Improvement with Look-ahead on Cooperative Pursuit Games

Abstract

Abstract-The multi-player Pursuit-Evasion (PE) game problem has recently received a lot of attention. Hierarchical decomposition is previously proposed for multi-player differential game for a suboptimal solution [5]. Furthermore, optimization based on limited look-ahead is used to improve such a suboptimal solution [4]. However, it requires intensive computation. In this paper, through the further study on the properties of the suboptimal value function of a cooperative pursuit game, it becomes evident that the performance improvement by limited look-ahead results from the structure relaxation on pursuers' strategies when optimization is conducted. Based on a problem with certain objective and dynamics, we prove a linear structure of the improving strategies in terms of the structured controls associated with the suboptimal solution, and then optimization is parameterized by the linear weights. The problem is further transformed into a nonlinear programming problem. It is shown that computation can be reduced the decentralized implementation is possible.

Graph-based strategies for multi-player pursuit evasion games

“…Fig.3 illustrates the evolution of all the eigenvalues under u 2−6 46th IEEE CDC, New Orleans, USA, Dec. [12][13][14]2007 ThC05.3…”

“…In a (bipartite) graph model of a multi-player problem, this relation is not that clear since all possible links between the pursuers and the evaders are taken into account. This is very important in a cooperative pursuit problem [12], [13]. In what follows, we study the feasibility of designing control laws based on the generalized connectivity and the emerging cooperative players' behavior.…”

“…We select K = min{M, N }, i.e., the links associated with the M evaders (or N pursuers) 46th IEEE CDC, New Orleans, USA, Dec. [12][13][14]2007 ThC05.3 are considered. Here, the control based on λ 2 are no longer feasible because it only focuses on the "weakest" links.…”

“…In [12], the optimization based on limited look-ahead is used to improve the suboptimal solutions iteratively. The performance enhancement by limited lookahead is further analyzed in [13].…”

Game of Defending a Target: A Linear Quadratic Differential Game Approach

“…The increasing use of autonomous assets in modern military operations has recently led to renewed interest in Pursuit-Evasion (PE) differential games (Hespanha et al [2000], Schenato et al [2005], Li and Cruz [2006], Li et al [2008]). The PE problem is usually formulated as a zerosum game, in which the pursuer(s) tries to minimize a prescribed cost functional while the evader(s) tries to maximize the same functional (Isaacs [1965], Başar and Olsder [1998]).…”