A geometrical approach to problems of pursuit-evasion games

Pursuit-evasion games in dynamic flow fields via reachability set analysis

“…These definitions with respect to the reachable sets lead to the following proposition, which is an extension of Theorem I in [10], where the authors derive the condition for capture under the assumption of linear dynamics for both players and a finite energy constraint for the controls.…”

“…The algorithm contains the following three steps: 1. Evolution of Forward Reachable Sets: In cases when u ≥v, the forward reachable sets of the pursuer and the evader are evolved by computing the viscosity solutions to the unsteady HJ equations (10) and (11) respectively. These evolutions are carried out until the reachable set of the evader is fully covered by that of the pursuer.…”

“…Our approach differs from those in [21], [22] since we do not attempt to solve the pursuit-evasion game directly by solving the HJI equation. Instead, we generate the forward reachable sets of the players separately and find the optimal time-to-capture as the first time when the reachable set of the evader is fully covered by the reachable set of the pursuer [10]. We then identify the first rendezvous point of the players and retrieve the optimal trajectories and controls of both players through backtracking of their respective trajectories [23]- [25].…”

Multiple-Pursuer/One-Evader Pursuit–Evasion Game in Dynamic Flowfields

“…Besides the HJI equation approach, another approach researchers have used when dealing with pursuit-evasion problems is based on reachable set analysis [13][14][15]. According to this approach, the reachable state space of the pursuers and the evaders is used to find the optimal controls of the pursuer and/or the evader.…”

“…Our approach differs from that in [25] because we do not attempt to solve the pursuit-evasion game directly by solving the corresponding HJI equation. Instead, we generate the forward reachable sets of the players, and we find the optimal time to capture as the first instance when the reachable set of the evader is fully covered by the reachable set of the pursuer [14]. We then identify the first rendezvous point of the players and retrieve the optimal trajectories and controls of both players through backtracking of their respective trajectories [27,28].…”