Pursuit-evasion (P-E) problem has been studied as a noncooperative zero-sum game in homicidal chauffer problem in 1960s and in the game of two identical cars most recently. The capture conditions in the two games, which govern the capture behavior, can be determined by solving Hamilton-Jacobi-Isaacs equations. However, the existing game theoretic solution does not consider wheel slip, and consequently, cannot answer the escape and capture conditions in the presence of wheel slip. In this paper, we investigate how to predict capture and escape conditions when the pursuer has wheel slip. We study a dynamic P-E game problem with a nonholonomic wheeled mobile robot (WMR) pursuer subject to wheel slip and propose an equivalent kinematic model to develop escape and capture conditions in the presence of wheel slip. To our knowledge, this is the first time the P-E game problems with WMR have been analyzed with wheel slip. The presented framework will allow future development of realistic P-E strategies that do not ignore wheel slip and thus will be able to model high-speed P-E on different terrains.
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