Metaheuristics for robotics

189 Pages·2020·9.807 MB·English

by  Oulhadj, Hamouche;Daachi, Boubaker;Menasri, Riad

Metaheuristics for Robotics

Optimization Heuristics Set
coordinated by
Nicolas Monmarché and Patrick Siarry
Volume 2
Metaheuristics for Robotics

Hamouche Oulhadj
Boubaker Daachi
Riad Menasri
First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
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© ISTE Ltd 2020
The rights of Hamouche Oulhadj, Boubaker Daachi and Riad Menasri to be identified as the authors of
this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2019952981

British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-380-6
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Chapter 1. Optimization: Theoretical
Foundations and Methods . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. The formalization of an optimization
problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Constrained optimization methods . . . . . . . . . . . . . 5
1.2.1. The method of Lagrange multipliers . . . . . . . . . 9
1.2.2. Method of the quadratic penalization . . . . . . . . . 11
1.2.3. Methods of interior penalties . . . . . . . . . . . . . . 12
1.2.4. Methods of exterior penalties . . . . . . . . . . . . . . 13
1.2.5. Augmented Lagrangian method . . . . . . . . . . . . 14
1.3. Classification of optimization methods . . . . . . . . . . 15
1.3.1. Deterministic methods . . . . . . . . . . . . . . . . . . . 16
1.3.2. Stochastic methods . . . . . . . . . . . . . . . . . . . . . 18
1.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Chapter 2. Metaheuristics for Robotics . . . . . . . . . . . . . . . 27
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2. Metaheuristics for trajectory
planning problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.1. Path planning . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.2. Trajectory generation . . . . . . . . . . . . . . . . . . . . 43
vi Metaheuristics for Robotics
2.3. Metaheuristics for automatic
control problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.5. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Chapter 3. Metaheuristics for Constrained and
Unconstrained Trajectory Planning . . . . . . . . . . . . . . . . . 53
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2. Obstacle avoidance . . . . . . . . . . . . . . . . . . . . . . . 54
3.3. Bilevel optimization problem . . . . . . . . . . . . . . . . 58
3.4. Formulation of the trajectory
planning problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.4.1. Objective functions . . . . . . . . . . . . . . . . . . . . . 60
3.4.2. Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5. Resolution with a bigenetic algorithm . . . . . . . . . . 63
3.6. Simulation with the model of
the Neuromate robot . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.6.1. Geometric model of
the Neuromate robot . . . . . . . . . . . . . . . . . . . . . . . . 67
3.6.2. Kinematic model of
the Neuromate robot . . . . . . . . . . . . . . . . . . . . . . . . 71
3.6.3. Simulation results . . . . . . . . . . . . . . . . . . . . . 72
3.7. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.8. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Chapter 4. Metaheuristics for Trajectory Generation by
Polynomial Interpolation . . . . . . . . . . . . . . . . . . . . . . . . 87
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2. Description of the problem addressed . . . . . . . . . . . 88
4.3. Formalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3.1. Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3.2. Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.4. Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.4.1. Augmented Lagrangian . . . . . . . . . . . . . . . . . . 95
4.4.2. Genetic operators . . . . . . . . . . . . . . . . . . . . . . 97
4.4.3. Solution coding . . . . . . . . . . . . . . . . . . . . . . . 99
4.5. Simulation results . . . . . . . . . . . . . . . . . . . . . . . . 100
4.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.7. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Contents vii
Chapter 5. Particle Swarm Optimization for
Exoskeleton Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2. The system and the problem under consideration . . . 123
5.2.1. Representation and model of the system under
consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.2.2. The problem under consideration . . . . . . . . . . . 125
5.3. Proposed control algorithm . . . . . . . . . . . . . . . . . . 126
5.3.1. The standard PSO algorithm . . . . . . . . . . . . . . 126
5.3.2. Proposed control approach . . . . . . . . . . . . . . . . 128
5.4. Experimental results . . . . . . . . . . . . . . . . . . . . . . 135
5.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.6. Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153