PhD-Thesis by Kaspar Althoefer - "Neuro-Fuzzy Motion Planning ...."
Althoefer, Kaspar
kaspar.althoefer at kcl.ac.uk
Fri Oct 17 13:11:36 EDT 1997
The following PhD thesis is now available:
"Neuro-Fuzzy Motion Planning for Robotic Manipulators"
by Kaspar ALTHOEFER.
The thesis will not be available on a Web or ftp site, but I would be
pleased to send my thesis as a postscript file to everybody who wants a
copy. Please, contact me via e-mail, if you are interested. My e-mail
address is Kaspar.Althoefer at kcl.ac.uk.
Below you will find the abstract and the table of contents.
Best regards,
Kaspar Althoefer.
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Abstract
On-going research efforts in robotics aim at providing mechanical
systems, such as robotic manipulators and mobile robots, with more
intelligence so that they can operate autonomously. Advancing in this
direction, this thesis proposes and investigates novel manipulator path
planning and navigation techniques which have their roots in the field
of neural networks and fuzzy logic.
Path planning in the configuration space makes necessary a
transformation of the workspace into a configuration space. A
radial-basis-function neural network is proposed to construct the
configuration space by repeatedly mapping individual workspace obstacle
points into so-called C-space patterns. The method is extended to
compute the transformation for planar manipulators with n links as well
as for manipulators with revolute and prismatic joints.
A neural-network-based implementation of a computer emulated resistive
grid is described and investigated. The grid, which is a collection of
nodes laterally connected by weights, carries out global path planning
in the manipulator’s configuration space. In response to a specific
obstacle constellation, the grid generates an activity distribution
whose gradient can be exploited to construct collision-free paths. A
novel update algorithm, the To&Fro algorithm, which rapidly spreads the
activity distribution over the nodes is proposed. Extensions to the
basic grid technique are presented.
A novel fuzzy-based system, the fuzzy navigator, is proposed to solve
the navigation and obstacle avoidance problem for robotic manipulators.
The presented system is divided into separate fuzzy units which
individually control each manipulator link. The competing functions of
goal following and obstacle avoidance are combined in each unit
providing an intelligent behaviour. An on-line reinforcement learning
method is introduced which adapts the performance of the fuzzy units
continuously to any changes in the environment.
All above methods have been tested in different environments on
simulated manipulators as well as on a physical manipulator. The results
proved these methods to be feasible for real-world applications.
........................................................................................
TABLE OF CONTENTS
Abstract ii
Acknowledgments iii
Table of Contents iv
List of Figures vii
List of Tables ix
1 Introduction 1
1.1 Methodology 2
1.2 Constructing the C-space, Global Path Planning,
Local Navigation: An Overview 4
1.2.1 Manipulator Motion Planning 4
1.2.2 The Computation of the C-space and
the Building of Maps 5
1.2.3 Global Path Planning in C-space 6
1.2.4 Local Navigation 8
1.3 Contributions made by this Thesis 10
2 Workspace to C-space Transformation 11
2.1 Introduction 11
2.2 The Configuration Space in Context 13
2.3 The Configuration Space of a Robotic Manipulator 15
2.4 The Mapping of Obstacle Points
into their C-space Counterpart 16
2.4.1 The Single Point Mapping 16
2.4.2 The C-space of a 2-Link Revolute Arm 18
2.4.3 The C-space of a 2-Link Arm
with Prismatic and Revolute Joints 23
2.5 The C-space of an n-Link Arm 26
2.5.1.1 Comparison of configuration space representations 32
2.5.1.2 Reduction in Complexity 33
2.6 A Radial Basis Function Network
for the Workspace to C-space Transformation 35
2.6.1 The RBF-Network for the C-space Calculation 35
2.6.2 The Training of the Network: Insertion of Nodes 37
2.7 A Three-link Manipulator 39
2.8 Real-world Applications 41
2.8.1 C-space Patterns for a Physical Manipulator 41
2.8.2 Timing Considerations 45
2.8.3 A Real-World Planning System 47
2.8.3.1 Image Processing 48
2.8.3.2 Input to the Radial-Basis-Function Network 50
2.9 Summary 51
3 A Neuro-Resistive Grid for Path Planning 53
3.1 Problem Definition and Overview of the Algorithm 53
3.2 Related Work 55
3.2.1 Resistive Grids for Path Planning 55
3.2.2 The Hopfield Network 56
3.2.3 Cellular Neural Network 57
3.2.4 Dynamic Programming 58
3.3 Path Planning in the Configuration Space 60
3.4 The Neuro-Resistive Grid 61
3.4.1 Implementation of the Neuro-Resistive Grid 61
3.4.2 Functioning of the Resistive Grid 63
3.4.3 Harmonic Functions 66
3.4.4 Boundary Conditions - Dirichlet vs. Neumann 68
3.4.5 Convergence Criterion for the Neuro-resistive Grid 72
3.5 Enhanced Activity Propagation 74
3.5.1 Methodology 74
3.5.2 Higher Dimensions 77
3.5.3 Global Extremum and Collision-free Path 78
3.5.4 A Non-Topologically-Ordered Grid 82
3.5.5 Soft Safety Margin 83
3.6 Experiments 84
3.6.1 Real-World Experiments with the MA 2000 Manipulator 84
3.6.2 A Planar Three-Link Manipulator 94
3.6.3 A Three-dimensional SCARA Manipulator 101
3.6.4 A Mobile Robot in a 3D-Workspace 101
3.7 Comparative Studies 102
3.7.1 Comparisons to Other Update Rules 102
3.7.2 Comparison to Other Update Sequences 105
3.7.3 Comparison to the A*-Algorithm 106
3.8 Summary 108
4 Fuzzy-Based Navigation and Obstacle Avoidance
for Robotic Manipulators 110
4.1 Problem Definition and System Overview 110
4.2 Local Navigation in Context 113
4.2.1 Artificial Potential Fields 113
4.2.2 An Overview of Fuzzy-Based Navigation Techniques
for Mobile Robots 115
4.2.3 Unreachable Situations and Local Minima 116
4.3 Fuzzy Navigation and Obstacle Avoidance
for Robotic Manipulators 117
4.3.1 Introduction to Fuzzy Control 117
4.3.2 Manipulator-Specific Implementation Aspects 121
4.3.3 The Fuzzy Algorithm 123
4.4 Computer Simulations 128
4.4.1 Two-Link Manipulator 128
4.4.2 Three-Link Manipulator 132
4.4.3 Moving Obstacles 134
4.4.4 Safety Aspects 134
4.5 Fuzzy Navigation for the MA 2000 Manipulator 135
4.5.1 Simulated MA 2000 and Comparison
to the Resistive Grid Approach 135
4.5.2 Real-World Results 138
4.6 Reinforcement Learning 138
4.7 Summary and Discussion 144
5 Conclusions and Future Work 147
5.1 Conclusions 147
5.1.1 Workspace to C-space Transformation
for Robotic Manipulators 147
5.1.2 A Neural Resistive Grid for Path Planning 147
5.1.3 Fuzzy-based Navigation and Obstacle Avoidance
for Robotic Manipulators 149
5.2 Future work 150
5.2.1 Hybrid System 150
5.2.2 Implementational Aspects 151
5.2.3 Sensors 152
5.2.4 Transformation of Complex Obstacle Primitives 152
Appendix A-1 153
Appendix A-2 155
Appendix A-3 160
Appendix B 165
Bibliography 169
--
|_/ I N G'S Dr Kaspar ALTHOEFER
| \ COLLEGE Ph.D., Dipl.-Ing., AMIEE
L O N D O N Department of Mechanical Engineering
Founded1829 King's College, Strand, London WC2R 2LS, UK
TEL: +44 (0)171 873 2431, FAX: +44 (0)171 836 4781
http://www.eee.kcl.ac.uk/~kaspar
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