix 
List of Tables 
4.1 Simulation way points 25 
6.1 Ziegler-Nichols parameter tuning 39 
x