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We study a pursuit-evasion problem which can be viewed as an extension of thekeep-away game. In the game, pursuer(s) will attempt to intersect or catch theevader, while the evader can visit a fixed set of locations, which we denote asthe anchors. These anchors may or may not be stationary. When the velocity ofthe pursuers is limited and considered low compared to the evaders, we areinterested in whether a winning strategy exists for the pursuers or theevaders, or the game will draw. When the anchors are stationary, we show analgorithm that can help answer the above question.  The primary motivation for this study is to explore the boundaries betweenkinematic and dynamic constraints. In particular, whether the solution of thekinematic problem can be used to speed up the search for the problems withdynamic constraints and how to discretize the problem to utilize such relationsbest. In this work, we show that a geometric branch-and-bound type of approachcan be used to solve the stationary anchor problem, and the approach and thesolution can be extended to solve the dynamic problem where the pursuers havedynamic constraints, including velocity and acceleration bounds.

Planning and Formulations in Pursuit-Evasion: Keep-away Games and Their Strategies