UAV Collision Avoidance based on the Solution of the Suicidal Pedestrian Differential Game

We consider the following differential game of pursuit and evasion involving two unmanned aerial vehicle agents (UAVs): an evading UAV (“evader”), which has limited maneuverability, and a pursuing UAV (“pursuer”), which is assumed to be completely agile. The two UAVs move on the Euclidean plane with different but constant speeds. Whereas the pursuer can change the orientation of its velocity vector arbitrarily fast, that is, she is a “pedestrian” á la Isaacs, the evader cannot make turns having a radius smaller than a specified minimum turning radius. This problem can be seen as a reversed roles Homicidal Chauffeur game, hence the name “Suicidal Pedestrian” differential game. The aim of this paper is to derive the optimal strategies of the two players and characterize the initial conditions that lead to capture if the pursuer acts optimally, along with the states that guarantee evasion regardless of the pursuer’s strategy. Both proximity-capture and point-capture are considered. This is a rare instance where a complete solution of a differential game can be obtained in closed-form. Utilizing the connection to Zermelo’s Navigation Problem, the two-player solution is generalized under some assumptions for the case of multiple pursuer UAVs. The results are directly applicable to collision avoidance, in the sense that safety regions are delineated in which no collision is possible, even in the worst case of malicious intent by one of the pursuers.