Optimal Evasion Against Dual Pure Pursuit *

Abstract

The Pure Pursuit strategy is ubiquitous both in the control literature but also in real-world implementation. In this paper, we pose and solve a variant of Isaacs’ Two Cutters and Fugitive Ship problem wherein the Pursuers’ strategy is fixed to Pure Pursuit, thus making it an optimal control problem. The Pursuers are faster than the Evader and are endowed with a finite capture radius. All agents move with constant velocity and can change heading instantaneously. Although capture is inevitable, the Evader wishes to delay capture as long as possible. The optimal trajectories cover the entire state space. Regions corresponding to either solo capture or isochronous (dual) capture are computed and both types of maximal time-to-capture optimal trajectories are characterized.