A computationally efficient feedback solution for a particular case of the game of two cars

Abstract

In this paper, a time-optimal feedback solution to the game of two cars is obtained for the case where the pursuer is faster and more agile than the evader. It is shown that the saddle point strategies for both the pursuer and the evader are coincident with one of the common tangents from the minimum radius turning circles of the pursuer to the minimum radius turning circles of the evader when the evader is distant enough from the pursuer. Four valid tangents are identified using geometry and a $2\times 2$ matrix game is formulated corresponding to these tangents. The solution of this game, at each instant, provides feedback strategies for the pursuer and the evader. The computations required to implement this law are insignificant and hence the proposed feedback law is suitable for real time implementation.