A Parallelizable Reachable Set Method for Pursuit-Evasion Games Using Interior-Point Methods

This paper focuses on time-optimal pursuit-evasion games. The paper describes a method to compute reachable sets for deterministic systems with convex constraints. For stochastic systems, a conservative approximation is introduced so that a deterministic system results. Reachable sets are calculated using an algorithm that produces a polytopic inner estimate of the actual reachable set. A pursuit-evasion game is then introduced, and it is shown that it can be solved using reachable set analysis. The optimal termination point for the game lies on the boundary of the pursuer's and evader's reachable sets. Several examples are worked for deterministic and stochastic capture problems. A deterministic Sun blocking problem is also solved wherein one player blocks sunlight from the other.