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In this paper, a time-optimal feedback solution to the game of two cars, forthe case where the pursuer is faster and more agile than the evader, ispresented. The concept of continuous subsets of the reachable set is introducedto characterize the time-optimal pursuit-evasion game under feedbackstrategies. Using these subsets it is shown that, if initially the pursuer isdistant enough from the evader, then the feedback saddle point strategies forboth the pursuer and the evader are coincident with one of the common tangentsfrom the minimum radius turning circles of the pursuer to the minimum radiusturning circles of the evader. Using geometry, four feasible tangents areidentified and the feedback min-max strategy for the pursuer and the max-minstrategy for the evader are derived by solving a $2 \times 2$ matrix game ateach instant. Insignificant computational effort is involved in evaluating thepursuer and evader inputs using the proposed feedback control law and hence itis suitable for real-time implementation. The proposed law is validated furtherby comparing the resulting trajectories with those obtained by solving thedifferential game using numerical techniques.

A time-optimal feedback control for a particular case of the game of two cars