Distributed Coverage Games for Energy-Aware Mobile Sensor Networks

Inspired by current challenges in data-intensive and energy-limited sensor networks, we formulate a coverage optimization problem for mobile sensors as a (constrained) repeated multiplayer game. Each sensor tries to optimize its own coverage while minimizing the processing/energy cost. The sensors are subject to the informational restriction that the environmental distribution function is unknown a priori. We present two distributed learning algorithms where each sensor only remembers its own utility values and actions played during the last plays. These algorithms are proven to be convergent in probability to the set of (constrained) Nash equilibria and global optima of a certain coverage performance metric, respectively. Numerical examples are provided to verify the performance of our proposed algorithms.

[1]  Jason R. Marden,et al.  Payoff-Based Dynamics for Multiplayer Weakly Acyclic Games , 2009, SIAM J. Control. Optim..

[2]  Sonia Martínez,et al.  Deployment algorithms for a power-constrained mobile sensor network , 2008, 2008 IEEE International Conference on Robotics and Automation.

[3]  Yingshu Li,et al.  Distributed energy-efficient solutions for area coverage problems in wireless sensor networks , 2009 .

[4]  Awi Federgruen,et al.  Ergodicity in Parametric Nonstationary Markov Chains: An Application to Simulated Annealing Methods , 1987, Oper. Res..

[5]  C. Istin,et al.  Energy saving strategy for video-based Wireless Sensor Networks under field coverage preservation , 2008, 2008 IEEE International Conference on Automation, Quality and Testing, Robotics.

[6]  Jason R. Marden,et al.  Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[7]  D. Vere-Jones.  Markov Chains , 1972, Nature.

[8]  Tansu Alpcan,et al.  A power control game based on outage probabilities for multicell wireless data networks , 2004, IEEE Transactions on Wireless Communications.

[9]  Robert Murphey,et al.  Target-Based Weapon Target Assignment Problems , 2000 .

[10]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[11]  Sonia Martínez,et al.  Distributed coverage games for mobile visual sensors (I): Reaching the set of Nash equilibria , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[12]  Jason R. Marden,et al.  Cooperative Control and Potential Games , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Tim Roughgarden,et al.  Selfish routing and the price of anarchy , 2005 .

[14]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[15]  B. Gidas.  Nonstationary Markov chains and convergence of the annealing algorithm , 1985 .

[16]  Sonia Martínez,et al.  Distributed coverage games for mobile visual sensors (II) : Reaching the set of global optima , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[17]  E. D. Evans,et al.  Search Radar Detection and Track with the Hough Transform , 1994 .

[18]  Lachlan L. H. Andrew,et al.  Game theory for heterogeneous flow control , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[19]  Jorge Urrutia,et al.  Art Gallery and Illumination Problems , 2000, Handbook of Computational Geometry.

[20]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 1998, IEEE Trans. Neural Networks.

[21]  Jorge Cortés,et al.  Coverage control by multi-robot networks with limited-range anisotropic sensory , 2009, Int. J. Control.

[22]  R. Cucchiara.  Multimedia surveillance systems , 2005, VSSN@MM.

[23]  F. Bullo,et al.  Visibility-based multi-agent deployment in orthogonal environments , 2007, 2007 American Control Conference.

[25]  L. Shapley,et al.  Potential Games , 1994 .

[26]  R. Lienhart,et al.  On the optimal placement of multiple visual sensors , 2006, VSSN '06.

[27]  Sonia Martinez,et al.  Deployment algorithms for a power‐constrained mobile sensor network , 2010 .

[28]  Richard W. Madsen,et al.  Markov Chains: Theory and Applications , 1976 .

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

[30]  H. Young,et al.  The Evolution of Conventions , 1993 .

[31]  Edmund Y. Lam,et al.  Maximizing Angle Coverage in Visual Sensor Networks , 2007, 2007 IEEE International Conference on Communications.

[32]  J. O'Rourke.  Art gallery theorems and algorithms , 1987 .

[33]  D. Mitra,et al.  Convergence and finite-time behavior of simulated annealing , 1985, 1985 24th IEEE Conference on Decision and Control.

[34]  Francesco Bullo,et al.  Distributed Control of Robotic Networks , 2009 .

[35]  Stephen P. Boyd,et al.  Randomized gossip algorithms , 2006, IEEE Transactions on Information Theory.

[36]  Ian F. Akyildiz,et al.  Wireless multimedia sensor networks: A survey , 2007, IEEE Wireless Communications.

[37]  Francesco Bullo,et al.  Multirobot Rendezvous With Visibility Sensors in Nonconvex Environments , 2006, IEEE Transactions on Robotics.

[38]  Roberto Manduchi,et al.  Characterizing energy consumption in a visual sensor network testbed , 2006, 2nd International Conference on Testbeds and Research Infrastructures for the Development of Networks and Communities, 2006. TRIDENTCOM 2006..

[39]  Francesco Bullo,et al.  Esaim: Control, Optimisation and Calculus of Variations Spatially-distributed Coverage Optimization and Control with Limited-range Interactions , 2022 .

[40]  Huadong Ma,et al.  Energy-Efficient Cooperative Image Processing in Video Sensor Networks , 2005, PCM.

[41]  T. Shermer.  Recent Results in Art Galleries , 1992 .

[42]  P. Bahr,et al.  Sampling: Theory and Applications , 2020, Applied and Numerical Harmonic Analysis.

[43]  Adam Wierman,et al.  Distributed Welfare Games , 2013, Oper. Res..