Construction of Barrier in a Fishing Game With Point Capture

Abstract

This paper addresses a particular pursuit-evasion game, called as "fishing game" where a faster evader attempts to pass the gap between two pursuers. We are concerned with the conditions under which the evader or pursuers can win the game. This is a game of kind in which an essential aspect, barrier, separates the state space into disjoint parts associated with each player's winning region. We present a method of explicit policy to construct the barrier. This method divides the fishing game into two subgames related to the included angle and the relative distances between the evader and the pursuers, respectively, and then analyzes the possibility of capture or escape for each subgame to ascertain the analytical forms of the barrier. Furthermore, we fuse the games of kind and degree by solving the optimal control strategies in the minimum time for each player when the initial state lies in their winning regions. Along with the optimal strategies, the trajectories of the players are delineated and the upper bounds of their winning times are also derived.

Multi-player pursuit–evasion games with one superior evader

“…First, we provide a brief introduction to our previous work on the fishing game [26], which is played in the plane by two pursuers and one superior evader. The evader attempts to pass the gap between the two pursuers (as shown in Fig.…”

“…4 shows the possible position of the evader (shaded region) satisfying the conditions (12)∼ (13). According to the characteristics of barrier [26], we know that the boundary of shaded region is exactly the barrier of multiplayer fishing game, and correspondingly the shaded region represents the capture zone. Based on the previous work [26], the optimal strategies of the players are accessible to describe as follows:…”

“…To cope with the above challenges, researchers generally demonstrate the possibility of capture or escape by exhibiting some particular strategies or policies of the players [1,3,5,6,16,26]. These methods can be collectively referred to as "method of explicit policy" [14,26]. For example, [5] proposed a sweep-pursuit-capture strategy to capture a single evader for multiple pursuers in an unbounded planar environment and determined the minimum probability of capture.…”

“…In our previous work [26], a fishing game is introduced, which bears resemblance to the pursuit game in [13], i.e., the superior evader must pass the gap between two pursuers. We obtained a complete solution which can be utilized to induce the analysis of capture conditions for the current multi-player game, because the evader will exert itself to break through the encirclement against some two adjacent pursuers on each instant of time.…”

Reach-Avoid Problems via Sum-or-Squares Optimization and Dynamic Programming

“…Compared to previous dynamic programming-based work such as [6], [8], [15], we trade off optimality of solution for computational complexity: although our method produces conservative reach-avoid sets, we are able to analyze systems with higher-dimensional state spaces. Unlike analytic approaches such as [17], [20], [22], our approach applies much more broadly to different problem setups and system dynamics. We demonstrate our method in simulations.…”