Characterization of the game of two cars using reachable sets for feedback strategies

摘要

In this paper, a capture criterion for the game of two cars is derived in terms of subsets of the reachable sets of pursuer and evader. A special case of the game of two cars is considered where the pursuer is faster and more agile than the evader. It is shown that, mere containment of the evader's reachable set in the reachable set of pursuer is not a sufficient condition for capture. Some special subsets of reachable sets called the continuous subsets are introduced for the pursuer and the evader. Time optimal capture of the evader by the pursuer is characterized in terms of these continuous subsets. The trajectories predicted by this criterion match the trajectories obtained by numerically solving the pursuit-evasion game.