Encirclement Guaranteed Finite-Time Capture against Unknown Evader Strategies

Abstract

We consider a pursuit-evasion scenario involving a group of pursuers and a single evader in a two-dimensional unbounded environment. The pursuers aim to capture the evader in finite time while ensuring the evader remains enclosed within the convex hull of their positions until capture, without knowledge of the evader's heading angle. Prior works have addressed the problem of encirclement and capture separately in different contexts. In this paper, we present a class of strategies for the pursuers that guarantee capture in finite time while maintaining encirclement, irrespective of the evader's strategy. Furthermore, we derive an upper bound on the time to capture. Numerical results highlight the effectiveness of the proposed framework against a range of evader strategies.

Figures (9)

• Figure 1: Examples of triangulation with an evader lying inside the convex hull of $3$ pursuers (left) and $8$ pursuers (right).
• Figure 2: Range of strategies for the active pursuers that guarantee encirclement of the evader, regardless of its strategy, when $v_i=1$ for all $i \in [n]$ and $\mu_m \leq 1$. In this figure, the angles $\varphi_1$ and $\varphi_2$ are given by $\varphi_1=\sin^{-1}(\mu_m)$ and $\varphi_2=\pi-\sin^{-1}(\mu_m)$. Thus, $\varphi_l \in [\varphi_1,\varphi_2]$, where $l \in \{j,k\}$ and the angles are measured from the direction of the respective unit vectors towards the evader for $p_j$ and $p_k$ and considered as positive in the outward direction from $\mathcal{H}$.
• Figure 3: Encirclement guaranteed capture under the greedy policy of the evader with three pursuers. The evader moves away from the nearest pursuer at each instant throughout the pursuit. The evader is always encircled and is captured at $t=1.25 \, \text{s}$.
• Figure 4: Encirclement guaranteed capture under the switching policy of the evader with three pursuers. The evader moves to the closest edge by $0.5 \, \text{s}$ and switches between moving to the closest edge and moving towards the interior for every $0.15 \, \text{s}$. The evader is always encircled and is captured at $1.2 \, \text{s}$.
• Figure 5: Encirclement guaranteed capture with three pursuers under random policies adopted by a human-like evader. The evader remains encircled and is captured at $1.19 \, \text{s}$.

Theorems & Definitions (14)

• Definition 1: Encirclement Condition
• Definition 2: Finite-Time Capture Condition
• Definition 3: Redundant Pursuers
• Definition 4: Active Edge and Active Pursuers
• Proposition 1
• Theorem 1
• proof
• Corollary 1
• proof
• Remark 1