Planning and Decision Making for Aerial Robots

420 Pages·2014·5.65 MB·English

by  Yasmina Bestaoui Sebbane (auth.)

Intelligent Systems, Control and Automation:
Science and Engineering
Yasmina Bestaoui Sebbane
Planning
and Decision
Making for
Aerial Robots
Intelligent Systems, Control and Automation:
Science and Engineering
Volume 71
Series editor
S. G. Tzafestas, Zografou, Athens, Greece
Editorial Advisory Board
P. Antsaklis, Notre Dame, IN, USA
P. Borne, Lille, France
D. G. Caldwell, Salford, UK
C. S. Chen, Akron, OH, USA
T. Fukuda, Nagoya, Japan
S. Monaco, Rome, Italy
G. Schmidt, Munich, Germany
S. G. Tzafestas, Athens, Greece
F. Harashima, Tokyo, Japan
N. K. Sinha, Hamilton ON, Canada
D. Tabak, Fairfax, VA, USA
K. Valavanis, Lafayette, LA, USA
For furthervolumes:
http://www.springer.com/series/6259
Yasmina Bestaoui Sebbane
Planning and Decision
Making for Aerial Robots
123
Yasmina Bestaoui Sebbane
UFRSciences and Technologies
Université d’Evry Val-D’Essone
Evry,Essonne
France
ISSN 2213-8986 ISSN 2213-8994 (electronic)
ISBN 978-3-319-03706-6 ISBN 978-3-319-03707-3 (eBook)
DOI 10.1007/978-3-319-03707-3
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013956331
(cid:2)SpringerInternationalPublishingSwitzerland2014
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor
informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodology now known or hereafter developed. Exempted from this legal reservation are brief
excerpts in connection with reviews or scholarly analysis or material supplied specifically for the
purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe
work. Duplication of this publication or parts thereof is permitted only under the provisions of
theCopyright Law of the Publisher’s location, in its current version, and permission for use must
always be obtained from Springer. Permissions for use may be obtained through RightsLink at the
CopyrightClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt
fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
While the advice and information in this book are believed to be true and accurate at the date of
publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor
anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with
respecttothematerialcontainedherein.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
To my family
Preface
This book provides an introduction into the emerging field of planning and
decision making of aerial robots. An aerial robot is the ultimate of Unmanned
Aerial Vehicles, an aircraft endowed with built-in intelligence, no direct human
control,andabletoperformaspecifictask.Itmustbeabletoflywithinapartially
structured environment, to react and adapt to changing environmental conditions,
and to accommodate the uncertainty that exists in the physical world. An aerial
robot can be termed as a physical agent that exists and flies in the real 3D world,
cansenseitsenvironment,andactonittoachievesomegoals.Sothroughoutthis
book, an aerial robot will also be termed as an agent.
Fundamentalproblemsinaerialroboticsarethetasksofmovingthroughspace,
sensing about space, and reasoning about space. Reasoning in the case of a
complex environment represents a difficult problem. The issues specific to rea-
soning about space are planning and decision making. Planning deals with the
trajectory algorithmic development based on the available information. Decision
making determines the most important requirements and evaluates possible
environment uncertainties.
The issues specific to planning and decision making of aerial robots in their
environment are examined in this book, leading to the contents of this book:
Motion planning, Deterministic decision making, Decision making under uncer-
tainty, and finally Multi-robot planning. A variety of techniques are presented in
thisbook,andsomecasestudiesaredeveloped.Thetopicsconsideredinthisbook
are multidisciplinary and lie at the intersection of Robotics, Control Theory,
Operational Research, and Artificial Intelligence.
Paris, France Yasmina Bestaoui Sebbane
vii
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Aerial Robots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Aerial Robotics and Artificial Intelligence . . . . . . . . . . . . . . . . 6
1.4 Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Probability Fundamentals. . . . . . . . . . . . . . . . . . . . . . . 9
1.4.2 Uncertainty Fundamentals . . . . . . . . . . . . . . . . . . . . . . 12
1.4.3 Nonlinear Control Fundamentals. . . . . . . . . . . . . . . . . . 18
1.4.4 Graph Theory Fundamentals. . . . . . . . . . . . . . . . . . . . . 21
1.4.5 Linear Temporal Logic Fundamentals. . . . . . . . . . . . . . 24
1.4.6 Rough Sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.5 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.5.1 Modeling of the Environment. . . . . . . . . . . . . . . . . . . . 37
1.5.2 Modeling of the Aerial Robot. . . . . . . . . . . . . . . . . . . . 37
1.5.3 Aerial Robots in Winds. . . . . . . . . . . . . . . . . . . . . . . . 43
1.6 Conflict Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
1.6.1 Deterministic Approach. . . . . . . . . . . . . . . . . . . . . . . . 46
1.6.2 Probabilistic Approach. . . . . . . . . . . . . . . . . . . . . . . . . 51
1.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2 Motion Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2 Controllability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.3 Trajectory Planning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.3.1 Trim Trajectory Generation . . . . . . . . . . . . . . . . . . . . . 66
2.3.2 Leg-Based Guidance. . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.3.3 Dubins and Zermelo Problems . . . . . . . . . . . . . . . . . . . 69
2.3.4 Optimal Control Based Approaches. . . . . . . . . . . . . . . . 77
2.3.5 Parametric Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
2.4 Nonholonomic Motion Planning . . . . . . . . . . . . . . . . . . . . . . . 99
2.4.1 Differential Flatness . . . . . . . . . . . . . . . . . . . . . . . . . . 99
2.4.2 Nilpotence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
2.4.3 Constrained Motion Planning. . . . . . . . . . . . . . . . . . . . 106
ix
x Contents
2.4.4 Motion Planning for Highly Congested Spaces. . . . . . . . 109
2.5 Obstacle/Collision Avoidance . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.5.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . 111
2.5.2 Discrete Search Methods . . . . . . . . . . . . . . . . . . . . . . . 115
2.5.3 Continuous Search Methods. . . . . . . . . . . . . . . . . . . . . 139
2.6 Replanning Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
2.6.1 Incremental Replanning. . . . . . . . . . . . . . . . . . . . . . . . 149
2.6.2 Anytime Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 157
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
3 Deterministic Decision Making. . . . . . . . . . . . . . . . . . . . . . . . . . . 171
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
3.2 Symbolic Planning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
3.2.1 Hybrid Automaton . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
3.2.2 Temporal Logic Motion Planning. . . . . . . . . . . . . . . . . 180
3.3 Computational Intelligence. . . . . . . . . . . . . . . . . . . . . . . . . . . 181
3.3.1 Neural Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
3.3.2 Evolution Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 185
3.3.3 Decision Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
3.3.4 Fuzzy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
3.4 Arc Routing Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
3.4.1 Traveling Salesman Problem . . . . . . . . . . . . . . . . . . . . 193
3.4.2 Dubins Traveling Salesman Problem. . . . . . . . . . . . . . . 199
3.4.3 Chinese Postman Problem . . . . . . . . . . . . . . . . . . . . . . 202
3.4.4 Rural Postman Problem. . . . . . . . . . . . . . . . . . . . . . . . 203
3.5 Case Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
3.5.1 Surveillance Mission. . . . . . . . . . . . . . . . . . . . . . . . . . 207
3.5.2 Evolutionary Planner. . . . . . . . . . . . . . . . . . . . . . . . . . 213
3.5.3 Bridge Monitoring. . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
3.5.4 Soaring Flight for Fixed Wing Aerial Robot . . . . . . . . . 231
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
4 Decision Making Under Uncertainty. . . . . . . . . . . . . . . . . . . . . . . 245
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
4.2 Generic Framework for Dynamic Decisions . . . . . . . . . . . . . . . 248
4.2.1 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . 248
4.2.2 Utility Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
4.2.3 Decision Trees and Path Utility . . . . . . . . . . . . . . . . . . 252
4.2.4 Bayesian Inference and Bayes Nets. . . . . . . . . . . . . . . . 252
4.2.5 Influence Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . 255
4.3 Markov Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Contents xi
4.3.1 Markov Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
4.3.2 Markov Decision Process Presentation. . . . . . . . . . . . . . 256
4.3.3 Partially Observable Markov Decision Process. . . . . . . . 262
4.3.4 Bayesian Connection with Partially Observable
Markov Decision Process. . . . . . . . . . . . . . . . . . . . . . . 264
4.3.5 Learning Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
4.3.6 Monte Carlo Value Iteration. . . . . . . . . . . . . . . . . . . . . 266
4.3.7 Markov Logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
4.3.8 Belief Space Approach . . . . . . . . . . . . . . . . . . . . . . . . 270
4.4 Stochastic Optimal Control Theory . . . . . . . . . . . . . . . . . . . . . 275
4.4.1 Bayesian Connection with State Space Models. . . . . . . . 276
4.4.2 Learning to Control. . . . . . . . . . . . . . . . . . . . . . . . . . . 277
4.4.3 Chance Constrained Algorithms . . . . . . . . . . . . . . . . . . 278
4.4.4 Probabilistic Traveling Salesman Problem . . . . . . . . . . . 280
4.4.5 Type 2 Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . 283
4.5 Motion Grammar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
4.5.1 Description of the Approach. . . . . . . . . . . . . . . . . . . . . 286
4.5.2 Grammars for Aerial Robots . . . . . . . . . . . . . . . . . . . . 287
4.5.3 Temporal Logic Specifications. . . . . . . . . . . . . . . . . . . 289
4.6 Case Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
4.6.1 Robust Orienteering Problem . . . . . . . . . . . . . . . . . . . . 292
4.6.2 Exploration of an Uncertain Terrain . . . . . . . . . . . . . . . 299
4.6.3 Rescue Path Planning in Uncertain
Adversarial Environment . . . . . . . . . . . . . . . . . . . . . . . 301
4.6.4 Receding Horizon Path Planning with Temporal
Logic Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
4.7 Real-Time Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
4.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
5 Multi Aerial Robot Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
5.2 Team Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
5.2.1 Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
5.2.2 Cascade-Type Guidance Law. . . . . . . . . . . . . . . . . . . . 323
5.2.3 Consensus Approach. . . . . . . . . . . . . . . . . . . . . . . . . . 327
5.2.4 Flocking Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
5.2.5 Connectivity and Convergence of Formations. . . . . . . . . 333
5.3 Deterministic Decision Making. . . . . . . . . . . . . . . . . . . . . . . . 336
5.3.1 Distributed Receding Horizon Control. . . . . . . . . . . . . . 338
5.3.2 Conflict Resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . 340
5.3.3 Artificial Potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
5.3.4 Symbolic Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
xii Contents
5.4 Association with Limited Communications. . . . . . . . . . . . . . . . 348
5.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
5.4.2 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . 349
5.4.3 Genetic Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . 353
5.4.4 Games Theory Reasoning . . . . . . . . . . . . . . . . . . . . . . 355
5.5 Multi-Agent Decision Making Under Uncertainty . . . . . . . . . . . 356
5.5.1 Decentralized Team Decision Problem . . . . . . . . . . . . . 357
5.5.2 Algorithms for Optimal Planning . . . . . . . . . . . . . . . . . 365
5.5.3 Task Allocation: Optimal Assignment. . . . . . . . . . . . . . 368
5.5.4 Distributed Chance Constrained Task Allocation . . . . . . 374
5.6 Case Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
5.6.1 Reconnaissance Mission. . . . . . . . . . . . . . . . . . . . . . . . 377
5.6.2 Expanding Grid Coverage . . . . . . . . . . . . . . . . . . . . . . 381
5.6.3 Optimization of Perimeter Patrol Operations . . . . . . . . . 383
5.6.4 Stochastic Strategies for Surveillance . . . . . . . . . . . . . . 388
5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
6 General Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399