\r\nfor the problem of unknown area coverage by a network of robots.

\r\nThe coverage objective is to locate a set of targets in the area and

\r\nto minimize the robots’ energy consumption. The robots have no

\r\nprior knowledge about the location and also about the number of the

\r\ntargets in the area. One efficient approach that can be used to relax

\r\nthe robots’ lack of knowledge is to incorporate an auxiliary learning

\r\nalgorithm into the control scheme. A learning algorithm actually

\r\nallows the robots to explore and study the unknown environment

\r\nand to eventually overcome their lack of knowledge. The control

\r\nalgorithm itself is modeled based on game theory where the network

\r\nof the robots use their collective information to play a non-cooperative

\r\npotential game. The algorithm is tested via simulations to verify its

\r\nperformance and adaptability.","references":"[1] S. Dhillon, K. Chakrabarty, S. Iyengar, \u201cSensor Placement for\r\nGrid Coverage under Imprecise Detections\u201d, in Proc. Intl. Conf. on\r\nInformation Fusion, pp. 1571-1587, 2002.\r\n[2] D. Ucinski, \u201cMeasurement Optimization for Parameter Estimation in\r\nDistributed Systems\u201d, CRC Press, 1999.\r\n[3] Li, W., Cassandras, C.G., \u201cDistributed Cooperative coverage Control of\r\nSensor Networks\u201d, 44th IEEE Conference on Decision and Control and\r\nEuropean Control Conference (CDC-ECC \u201905), pp. 2542-2547, 2005.\r\n[4] J. R. Spletzer and C. J. Taylor, \u201cDynamic Sensor Planning and Control\r\nfor Optimally Tracking Targets\u201d, International Journal of Robotics\r\nResearch, vol. 22, no. 1, pp. 7-20, 2003.\r\n[5] T. Nakamoto, H. Ishida, and T. Moriizumi, \u201cActive Odor Sensing\r\nSystem\u201d, in Proc. Intl. Symposium on Industrial Electronics, vol. 1,\r\npp. SS128-SS133, 1997.\r\n[6] J.R. Frost and L.D. Stone, \u201cReview of Search Theory: Advances and\r\nApplications to Search and Rescue Decision Support\u201d, Technical Report\r\nCG-D-15-01, U.S. Coast Guard Research and Development Center,\r\nGronton, CT, 2001.\r\n[7] T. Heng, Y. Kuno, and Y. Shirai, \u201cActive Sensor Fusion for Collision\r\nAvoidance\u201d, in Proc of the IEEE\/RSJ Int. Conf. on Intelligent Robots\r\nand Systems, vol. 3, pp. 1244-1249, 1997.\r\n[8] Rahili, S., Ren, W., \u201cGame Theory Control Solution for Sensor Coverage\r\nProblem in Unknown Environment\u201d, 53rd IEEE Conference on Decision\r\nand Control (CDC), pp.1173-1178, 2014.\r\n[9] W. Yatao and L. Pavel,\u201cA Modified Q-Learning Algorithm for Potential\r\nGames\u201d, Proceedings of the 19th IFAC World Congress, vol.19, pp.\r\n8710-8718, 2014.\r\n[10] J. Marden and A. Wierman, \u201cDistributed Welfare Games with\r\nApplications to Sensor Coverage\u201d, 47th IEEE Conference on Decision\r\nand Control, pp. 1708-1713, 2008.\r\n[11] Pavel, L.,\u201cGame Theory and Evolutionary Games\u201d, ECE1657,\r\nUniversity of Toronto, Toronto, 2014.\r\n[12] H. Bayram and H. Bozma, \u201cMulti-robot Communication Network\r\nTopology via Centralized Pairwise Games\u201d, 2013 IEEE International\r\nConference on Robotics and Automation, 2013.\r\n[13] Chung, T.H., Gupta, V., Burdick, J.W., Murray, R.M.,\u201cOn a\r\nDecentralized Active Sensing Strategy using Mobile Sensor Platforms\r\nin a Network\u201d, 43rd IEEE Conference on Decision and Control (CDC),\r\npp.1914-1919, Vol. 2, 2004.\r\n[14] J. Cortes, S. Martinez, T. Karatas, and F. Bullo, \u201cCoverage Control\r\nfor Mobile Sensing Networks\u201d, IEEE Transactions on Robotics and\r\nAutomation, vol. 20, no. 2, pp. 243-255, 2004.\r\n[15] J. Cortes, S. Martinez and F. Bullo, \u201cSpatially-distributed Coverage\r\nOptimization and Control with Limited-range Interactions\u201d, ESAIM:\r\nControl, Optimisation and Calculus of Variations, vol. 11, no. 4, pp.\r\n691-719, 2005.\r\n[16] A. Kwok and S. Martinez, \u201cDeployment Algorithms for A\r\nPower-constrained Mobile Sensor Network\u201d, IEEE International\r\nConference on Robotics and Automation, 2008.\r\n[17] J. R. Marden and J. S. Shamma, \u201cRevisiting Log-linear Learning:\r\nAsynchrony, Completeness and Payoff-based Implementation\u201d, Games\r\nand Economic Behavior, vol. 75, no. 2, pp. 788-808, 2012.\r\n[18] A. P. Dempster, N. M. Laird, and D. B. Rubin, \u201cMaximum Likelihood\r\nfrom Incomplete Data via The EM Algorithm\u201d, Journal of the Royal\r\nStatistical Society Series B, vol. 39, no. 1, pp. 1-38, 1977.\r\n[19] V. Lakshmanan and J. S. Kain, \u201cA Gaussian Mixture Model Approach\r\nto Forecast Verification\u201d, Weather and Forecasting, vol. 25, pp. 908-920,\r\n2010.\r\n[20] Y. Lim and J. S. Shamma, \u201cRobustness of Stochastic Stability in Game\r\nTheoretic Learning\u201d, ACC, pp. 6145-6150, 2013.\r\n[21] Akaike, H., \u201cA New Look at The Statistical Model Identification\u201d, IEEE\r\nTransactions on Automatic Control, vol.19, no.6, pp. 716-723, 1974\r\n[22] N. Ueda, R. Nakano, Z. Ghahramani and G. Hinton, \u201dSplit and Merge\r\nEM Algorithm for Improving Gaussian Mixture Density Estimates\u201d, The\r\nJournal of VLSI Signal Processing, vol. 26, no. 12, pp. 133-140, 2000.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 127, 2017"}