Multi-player pursuit–evasion games with one superior evader

Inspired by the hunting and foraging behaviors of group predators, this paper addresses a class of multi-player pursuit–evasion games with one superior evader, who moves faster than the pursuers. We are concerned with the conditions under which the pursuers can capture the evader, involving the minimum number and initial spatial distribution required as well as the cooperative strategies of the pursuers. We present some necessary or sufficient conditions to regularize the encirclement formed by the pursuers to the evader. Then we provide a cooperative scheme for the pursuers to maintain and shrink the encirclement until the evader is captured. Finally, we give some examples to illustrate the theoretical results

Cooperative Pursuit with Multi-Pursuer and One Faster Free-moving Evader

This paper addresses a multi-pursuer single-evader pursuit-evasion game where the free-moving evader moves faster than the pursuers. Most of the existing works impose constraints on the faster evader such as limited moving area and moving direction. When the faster evader is allowed to move freely without any constraint, the main issues are how to form an encirclement to trap the evader into the capture domain, how to balance between forming an encirclement and approaching the faster evader, and what conditions make the capture possible. In this paper, a distributed pursuit algorithm is proposed to enable pursuers to form an encirclement and approach the faster evader. An algorithm that balances between forming an encirclement and approaching the faster evader is proposed. Moreover, sufficient capture conditions are derived based on the initial spatial distribution and the speed ratios of the pursuers and the evader. Simulation and experimental results on ground robots validate the effectiveness and practicability of the proposed method

Virtual Target Selection for a Multiple-Pursuer Multiple-Evader Scenario

This paper considers an M-pursuer N-evader scenario involving virtual targets. The virtual targets serve as an intermediary target for the pursuers, allowing the pursuers to delay their final assignment to the evaders. However, upon reaching the virtual target, the pursuers must decide which evader to capture. It is assumed that there are more pursuers than evaders and that the pursuers are faster than the evaders. The objective is two-part: first, assign each pursuer to a virtual target and evader such that the pursuer team's energy is minimized, and second, choose the virtual targets' locations for this minimization problem. The approach taken is to consider the Apollonius geometry between each pursuer's virtual target location and each evader. Using the constructed Apollonius circles, the pursuer's travel distance and maneuver at a virtual target are obtained. These metrics serve as a gauge for the total energy required to capture a particular evader and are used to solve the joint virtual target selection and pursuer-evader assignment problem. This paper provides a mathematical definition of this problem, the solution approach taken, and an example.Comment: AIAA SciTech 2024 Preprin

An All-Against-One Game Approach for the Multi-Player Pursuit-Evasion Problem

The traditional pursuit-evasion game considers a situation where one pursuer tries to capture an evader, while the evader is trying to escape. A more general formulation of this problem is to consider multiple pursuers trying to capture one evader. This general multi-pursuer one-evader problem can also be used to model a system of systems in which one of the subsystems decides to dissent (evade) from the others while the others (the pursuer subsystems) try to pursue a strategy to prevent it from doing so. An important challenge in analyzing these types of problems is to develop strategies for the pursuers along with the advantages and disadvantages of each. In this thesis, we investigate three possible and conceptually different strategies for pursuers: (1) act non-cooperatively as independent pursuers, (2) act cooperatively as a unified team of pursuers, and (3) act individually as greedy pursuers. The evader, on the other hand, will consider strategies against all possible strategies by the pursuers. We assume complete uncertainty in the game i.e. no player knows which strategies the other players are implementing and none of them has information about any of the parameters in the objective functions of the other players. To treat the three pursuers strategies under one general framework, an all-against-one linear quadratic dynamic game is considered and the corresponding closed-loop Nash solution is discussed. Additionally, different necessary and sufficient conditions regarding the stability of the system, and existence and definiteness of the closed-loop Nash strategies under different strategy assumptions are derived. We deal with the uncertainties in the strategies by first developing the Nash strategies for each of the resulting games for all possible options available to both sides. Then we deal with the parameter uncertainties by performing a Monte Carlo analysis to determine probabilities of capture for the pursuers (or escape for the evader) for each resulting game. Results of the Monte Carlo simulation show that in general, pursuers do not always benefit from cooperating as a team and that acting as non-cooperating players may yield a higher probability of capturing of the evader

Collision Free Navigation of a Multi-Robot Team for Intruder Interception

In this report, we propose a decentralised motion control algorithm for the mobile robots to intercept an intruder entering (k-intercepting) or escaping (e-intercepting) a protected region. In continuation, we propose a decentralized navigation strategy (dynamic-intercepting) for a multi-robot team known as predators to intercept the intruders or in the other words, preys, from escaping a siege ring which is created by the predators. A necessary and sufficient condition for the existence of a solution of this problem is obtained. Furthermore, we propose an intelligent game-based decision-making algorithm (IGD) for a fleet of mobile robots to maximize the probability of detection in a bounded region. We prove that the proposed decentralised cooperative and non-cooperative game-based decision-making algorithm enables each robot to make the best decision to choose the shortest path with minimum local information. Then we propose a leader-follower based collision-free navigation control method for a fleet of mobile robots to traverse an unknown cluttered environment where is occupied by multiple obstacles to trap a target. We prove that each individual team member is able to traverse safely in the region, which is cluttered by many obstacles with any shapes to trap the target while using the sensors in some indefinite switching points and not continuously, which leads to saving energy consumption and increasing the battery life of the robots consequently. And finally, we propose a novel navigation strategy for a unicycle mobile robot in a cluttered area with moving obstacles based on virtual field force algorithm. The mathematical proof of the navigation laws and the computer simulations are provided to confirm the validity, robustness, and reliability of the proposed methods