Cooperative Target Capture using Voronoi Region Shaping

TL;DR

A cooperative strategy for capturing a target using multiple pursuers in a planar scenario and the Voronoi Diagram is employed to dynamically shape that region using a policy that directs its vertices towards its instantaneous centroid.

Abstract

This paper discusses a cooperative strategy for capturing a target using multiple pursuers in a planar scenario. Given an initial position distribution of pursuers, the Voronoi Diagram is employed to characterize the target's proximity region. The key idea is to dynamically shape that region using a policy that directs its vertices towards its instantaneous centroid. Analysis of the resulting dynamics deduces the velocity control inputs for the pursuers. As the main result, target's proximity region is shown to shrink exponentially irrespective of its speed and evasion policy. Simulation results demonstrate the characteristics of the proposed method.

Figures (14)

• Figure 1: Voronoi partition with multiple agents in the region. (Square and circular markers indicate the position of the evader and pursuers, respectively.)
• Figure 2: An example scenario depicting boundary shared between $S(\mathbf{x}^P_i)$ and $S(\mathbf{x}^E)$.
• Figure 3: Motion policy for the vertices of $S(\mathbf{x}^E)$.
• Figure 4: Comparison of the Chebyshev radii of $\mathcal{P}_1,\mathcal{P}_2,\mathcal{P}_3$ ($A_{\mathcal{P}_1}=A_{\mathcal{P}_2}>A_{\mathcal{P}_3}$).
• Figure 5: Largest possible circle drawn in $S(\mathbf{x}_E)$ considering $\mathbf{x}_E$ as the Chebyshev center.

Theorems & Definitions (12)

• Remark 1
• Remark 2
• Theorem 1
• proof
• Remark 3
• Proposition 1
• proof
• Definition 1
• Lemma 1
• proof