Abstract. 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 certain coverage performance metric, respectively. Numerical examples are provided to verify the performance of our proposed algorithms. There is a widespread belief that continuous and pervasive monitoring will be possible in the near future with large numbers of networked, mobile, and wireless sensors. Thus, we are witnessing an intense research activity that focuses on the design of efficient control mechanisms for these systems. In particular, distributed algorithms would allow sensor networks to react autonomously to unanticipated changes with minimal human supervision. A substantial body of research on sensor networks has concentrated on simple sensors that can collect scalar data; e.g., temperature, humidity, or pressure data. A main objective is the design of algorithms that can lead to optimal collective sensing through efficient motion control and communication schemes. However, scalar measurements can be insufficient in many situations; e.g., automated surveillance or traffic monitoring. In contrast, data-intensive sensors such as cameras can collect visual data that are rich in information, thus having tremendous potential for monitoring applications, but at the cost of a higher processing overhead or energy cost. Precisely, this paper aims to solve a coverage optimization problem taking into account part of the sensing/processing trade-off. Coverage optimization problems have mainly been formulated as cooperative problems where each sensor benefits from sensing the environment as a member of a group. However, sensing may also require expenditure; e.g., the energy consumed or the time spent by data processing algorithms in sensor networks. Because of this, we endow each sensor with a utility function that quantifies this trade-off, formulating a coverage problem as a variation of the congestion games in [29] . Literature review. In broad terms, the problem studied here is related to a bevy of sensor location and planning problems in the Computational Geometry, Geometric Optimization, and Robotics literature. Regarding camera networks (a class of sensors that motivated this work), we can refer to different variations on the (combinatorial) Art Gallery problem include [27] [31] [35] . The objective here is how to find the optimum number of guards in a non-convex environment so that each point is visible from at least one guard. A related set of references for the deployment of mobile robots with omnidirectional cameras includes [13] [12] . Unlike the Art Gallery classic algorithms, the latter papers assume that robots have local knowledge of the environ-
Zhu and Martínez REF developed a repeated game to solve the coverage optimization problem of mobile sensors.
DISTRIBUTED COVERAGE GAMES FOR ENERGY-AWARE MOBILE SENSOR NETWORKS
SIAM J. Control and Optimization
SIAM J. Control and Optimization
Mathematics Computer Science