Multiple Pursuer Multiple Evader Differential Games

2020 American Control Conference (ACC), 2020

Pursuit and evasion conflicts represent challenging problems with important applications in aerospace and robotics. In pursuit-evasion problems, synthesis of intelligent actions must consider the adversary's potential strategies. Differential game theory provides an adequate framework to analyze possible outcomes of the conflict without assuming particular behaviors by the opponent. This article presents an organized introduction of pursuit-evasion differential games with an overview of recent advances in the area. First, a summary of the seminal work is outlined, highlighting important contributions. Next, more recent results are described by employing a classification based on the number of players: one-pursuer-one-evader, N-pursuers-one-evader, one-pursuer-M-evaders, and N-pursuer-M-evader games. In each scenario, a brief summary of the literature is presented. Finally, two representative pursuit-evasion differential games are studied in detail: the two-cutters and fugitive ship differential game and the active target defense differential game. These problems provide two important applications and, more importantly, they give great insight into the realization of cooperation between friendly agents in order to form a team and defeat the adversary.

—The increasing use of unmanned assets and robots in modern military operations renews an interest in the study of general pursuit-evasion games involving multiple pursuers and multiple evaders. Due to the difficulty in formulation and rigorous treatment, the literature in this field is very limited. This paper presents a hierarchical approach to this kind of problem. With an additional structure imposed on decision-making of pursuers, this approach provides conservative guidance to pursuers by finding certain engagement between pursuers and evaders, and the saddle-point strategies are utilized by each pursuer in chasing the engaged evaders. A combinatorial optimization problem is formulated and scenarios are created to demonstrate the feasibility of the algorithm. This is a preliminary study on multi-player pursuit-evasion games and future directions are suggested.

2008

This paper considers a game problem with many pursuers described by infinite systems of differential equations of second order. On the controls of players geometric constraints are imposed. The aim of the pursuers is to capture the evader, while the aim of the evader is the opposite. The theorem on evasion is proved in this paper.

Proceedings of the 44th IEEE Conference on Decision and Control, 2005

The increasing use of unmanned assets and robots in modern military operations renews an interest in the study of general pursuit-evasion games involving multiple pursuers and multiple evaders. Due to the difficulty in formulation and rigorous treatment, the literature in this field is very limited. This paper presents a hierarchical approach to this kind of problem. With an additional structure imposed on decision-making of pursuers, this approach provides conservative guidance to pursuers by finding certain engagement between pursuers and evaders, and the saddle-point strategies are utilized by each pursuer in chasing the engaged evaders. A combinatorial optimization problem is formulated and scenarios are created to demonstrate the feasibility of the algorithm. This is a preliminary study on multi-player pursuit-evasion games and future directions are suggested.

Automatica, 2019

Multi-player pursuit-evasion games are crucial for addressing the maneuver decision problem arising in the cooperative control of multi-agent systems. This work addresses a particular pursuit-evasion game with three players, Target, Attacker, and Defender. The Attacker aims to capture the Target, while avoiding being captured by the Defender and the Defender tries to defend the Target from being captured by the Attacker, while trying to capture the Attacker at an opportune moment. A two-pronged pursuit-evasion problem in this game is considered and we focus on two aspects: the cooperation between the Target and Defender and balancing the roles of the Attacker between pursuer and evader. A barrier based on the explicit policy method and geometric analysis method is constructed to separate the whole state space into two disjoint parts that correspond to two winning regions for the Attacker and Target-Defender team. The main contributions of this work are obtaining the players' winning regions and providing a complete game solution by analyzing the optimal strategies and trajectories of the players based on the barrier.

Journal of Applied Mathematics, 2012

We consider an evasion differential game of many pursuers and one evader with integral constraints in the plane. The game is described by simple equations. Each component of the control functions of players is subjected to integral constraint. Evasion is said to be possible if the state of the evader does not coincide with that of any pursuer. Strategy of the evader is constructed based on controls of the pursuers with lag. A sufficient condition of evasion from many pursuers is obtained and an illustrative example is provided.

2013

We consider an evasion differential game of many pursuers and one evader with integral constraints in the space R3. The game is described by simple equations. Control functions of the players are subjected to coordinate-wise integral constraints. Evasion is said to be possible if the state of the evader does not coincide with that of any pursuer. Strategy of the evader is constructed based on controls of the pursuers with lag. A sufficient condition of evasion from many pursuers is obtained and an illustrative example is provided.

Proceedings of the 17th IFAC World Congress, 2008, 2008

Pursuit-evasion (PE) differential games have recently received much attention in military applications involving adversaries. We extend the PE game problem to a problem of defending target, where the roles of the players are changed. The evader is to attack some fixed target, whereas the pursuer is to defend the target by intercepting the evader. We propose a practical strategy design approach based on the linear quadratic game theory with a receding horizon implementation. We prove the existence of solutions for the Riccati equations associated with games with simple dynamics. Simulation results justify the method.

Dynamic Games and Applications, 2018

A novel pursuit-evasion differential game involving three agents is considered. An Attacker missile is pursuing a Target aircraft. The Target aircraft is aided by a Defender missile launched by, say, the wingman, to intercept the Attacker before it reaches the Target aircraft. Thus, a team is formed by the Target and the Defender which cooperate to maximize the separation between the Target aircraft and the point where the Attacker missile is intercepted by the Defender missile, while at the same time the Attacker tries to minimize said distance. A long-range Beyond Visual Range engagement which is in line with current CONcepts of OPeration is envisaged, and it is therefore assumed that the players have simple motion kinematics á la Isaacs. Also, the speed of the Attacker is equal to the speed of the Defender and the latter is interested in point capture. It is also assumed that at all time the Attacker is aware of the Defender's position, i.e., it is a perfect information game. The analytic/closedform solution of the target defense pursuit-evasion differential game delineates the state space region where the Attacker can reach the Target without being intercepted by the Defender, thus disposing of the Game of Kind. The target defense Game of Degree is played in the remaining state space. The analytic solution of the Game of Degree yields the agents' optimal state feedback strategies, that is, the instantaneous heading angles for the Target and the Defender team to maximize the terminal separation between Target and Attacker at the instant of Electronic supplementary material The online version of this article (

Journal of Optimization Theory and Applications, 2021