Occupation Point Planning and Tracking Control of an Underactuated Multi-Robot System to Capture a Fast Evader

This paper presents a cooperative mechanism for capturing a fast evader in a 2D space with obstacles, using a multi-robot system with a positive capture radius. First, we define the dominance region with a Cartesian oval, parameterized by the speed ratio and capture radius, and derive the minimum number of pursuers required for successful capture. Second, we develop explicit strategies to construct a defense manifold and a coverage mapping rule for occupation points, ensuring that pursuers maintain and shrink the defensible area until the evader is captured. Finally, we design a state- feedback control law for the pursuers described by second-order nonlinear underactuated dynamics, enabling finite-time tracking of occupation points while avoiding collisions and exposure. The proposed method is also applicable to heterogeneous scenarios with both high- and low-speed pursuers. Simulations and experiments with ground mobile robots validate the effectiveness of our approach.