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

Abstract

In this paper, a reachability-based approach is adopted to deal with the pursuit-evasion differential game between one evader and multiple pursuers in the presence of dynamic environmental disturbances (for example, winds or sea currents). Conditions for the game to be terminated are given in terms of reachable set inclusions. Level set equations are defined and solved to generate the forward reachable sets of the pursuers and the evader. The time-optimal trajectories and the corresponding optimal strategies are subsequently retrieved from these level sets. The pursuers are divided into active pursuers, guards, and redundant pursuers according to their respective roles in the pursuitevasion game. The proposed scheme is implemented on problems with both simple and realistic time-dependent flowfields, with and without obstacles.

Game Theory for Unmanned Vehicle Path Planning in the Marine Domain: State of the Art and New Possibilities

“…In [24], a reachability-based approach is proposed to deal with the pursuit-evasion differential game between two players in the presence of dynamic environmental disturbances (e.g., winds, sea currents). In [33], the authors extend the previous work to the case of multiple pursuers. In [29], the authors validate the efficacy of the proposed methodology with testing in realistic data-assimilative simulated environments.…”

Graph-Search and Differential Equations for Time-Optimal Vessel Route Planning in Dynamic Ocean Waves

“…Additional areas of development for VISIR may include some problems already addressed through the LSE, such as interceptions and multi-waypoint missions [29], [55], [56], energy optimization [54], onboard learning [57], and clustering of vessels to low-risk routes in uncertain flow environments [67]- [69].…”

“…Thus, time-optimal path planning consists of two steps: i) the propagation of the reachability front by numerically computing the viscosity solution of (2); ii) computation of the time-optimal trajectory by solving (3) (to be understood in the generalized gradient sense). Numerical schemes have been developed to complete the above steps [25] and generalized for various optimality criteria, including the time-, energy-, coordination-, and interception-optimal planning of swarms of AUVs in realistic data-assimilative dynamic ocean re-analyses [26], [51]- [56]. This was also recently utilized successfully in real-time exercises at sea with real AUVs [28], [57].…”

Sequential pursuit of multiple targets under external disturbances via Zermelo–Voronoi diagrams

“…Another promising direction is to develop new ZVD update algorithms as well as consideration of more complicated flow fields, including pursuit-evasion scenarios with obstacles, etc. For some initial results along this direction, see [26].…”