Mobile sensors cover more area over a period of time than the same number of stationary sensors. However, the quality of coverage achieved by mobile sensors depends on the velocity, mobility pattern, number of mobile sensors deployed and the dynamics of the phenomenon being sensed. The gains attained by mobile sensors over static sensors and the optimal motion strategies for mobile sensors are not well understood. In this paper we consider the problem of event capture using mobile sensors. The events of interest arrive at certain points in the sensor field and fade away according to arrival and departure time distributions. An event is said to be captured if it is sensed by one of the mobile sensors before it fades away. For this scenario we analyze how the quality of coverage scales with the velocity, path and number of mobile sensors. We characterize the cases where the deployment of mobile sensors has no advantage over static sensors and find the optimal velocity pattern that a mobile sensor should adopt.We also present algorithms for two motion planning problems: (i) for a single sensor, what is the minimum speed and sensor trajectory required to satisfy a bound on event loss probability and (ii) for sensors with fixed speed, what is the minimum number of sensors required to satisfy a bound on event loss probability. When events occur only along a line or a closed curve our algorithms return optimal velocity for the minimum velocity problem. For the minimum sensor problem, the number of sensors used is within a factor two of the optimal solution. For the case where the events occur at arbitrary points on a plane we present heuristic algorithms for the above motion planning problems and bound their performance with respect to the optimal. The results of this paper have wide range of applications in areas like surveillance, wildlife monitoring, hybrid sensor networks and under-water sensor networks.
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