Stochastic Event Capture Using Mobile Sensors

Mobile sensors cover more area over a fixed period of time than the same number of stationary sensors. However, the quality ofcoverage achieved by mobile sensors depends on the velocity, mobility pattern, number of mobile sensors deployed and the dynamicsof the phenomenon being sensed. The gains attained by mobile sensors over static sensors and the optimal motion strategies formobile sensors are not well understood. In this paper we consider the following event capture problem: The events of interest arriveat certain points in the sensor field and fade away according to arrival and departure time distributions. An event is said to be capturedif it is sensed by one of the mobile sensors before it fades away. We analyze how the quality of coverage scales with velocity, pathand number of mobile sensors. We characterize cases where the deployment of mobile sensors has no advantage over static sensorsand 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 sensor trajectory and theminimum speed required to satisfy a bound on the event loss probability and (ii) for sensors with fixed speed, what is the minimumnumber of sensors required to satisfy a bound on the event loss probability.When the robots are restricted to move along a line or a closed curve, our algorithms return the optimal velocity for the minimumvelocity problem. For the minimum sensor problem, the number of sensors used is within a factor of 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 planningproblems and bound their performance with respect to the optimal.