Multiple Pursuers Versus One Evader Reach-Avoid Differential Games With Asymmetric Observations

Abstract

This paper considers a multiple-pursuer-one-evader reach-avoid (RA) differential game in a two-dimensional (2D) plane that is split by a straight line into a goal region and a play region. The evader aims to enter the goal region from the play region without being captured, while the pursuers try to intercept the evader in the play region. In terms of information structures, we assume that the evader has perfect information about the game, while the pursuers have uncertain observations of the evader’s location and speed. First, a robust estimation of the safe region (RESR) is constructed by computing the safe region boundary beliefs with respect to these uncertainties. Based on the RESR, the winning condition for the one-on-one RA game is analyzed, and an optimal interception strategy is derived. A proximity strategy is also proposed when the winning condition is not satisfied. Then, the concept of effective coalition is studied and its properties are proposed to enhance the robustness of the strategy. Additionally, a receding horizon cooperation algorithm with a strategy switching mechanism is designed for the pursuers to cooperatively capture the evader under distance-related observation uncertainties. Finally, simulations and experiments are conducted to validate the effectiveness of the proposed strategies. Note to Practitioners—This paper is motivated by practical considerations of the reach-avoid game, in which players have different capacities for observation. In most related works, pursuers and evaders are assumed to have perfect information about the game. Optimal strategies are derived from safe regions (SR) determined by perfect information. Our objective is to challenge this assumption and study the robust pursuit strategy from the perspective of the pursuers under observational uncertainty. We approach observational uncertainty in two ways. On the one hand, to obtain the SR of the evader, we construct the robust estimation of the safe region (RESR) and identify its <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\sigma $ </tex-math></inline-formula> principle boundary with theoretical guarantees. On the other hand, to mitigate the impact of observational uncertainty on pursuit strategies, we propose the concept of effective coalition, which can compress the RESR of the evader and capture the evader farther if acting individually. By combining these contributions, we design a receding horizon strategy for the pursuit coalition that is tailored for the autonomous multi-agent system in robotics, defense, and surveillance. At present, this method cannot be used directly in the multi-pursuer versus multi-evader game scenario. Future studies will investigate the scalability of this method.