Area-Optimal Control Strategies for Heterogeneous Multi-Agent Pursuit

TL;DR

This paper introduces a geometric, area-minimization pursuit strategy for heterogeneous multi-agent systems, enabling real-time, cooperative capture of a slower evader through gradient-based control laws.

Contribution

It develops a novel geometric framework and analytical control laws for multi-agent pursuit, optimizing the evader's safe region to guarantee capture.

Findings

Gradient-based controls effectively reduce the evader's safe region.

The strategy enables real-time, cooperative pursuit with guaranteed capture.

Simulations confirm the approach's efficiency and robustness.

Abstract

This paper presents a novel strategy for a multi-agent pursuit-evasion game involving multiple faster pursuers with heterogenous speeds and a single slower evader. We define a geometric region, the evader's safe-reachable set, as the intersection of Apollonius circles derived from each pursuer-evader pair. The capture strategy is formulated as a zero-sum game where the pursuers cooperatively minimize the area of this set, while the evader seeks to maximize it, effectively playing a game of spatial containment. By deriving the analytical gradients of the safe-reachable set's area with respect to agent positions, we obtain closed-form, instantaneous optimal control laws for the heading of each agent. These strategies are computationally efficient, allowing for real-time implementation. Simulations demonstrate that the gradient-based controls effectively steer the pursuers to systematically shrink the evader's safe region, leading to guaranteed capture. This area-minimization approach provides a clear geometric objective for cooperative capture.