A Family of Switching Pursuit Strategies for a Multi-Pursuer Single-Evader Game

Abstract

This paper introduces a new family of pursuit strategies for multi-pursuer single-evader games in a planar environment. They leverage conditions under which the minimum-time solution of the game becomes equivalent to that of a suitable two-pursuer single-evader game. This enables the design of strategies in which the pursuers first aim to meet such conditions, and then transition to a two-pursuer game once they are satisfied. As a consequence, naive strategies that are in general unsuccessful, can be turned into winning strategies by switching to the appropriate two-pursuer game. Moreover, it is shown via numerical simulations that the switching mechanism significantly enhances the performance of existing pursuit algorithms, like those based on Voronoi partitions.

Figures (12)

• Figure 1: The 2-pursuer capture region for the 2P1EG.
• Figure 2: Example of multi-pursuer capture region $\mathcal{M}$ for $p=3$ (gray). Since $E\notin\mathcal{M}$, the evader can avoid capture by moving along the direction $v$.
• Figure 3: Sketch of the proof of Theorem \ref{['th:P_far1']}.
• Figure 4: (a) Set $\widehat{D}$ denoting the union of all the 2-pursuer capture regions; (b) set $\widehat{\mathcal{D}}\backslash\mathtt{int}\left\{\mathcal{P}\right\}$.
• Figure 5: Example \ref{['ex:1']}. The evader goes upwards while pursuers play S-PPS. Capture occurs at $t=22.66$.

Theorems & Definitions (24)

• Proposition 1
• Proposition 2
• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof
• Definition 1
• Theorem 4