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Vehicle Placement to Intercept Moving Targets

By Shaunak D. Bopardikar, Stephen L. Smith and Francesco Bullo


Abstract — We address optimal placement of vehicles with simple motion, to intercept a mobile target that arrives stochastically on a line segment. The optimality of vehicle placement is measured through a cost function associated with intercepting the target. With a single vehicle, we assume that the target either moves with fixed speed and in a fixed direction or moves to maximize the vertical height or intercept time. We show that each of the corresponding cost functions is convex, has smooth gradient and has a unique minimizing location, and so the optimal vehicle placement is obtained by any standard gradient-based optimization technique. With multiple vehicles, we assume that the target moves with fixed speed and in fixed direction. We present a discrete time partitioning and gradientbased algorithm, and characterize conditions under which the algorithm asymptotically leads the vehicles to a set of critical configurations of the cost function. I

Year: 2013
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