Cognitive Systems Monographs Volume 9 Editors: Rüdiger Dillmann Yoshihiko Nakamura Stefan Schaal David Vernon
Heiko Hamann Space-Time Continuous Models of Swarm Robotic Systems Supporting Global-to-Local Programming ABC
Rüdiger Dillmann, University of Karlsruhe, Faculty of Informatics, Institute of Anthropomatics, Humanoids and Intelligence Systems Laboratories, Kaiserstr. 12, 76131 Karlsruhe, Germany Yoshihiko Nakamura, Tokyo University Fac. Engineering, Dept. Mechano-Informatics, 7-3-1 Hongo, Bukyo-ku Tokyo, 113-8656, Japan Stefan Schaal, University of Southern California, Department Computer Science, Computational Learning & Motor Control Lab., Los Angeles, CA 90089-2905, USA David Vernon, Khalifa University Department of Computer Engineering, PO Box 573, Sharjah, United Arab Emirates Editors Dr.-Ing. Heiko Hamann University of Graz Department of Zoology Universitätsplatz 2/I 8010 Graz Austria E-mail: heiko.hamann@uni-graz.at ISBN 978-3-642-13376-3 e-isbn 978-3-642-13377-0 DOI 10.1007/978-3-642-13377-0 Cognitive Systems Monographs ISSN 1867-4925 Library of Congress Control Number: 2010928224 c 2010 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed on acid-free paper 543210 springer.com
Abstract In this work, a generic model in as far as possible mathematical closed-form is developed that predicts the behavior of large self-organizing robot groups (robot swarms) based on their control algorithm. In addition, an extensive subsumption of the relatively young and distinctive interdisciplinary research field of swarm robotics is emphasized. The connection to many related fields is highlighted and the concepts and methods borrowed from these fields are described shortly. Large groups of small robots, mostly of limited equipment are applied in swarm robotics forming a decentral system. All robots are autonomous and act on the basis of locally available information. The development of the control algorithm, that is to be executed locally on each robot, has proven to be difficult. This development of the local control algorithm is defined and constrained by the global task (global-to-local programming, or also micromacro problem). The classical reductionistic approach is of limited use here (problem of designing emergence). For example, the resulting behavior of the robot swarm often contradicts the intuition of the program developer due to effects of the many robot robot interactions that cannot be anticipated. The support of the swarm algorithm developer by models is an approach that has already been discussed in the literature several times. The quickly available predictions of the model are supposed to support the development early before the implementation on the robots. Even complete parameter intervals can be scanned for optimal values. Furthermore, the development and the application of models can result in a better understanding of the effective processes in swarms concerning both the general understanding and in a particular application. The modeling approach proposed in this work is particularly distinguished by the explicit representation of space and the, at least partially existent, formal connection between the micro- and the macro level. The basic model of the robot positions is motivated by Brownian motion and consists of a pair of corresponding equations. While the Langevin equation (a stochastic differential equation) gives a local (microscopic)
VI Abstract description of concrete trajectories, the Fokker Planck equation (also Kolmogorov forward equation, a partial differential equation), that can be analytically derived from the Langevin equation, gives a global (macroscopic) description by means of probability densities. This physical model was extended to a generic model of communicating robot groups based on heuristic arguments. This model approach has a variety of applications, however, the adaptation to a specific control algorithm is a demanding modeling step. The proposed model is validated against several swarm robotic scenarios applying real robots and simulations: collision-based adaptive aggregation, collective perception, collective phototaxis, foraging with virtual pheromones, and tree-like aggregation. The required adaptation of the model to the according situation is exemplified (modeling state transitions, parameter selection, measurement etc.). The achieved accuracy of the model predictions is good and sufficient to be a support in the algorithm development phase.
Contents 1 Introduction and Purpose... 1 1.1 Objectives... 2 1.2 Approach... 3 1.3 Outline... 3 2 Fundamentals of Swarm Robotics An Interdisciplinary Approach... 5 2.1 Definition of Fundamental Concepts..................... 5 2.1.1 Agent... 5 2.1.2 Agent AgentInteraction... 6 2.1.3 MacroscopicandMicroscopicLevel... 6 2.1.4 PhenomenologicalApproach... 6 2.1.5 Self-organization... 7 2.1.6 Emergence... 7 2.1.7 Stigmergy... 9 2.1.8 Micro-MacroLink... 9 2.2 Swarm Intelligence.................................... 9 2.2.1 From Natural to Artificial Swarms................. 10 2.2.2 SwarmsasProblemSolvers... 10 2.3 Robotics... 11 2.3.1 MobileRobotics... 11 2.3.2 Micro-Robotics... 11 2.3.3 SwarmRobotics... 12 2.3.4 EmbodiedCognitiveScience... 15 2.3.5 Sensor/ActuatorNetworks... 15 2.4 Software Concepts for Distributed Systems............... 16 2.4.1 (Distributed) Artificial Intelligence and Multi-robot Systems... 16 2.4.2 Multi-AgentSystems... 16
VIII Contents 2.4.3 ArtificialLife... 17 2.4.4 AmorphousComputing... 17 2.4.5 Self-awarenessinDistributedSystems... 18 2.5 ScienceofSelf-organization... 18 2.5.1 TheoryofDissipativeStructures... 18 2.5.2 Synergetics... 19 2.6 PhilosophicalIssues... 20 2.6.1 EmergenceandNovelty... 20 2.6.2 Multi-particle Systems and Computation........... 24 2.7 Summary... 25 3 State-of-the-Art in Modeling and Design of Swarms... 27 3.1 Modeling Swarm Behavior and Collective Behavior........ 27 3.1.1 Agent-BasedModeling... 27 3.1.2 ClassicalApproach ControlTheory... 28 3.1.3 SwarmRobotics... 28 3.1.4 Physics... 29 3.1.5 Chemistry... 30 3.1.6 Biology... 32 3.1.7 Micro, Macro, and Stochastic Modeling Road Traffic... 33 3.2 DesignofEmergentBehavior... 35 3.2.1 Global-to-Local Programming Engineering of Emergence... 35 3.2.2 Antagonism of Concepts......................... 35 3.2.3 Programming byhand... 36 3.2.4 Automatic and Semi-automatic Methods........... 38 3.3 Summary... 39 4 A Framework of Models for Swarm Robotic Systems... 41 4.1 Modeling Multi-particle Systems Example of Brownian Motion... 41 4.1.1 Introduction History of Brownian Motion......... 42 4.1.2 A Microscopic Model The Langevin Equation..... 42 4.1.3 A Macroscopic Model The Fokker Planck Equation... 47 4.2 DiscussionoftheMethodology... 56 4.2.1 Purpose of a Model in the Design of Swarm Algorithms... 57 4.2.2 BenefitsofaSymbolicModel... 58 4.2.3 ConsiderationofAlternativeMethods... 59 4.3 APhysicallyMotivatedApproach... 60 4.4 ModelingRobotMotion... 61 4.5 ModelingRobot-RobotInteractions... 65 4.5.1 External Influence Modeling the Environment..... 65
Contents IX 4.5.2 ChallengeofModelingCommunication... 66 4.6 Towards General Methodological Principles............... 67 4.7 RelevancetotheConceptofComputation... 68 4.7.1 From Swarm Behavior to World-Embedded Computation... 68 4.7.2 The Concept of Embodied Computation........... 69 4.8 Discussion... 71 4.8.1 DiscussionofLimitations... 71 4.8.2 DiscussionofBenefits... 73 4.8.3 Discussion of the Relevance to Computation........ 74 4.9 Summary... 75 5 Validation by Results of Experiments and Simulations... 77 5.1 Collision-Based Adaptive Swarm Aggregation............. 77 5.1.1 TheSwarmRobot Jasmine... 78 5.1.2 Scenario... 79 5.1.3 Model... 81 5.1.4 Results... 84 5.1.5 Discussion... 87 5.2 CollectivePerception... 89 5.2.1 Scenario... 89 5.2.2 Model... 92 5.2.3 ResultsandDiscussion... 96 5.3 EmergentTaxis... 100 5.3.1 Scenario... 100 5.3.2 Model... 101 5.3.3 Results... 104 5.4 Foraging... 105 5.4.1 Scenario... 105 5.4.2 Model... 107 5.4.3 Results... 109 5.5 Robot Aggregation as a Form of Computation............ 113 5.5.1 TheEuclideanSteinerTreeProblem... 114 5.5.2 GrowingRandomTrees... 115 5.5.3 Results... 118 5.5.4 Discussion... 121 5.6 Summary... 121 6 Conclusion and Outlook... 123 6.1 Conclusion... 123 6.2 Outlook... 124 6.3 Acknowledgments... 125
X Contents A Numerical Simulation of the Langevin Equation... 127 B Simple Numerical Solver of the Fokker Planck Equation... 129 References... 131 Index... 143