Visibility-Based Finite-Horizon Target Tracking Game

Abstract

In this letter, we address a visibility-based target-tracking problem in which a mobile observer tries to track a mobile target for a finite time. In order to ensure tracking guarantees for the observer, we formulate the problem as a finite-horizon zero-sum game between the observer and the target. First, we use optimal control theory in conjunction with geometric techniques to solve the problem around a corner. We show that the solution to the optimal control problem for both players is in Nash equilibrium. Next, we partition the visibility polygon of the pursuer and evader based on the winner of the game. These are the projections of the escape set and capture set on the workspace. Finally, we use the partition to construct a region that bounds the set of initial positions of the observer from which it can track the target in an environment containing multiple obstacles for the prespecified time horizon.