Cooperative Evasion by Translating Targets with Variable Speeds

We consider a problem of cooperative evasion between a single pursuer and multiple evaders in which the evaders are constrained to move in the positive Y direction. The evaders are slower than the vehicle and can choose their speeds from a bounded interval. The pursuer aims to intercept all evaders in a given sequence by executing a Manhattan pursuit strategy of moving parallel to the X axis, followed by moving parallel to the Y axis. The aim of the evaders is to cooperatively pick their individual speeds so that the total time to intercept all evaders is maximized. We first obtain conditions under which evaders should cooperate in order to maximize the total time to intercept as opposed to each moving greedily to optimize its own intercept time. Then, we propose and analyze an algorithm that assigns evasive strategies to the evaders in two iterations as opposed to performing an exponential search over the choice of evader speeds. We also characterize a fundamental limit on the total time taken by the pursuer to capture all evaders when the number of evaders is large. Finally, we provide numerical comparisons against random sampling heuristics

Min-Max Q-Learning for Multi-Player Pursuit-Evasion Games

In this paper, we address a pursuit-evasion game involving multiple players by utilizing tools and techniques from reinforcement learning and matrix game theory. In particular, we consider the problem of steering an evader to a goal destination while avoiding capture by multiple pursuers, which is a high-dimensional and computationally intractable problem in general. In our proposed approach, we first formulate the multi-agent pursuit-evasion game as a sequence of discrete matrix games. Next, in order to simplify the solution process, we transform the high-dimensional state space into a low-dimensional manifold and the continuous action space into a feature-based space, which is a discrete abstraction of the original space. Based on these transformed state and action spaces, we subsequently employ min-max Q-learning, to generate the entries of the payoff matrix of the game, and subsequently obtain the optimal action for the evader at each stage. Finally, we present extensive numerical simulations to evaluate the performance of the proposed learning-based evading strategy in terms of the evader's ability to reach the desired target location without being captured, as well as computational efficiency