Semi-Explicit Solutions to the Prying-Pedestrian Surveillance-Evasion Differential Game and Extensions to Two Pursuers

Philipp Braun, Daniel Coutinho, Timothy L. Molloy, Iman Shames

In [1], the authors recently proposed and solved a surveillance-evasion differential game in which an agile pursuer (the prying pedestrian) seeks to remain within a given surveillance range of a less agile evader for as long as possible while the evader seeks to escape as quickly as possible. In this paper, we provide initial results that extend this game from the 1 versus 1 (1v1) setting to a 2 versus 1 (2v1) setting with two pursuers and one evader. By deriving and exploiting semi-explicit or geometric reinterpretations of the existing 1v1 results, we derive partial solutions to the 2v1 game for the case of static pursuers and for the case of an evader that is at least twice as fast as the pursuers. While the 2v1 results of this paper build on the 1v1 results of [1], a different solution approach is developed to avoid a coordinate transformation that reduces the 1v1 game to two dimensions but which is ineffective at simplifying the 2v1 game. Beyond enabling progress on the 2v1 game, our new approach yields new geometric interpretations of the optimal pursuer and evader strategies in the 1v1 game, and opens further possible extensions.