Optimal Motion Strategies to Track and Capture a Predictable Target

We present an O(n log n)-time algorithm for computing the optimal mobile robot motion strategy that maintains line-of-sight visibility of a moving target inside a polygonal region with n vertices which may contain holes. The algorithm is optimal for the tracking robot (the observer) in the sense that the computed path will ensure that the target remains visible for the longest possible time, or succeeds in capturing the target in the minimum time when the target cannot escape the observer’s visibility. Thus, the algorithm maximizes the minimum time-to-escape. Our algorithm assumes that the target moves along a know path. Thus, it is an off-line algorithm. Our theoretical results for the algorithm’s runtime assume that the target is moving along a shortest path from its source to its destination. This assumption, however is not required to prove the optimality of the computed solution, hence the algorithm remains correct for the general case. Keywords— Target tracking, escape time, robotics, computational geometry, motion planning.