139,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
This book is dedicated to the application of metaheuristic optimization in trajectory generation and control issues in robotics. In this area, as in other fields of application, the algorithmic tools addressed do not require a comprehensive list of eligible solutions to effectively solve an optimization problem. This book investigates how, by reformulating the problems to be solved, it is possible to obtain results by means of metaheuristics. Through concrete examples and case studies particularly related to robotics this book outlines the essentials of what is needed to reformulate control laws into concrete optimization data. The resolution approaches implemented as well as the results obtained are described in detail, in order to give, as much as possible, an idea of metaheuristics and their performance within the context of their application to robotics.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 175
Veröffentlichungsjahr: 2020
Ähnliche
Table of Contents
Cover
Preface
Introduction
1 Optimization: Theoretical Foundations and Methods
1.1. The formalization of an optimization problem
1.2. Constrained optimization methods
1.3. Classification of optimization methods
1.4. Conclusion
1.5. Bibliography
2 Metaheuristics for Robotics
2.1. Introduction
2.2. Metaheuristics for trajectory planning problems
2.3. Metaheuristics for automatic control problems
2.4. Conclusion
2.5. Bibliography
3 Metaheuristics for Constrained and Unconstrained Trajectory Planning
3.1. Introduction
3.2. Obstacle avoidance
3.3. Bilevel optimization problem
3.4. Formulation of the trajectory planning problem
3.5. Resolution with a bigenetic algorithm
3.6. Simulation with the model of the Neuromate robot
3.7. Conclusion
3.8. Bibliography
4 Metaheuristics for Trajectory Generation by Polynomial Interpolation
4.1. Introduction
4.2. Description of the problem addressed
4.3. Formalization
4.4. Resolution
4.5. Simulation results
4.6. Conclusion
4.7. Bibliography
5 Particle Swarm Optimization for Exoskeleton Control
5.1. Introduction
5.2. The system and the problem under consideration
5.3. Proposed control algorithm
5.4. Experimental results
5.5. Conclusion
5.6. Bibliography
Conclusion
Index
End User License Agreement
List of Tables
Chapter 2
Table 2.1. Effects of the actions of the PID regulator
Chapter 3
Table 3.1. Limits of the robot joints
Table 3.2. Geometric parameters
Table 3.3. Position of obstacles in the robot workspace
Table 3.4. Algorithm parameters
Chapter 4
Table 4.1. Algorithm parameters
Table 4.2. Maximum values for the variables of the objective function
Table 4.3. Values of weighting parameters under test
Table 4.4. Characteristics of some interpolation methods
Chapter 5
Table 5.1. Characteristics of the participants
Table 5.2. Controller parameter values
List of Illustrations
Chapter 1
Figure 1.1. Domain of admissible solutions and forbidden domain
Figure 1.2. 1D multimodal objective function, in the absence of noise
Figure 1.3. 1D multimodal objective function, in the presence of noise
Figure 1.4. 2D multimodal objective function, in the absence of noise
Figure 1.5. 2D multimodal objective function, in the presence of noise
Figure 1.6. Constrained optimization. ■ Local minima. • Global minimum. For a co...
Figure 1.7. Constrained optimization. ■ Global minimum in the presence of constr...
Figure 1.8. Refinement of the performance of an algorithm
Figure 1.9. Some deterministic methods
Figure 1.10. Some stochastic methods
Chapter 2
Figure 2.1. Different stages of trajectory planning
Figure 2.2. Hybrid planning: joint space -> Cartesian space
Figure 2.3. An example of a hybrid planning strategy
Figure 2.4. Hybrid planning: Cartesian space -> joint space
Figure 2.5. Principle of a particle swarm algorithm
Figure 2.6. Principle of an evolutionary algorithm
Figure 2.7. Trajectory outline
Figure 2.8. Typical system response
Chapter 3
Figure 3.1. Obstacle modeling. For a color version of this figure, see www.iste....
Figure 3.2. Plane used to measure distances. For a color version of this figure,...
Figure 3.3. Planar robot with an obstacle
Figure 3.4. Illustrated example of obstacle detection
Figure 3.5. Description of the bigenetic algorithm
Figure 3.6. Neuromate robot. The Neuromate robot has five degrees of freedom. Al...
Figure 3.7. Geometric configuration of the robot. For a color version of this fi...
Figure 3.8. Chromosomes of the algorithm
Figure 3.9. Evolution of the best individual in the first level
Figure 3.10. Evolution of the best individual at the second level
Figure 3.11. End-effector position error
Figure 3.12. CPU time
Figure 3.13. Successive robot configurations. For a color version of this figure...
Figure 3.14. Two solutions found by the algorithm. For a color version of this f...
Figure 3.15. Variation in joint variables. For a color version of this figure, s...
Figure 3.16. Best individual evolution. For a color version of this figure, see ...
Chapter 4
Figure 4.1. Example of a polynomial curve
Figure 4.2. Algorithm overall outline
Figure 4.3. Solution coding
Figure 4.4. Angular position
Figure 4.5. Angular velocity
Figure 4.6. Angular acceleration
Figure 4.7. Mean and standard deviation of the objective function
Figure 4.8. Maximum velocities
Figure 4.9. Maximum and minimum accelerations
Figure 4.10. Maximum jerk
Figure 4.11. Maximum motion time
Figure 4.12. CPU time
Figure 4.13. Mean and standard deviation of the objective function after converg...
Figure 4.14. Maximum velocity
Figure 4.15. Maximum acceleration
Figure 4.16. Maximum jerk
Figure 4.17. Maximum time
Figure 4.18. Angular position with cubic splines
Figure 4.19. Angular velocity with cubic splines
Figure 4.20. Angular acceleration with cubic splines
Figure 4.21. Angular position for five nodes
Figure 4.22. Angular velocity for five nodes
Figure 4.23. Angular acceleration for five nodes
Chapter 5
Figure 5.1. Lower limb exoskeleton
Figure 5.2. Proposed controller
Organigram 1. Standard PSO control
Organigram 2. The proposed modified PSO-based control
Figure 5.3. Experimental environment [DAA 15, MAD 14]
Figure 5.4. The mechanical structure of the EICoSI [MAD 14, DAA 15, RIF 12]
Figure 5.5. Position trajectory tracking for individual 1. For a color version o...
Figure 5.6. Position trajectory tracking for individual 2. For a color version o...
Figure 5.7. Position trajectory tracking for individual 3. For a color version o...
Figure 5.8. RMS of position trajectory tracking errors. For a color version of t...
Figure 5.9. Control inputs for the three individuals 1, 2 and 3. For a color ver...
Figure 5.10. Evolution of the adaptive PID parameters. For a color version of th...
Guide
Cover
Table of Contents
Begin Reading
Pages
v
iii
iv
ix
x
xi
xiii
xiv
xv
xvi
xvii
xviii
xix
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
147
148
149
150
151
153
154
155
156
157
158
159
160
161
162
163
165
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 permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd
27-37 St George’s Road
London SW19 4EU
UK
www.iste.co.uk
John Wiley & Sons, Inc.
111 River Street
Hoboken, NJ 07030
USA
www.wiley.com
© 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
Preface
Optimization deals with methods that make it possible to optimize the use, operation and performance conditions of a system, whether it is physical or related to human activity. Situated at the crossroads of several disciplines, namely applied mathematics, computer science and artificial intelligence, optimization makes it possible to quickly find a solution to numerous problems which would otherwise be more difficult to solve relying solely on restricted mathematical analysis.
Based on heuristics or even metaheuristics at a higher level, optimization methods provide operational solutions, which are not necessarily optimal solutions but eligible suboptimal solutions, so-called acceptable solutions, because they demonstrate the level of performance required to reach a goal without conflicting with associated constraints. A number of problems whose resolution is based on optimization methods can be provided as examples:
— in finance, tax optimization is a means to minimize legal taxation;
— in databases, query optimization makes it possible to improve the accessibility of shared data, in particular by reducing transaction time;
— in telecommunications networks, routing optimization is a method for finding suitable paths for data exchange;
— in robotics, optimization allows, to take just one example, the identification of the best configurations (joint variables) that a robot must undergo in order to efficiently perform a task;
— in computer science, optimizing the code of a program makes it possible to reduce the memory space occupied and to increase the convergence time.
The applications outlined above are inherently very complex, which raises the problems of implementing accurate mathematical methods that provide admissible solutions without having to mobilize huge computational resources. In these circumstances, we are limited to considering approximated solutions, which are suboptimal solutions, but acceptable, ones since they guarantee goal realization while satisfying constraints.
In this book, we will address issues specifically related to the field of medical robotics. The focus of the applications being considered is on trajectory planning for redundant manipulative arms (articulated robots) within the context of surgical gesture assistance, and robust control for effort compensation or physical assistance in disability situations (exoskeleton). These applications are presented in detail, with the aim of understanding with the utmost clarity the problems to be solved, as well as the choices made to find effective solutions within a reasonable time frame.
The methods developed make use of optimization metaheuristics, which are high-level abstraction algorithms. Unlike heuristics, which are computational processes, often informally and “individually” adapted to specific problems, metaheuristics are general algorithms applicable to a very wide range of optimization problems, without the need to resort to a fundamental modification of the structure of these algorithms. The methods studied and results achieved are commented on and presented in detail for each of the applications addressed. Although the proposed methods are developed within the context of their application to medical robotics, their generic nature allows them to be easily expanded to other optimization problems which do not necessarily fall within the same scope of application.
Hamouche OULHADJBoubaker DAACHIRiad MENASRINovember 2019
Introduction
This work is part of a collection of books, published by ISTE and Wiley, devoted to metaheuristics and their applications. Known for being specific and particular algorithms, what practical interest do metaheuristics have to make them increasingly attractive to engineers, researchers and scientists from various areas interested in different fields of application? There are two important arguments that provide us with obvious answers: on the one hand, the scope of application of metaheuristics is constantly gaining momentum, without apparently being concerned with any limitations; on the other hand, these resolution methods possess a high level of abstraction, which makes them adaptable to a wide range of engineering problems. Furthermore, a small number of necessary adjustments that do not change the nature of algorithms are usually sufficient to solve new optimization problems without any particular links existing between them.
Moreover, metaheuristics belong to a particular class of algorithms, not always easy to configure and reserved for difficult optimization problems for which there are no accurate methods to solve them more efficiently. These problems are renowned for being complex and among them we can find problems whose mathematical models are not derivable; problems whose research space is too extended to exhaustively enumerate all feasible solutions, such as problems of a combinatorial nature or involving continuous decision variables; as well as any problem making use of highly noisy, erroneous or even incomplete data, which prove unsuitable for mathematical modeling. For all these categories of problems, we generally adopt approximated solutions belonging to the field of admissible solutions, which are capable of reaching a goal without violating constraints that might be a priori imposed.
In practice, there may be several existing solutions to an optimization problem, of which only one of these solutions is generally optimal. All others are suboptimal solutions, but are still eligible, so-called acceptable, solutions because they guarantee the completion of an objective without violating associated constraints. However, the notion of optimizing acceptability may appear to be overly abstract: how can the level of solution operability be identified when the level of appreciation of that solution may vary not only from one user to another, but also with the margin of error tolerated by each type of application? Clearly, there is no absolute answer to this question, because it is ultimately each individual who decides how to define the level of acceptability for a solution, based on individual needs and the quality of the results sought for the application to be addressed.
Are metaheuristics deterministic or stochastic algorithms? Providing a clear answer to this question is also not an easy task. In effect, while it is clear that metaheuristics are not deterministic algorithms, they are also not completely stochastic algorithms. In fact, they can be categorized halfway between these two families of algorithms, because solving an optimization problem by means of a metaheuristic systematically relies on a more or less random sampling process of the solution space. When the algorithm is started, chance plays an important role in the process of finding solutions. Then, as the iterations progress, this randomness is progressively attenuated as we approach the final phase of the algorithm. Therefore, a metaheuristic will behave as a stochastic algorithm during initial iterations, and will asymptotically tend towards a greedy and deterministic algorithm during the last iterations. As we might expect, the accuracy of a metaheuristic lies in the right balance to be found between exploration phases, in which chance plays an important role, and the phases of intensification of solutions, also called phases of exploitation, in which randomness is reduced in order to focus only on potentially promising solutions. At the moment, there is no automatic parameterization method for these two search phases, whose respective weights generally depend on the type of application under study, the type of computational effort to be sustained and the type of results sought after.
Today, metaheuristics have become almost unavoidable in numerous areas of engineering due to the difficulties that have to be overcome to properly solve common optimization problems. These difficulties generally lie in the complex nature of the systems under study: the number of constraints and decision variables to be taken into account can be very high, computational times can be very long and non-differentiable objective functions can be highly multimodal or even too complex to be mathematically formalized with accuracy. The field of robotics is by nature a very broad field of application. In fact, these very relevant algorithms can be found in many applications of robotics:
— trajectory planning for mobile robots;
— robust control of portable robots for motion assistance;
— cooperation tasks between robots;
— vision in robotics.
In this book, we will focus more specifically on using metaheuristics for solving trajectory planning problems for redundant manipulative arms, as well as automatic control problems involving collaborative robots for assistance. These studies are conducted with a view to eventually exploiting the results within a clinical framework, within the context of surgical or physical assistance in order to compensate for efforts or to increase motor capabilities in performing a task.
With regard to trajectory planning, the difficulties raised are related to the redundant nature of the robot being used (the manipulative arm with several degrees of freedom), the nature of the environment in which the robot evolves (the environment cluttered with obstacles, uncertainties about the environment, etc.) and of course the complexity of the task at hand (the level of accuracy required, the time allowed to perform this task, the amount of motor power needed in order to minimize consumed energy and avoid sudden movements which could deteriorate the mechanical structure of the robot). All of these parameters can induce an excessively high number of decision variables and constraints to be taken into account.
For the control of collaborative robots (force-feedback robots designed for physical assistance in carrying out a task), the complexity of the problem resides in the almost infinite number of combinatory solutions to be tested before finding the proper values of control parameters. These must provide the desired optimal effort, within a reasonable time frame, without anachronistic movements that could endanger the person under assistance or present a risk of resonance that could deteriorate the mechanical structure of the robot. Since the automatic control system is designed to operate in an uncertain and dynamic environment, the task becomes more complex due to the servo control that operates in real time, in order to take into account external disturbances and the permanent evolution of input data (setpoints) over time.
We underline that the optimization issues studied in this book have been the subject of research carried out in collaboration between university laboratories and hospitals. Despite the practical and experimental aspect of this work, the methods developed are generic overall and can be generalized to other areas of application without requiring significant changes in the structure of the algorithms. Given this last point, these methods might be of particular interest to a very wide audience including students of robotics, algorithmics, applied mathematics and operational research, as well as engineers or teachers/researchers whose work deals with difficult optimization problems.
This book is organized into five chapters.
Chapter 1 is a general study which reviews the mathematical foundations needed for modeling optimization problem in order to solve them using numerical methods. A list of basic methods can be found therein, including comments and a great deal of information about their characteristics and properties. This chapter is essential for understanding the approaches developed in the following chapters to solve more complex medical problems.
Chapter 2 focuses on the application of metaheuristics in optimization problems related to robotics. Particular emphasis is placed on issues related to the fields of trajectory planning and automatic control. The challenges encountered, the difficulties that have to be overcome and the pertinence of metaheuristics for their solution in an approximate but sufficiently effective manner are described with the utmost concern for clarity. Most common general algorithms within these two areas of application are also presented in detail.
Chapter 3 is dedicated to the specific problem of trajectory planning for redundant manipulative arms. A resolution method based on a bigenetic algorithm (two genetic algorithms running in parallel) is presented in this chapter. Inspired by two-tier optimization problems, this method distinguishes two planning spaces: the Cartesian space, in order to control and guide the movements of the effector (terminal organ of the manipulative arm) in the work environment, and the joint space, in order to operate the different segments of the motorized arm. The coordination of the movements of the robot within these two spaces is ensured by the collaboration of the two genetic algorithms. Each of these two algorithms uses its own decision variables and optimizes its own objective
