A Formal Framework for Mobile Robot Patrolling in Arbitrary Environments with Adversaries

Using mobile robots for autonomous patrolling of environments to prevent intrusions is a topic of increasing practical relevance. One of the most challenging scientific issues is the problem of finding effective patrolling strategies that, at each time point, determine the next moves of the patrollers in order to maximize some objective function. In the very last years this problem has been addressed in a game theoretical fashion, explicitly considering the presence of an adversarial intruder. The general idea is that of modeling a patrolling situation as a game, played by the patrollers and the intruder, and of studying the equilibria of this game to derive effective patrolling strategies. In this paper we present a game theoretical formal framework for the determination of effective patrolling strategies that extends the previous proposals appeared in the literature, by considering environments with arbitrary topology and arbitrary preferences for the agents. The main original contributions of this paper are the formulation of the patrolling game for generic graph environments, an algorithm for finding a deterministic equilibrium strategy, which is a fixed path through the vertices of the graph, and an algorithm for finding a non-deterministic equilibrium strategy, which is a set of probabilities for moving between adjacent vertices of the graph. Both the algorithms are analytically studied and experimentally validated, to assess their properties and efficiency.

[1]  Manish Jain,et al.  Computing optimal randomized resource allocations for massive security games , 2009, AAMAS 2009.

[2]  Nicholas Roy,et al.  Global A-Optimal Robot Exploration in SLAM , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[3]  Nicola Basilico,et al.  Finding the optimal strategies for robotic patrolling with adversaries in topologically-represented environments , 2009, 2009 IEEE International Conference on Robotics and Automation.

[4]  Sarit Kraus,et al.  An efficient heuristic approach for security against multiple adversaries , 2007, AAMAS '07.

[5]  Yann Chevaleyre,et al.  Theoretical analysis of the multi-agent patrolling problem , 2004, Proceedings. IEEE/WIC/ACM International Conference on Intelligent Agent Technology, 2004. (IAT 2004)..

[6]  Sarit Kraus,et al.  The impact of adversarial knowledge on adversarial planning in perimeter patrol , 2008, AAMAS.

[7]  Nicola Basilico,et al.  Leader-follower strategies for robotic patrolling in environments with arbitrary topologies , 2009, AAMAS.

[8]  Vincent Conitzer,et al.  Multi-Step Multi-Sensor Hider-Seeker Games , 2009, IJCAI.

[9]  Nicola Basilico,et al.  Capturing augmented sensing capabilities and intrusion delay in patrolling-intrusion games , 2009, 2009 IEEE Symposium on Computational Intelligence and Games.

[10]  Michal Tzur,et al.  The Period Vehicle Routing Problem with Service Choice , 2006, Transp. Sci..

[11]  A. Rubinstein Perfect Equilibrium in a Bargaining Model , 1982 .

[12]  Yong Yu,et al.  C-space Entropy: A Measure for View Planning and Exploration for General Robot-Sensor Systems in Unknown Environments , 2004, Int. J. Robotics Res..

[13]  Stefano Carpin,et al.  Extracting surveillance graphs from robot maps , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[14]  D. Koller,et al.  Efficient Computation of Equilibria for Extensive Two-Person Games , 1996 .

[15]  Francesco Amigoni,et al.  A Game-Theoretic Approach to Determining Efficient Patrolling Strategies for Mobile Robots , 2008, 2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology.

[16]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[17]  Nicos Christofides,et al.  The period routing problem , 1984, Networks.

[18]  Sarit Kraus,et al.  Deployed ARMOR protection: the application of a game theoretic model for security at the Los Angeles International Airport , 2008, AAMAS 2008.

[19]  Rui P. Rocha,et al.  Cooperative Multi-Robot Systems A study of Vision-based 3-D Mapping using Information Theory , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[20]  Wolfram Burgard,et al.  Exploring Unknown Environments with Mobile Robots using Coverage Maps , 2003, IJCAI.

[21]  Nicola Basilico,et al.  Developing a Deterministic Patrolling Strategy for Security Agents , 2009, 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology.

[22]  Olivier Buffet,et al.  Theoretical Study of Ant-based Algorithms for Multi-Agent Patrolling , 2008, ECAI.

[23]  O. Diaz-Parra,et al.  Search Algorithm for the Constraint Satisfaction Problem of VRPTW , 2007, Electronics, Robotics and Automotive Mechanics Conference (CERMA 2007).

[24]  El Houssaine Aghezzaf,et al.  Production , Manufacturing and Logistics A practical solution approach for the cyclic inventory routing problem , 2008 .

[25]  Vincent Conitzer,et al.  Learning and Approximating the Optimal Strategy to Commit To , 2009, SAGT.

[26]  Steven Dubowsky,et al.  Efficient Information-based Visual Robotic Mapping in Unstructured Environments , 2005, Int. J. Robotics Res..

[27]  Patrice Marcotte,et al.  Bilevel programming: A survey , 2005, 4OR.

[28]  Drew Fudenberg,et al.  Game theory (3. pr.) , 1991 .

[29]  S. Shankar Sastry,et al.  Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation , 2002, IEEE Trans. Robotics Autom..

[30]  Sarit Kraus,et al.  Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games , 2008, AAMAS.

[31]  Vincent Conitzer,et al.  Computing the optimal strategy to commit to , 2006, EC '06.

[32]  Ari K. Jónsson,et al.  Cyclic Scheduling , 1999, IJCAI.

[33]  B. Stengel,et al.  Leadership with commitment to mixed strategies , 2004 .

[34]  Christos H. Papadimitriou,et al.  Computational complexity , 1993 .

[35]  Sarit Kraus,et al.  Multi-robot perimeter patrol in adversarial settings , 2008, 2008 IEEE International Conference on Robotics and Automation.

[36]  Ronald L. Rivest,et al.  Introduction to Algorithms, Second Edition , 2001 .

[37]  Nicola Basilico,et al.  Extending Algorithms for Mobile Robot Patrolling in the Presence of Adversaries to More Realistic Settings , 2009, 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology.

[38]  Nicola Gatti,et al.  Game Theoretical Insights in Strategic Patrolling: Model and Algorithm in Normal-Form , 2008, ECAI.

[39]  Alexander H. G. Rinnooy Kan,et al.  Vehicle Routing with Time Windows , 1987, Oper. Res..

[40]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[41]  David M. Kreps,et al.  Sequential Equilibria Author ( s ) : , 1982 .

[42]  Yoav Shoham,et al.  Multiagent Systems - Algorithmic, Game-Theoretic, and Logical Foundations , 2009 .

[43]  John N. Tsitsiklis,et al.  Special cases of traveling salesman and repairman problems with time windows , 1992, Networks.

[44]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[45]  Sampath Kannan,et al.  Randomized pursuit-evasion in a polygonal environment , 2005, IEEE Transactions on Robotics.

[46]  Sarit Kraus,et al.  Uncertainties in adversarial patrol , 2009, AAMAS.