Encirclement Guaranteed Cooperative Pursuit with Robust Model Predictive Control

TL;DR

This work addresses encirclement guaranteed cooperative pursuit of a single evader by multiple pursuers in an unbounded 2D domain, under the constraint that the evader's action is unknown to the pursuers. It formulates a robust model predictive control approach that enforces both encirclement and capture by treating the evader's action as a disturbance, but faces bilinear encirclement constraints. To overcome this, the authors introduce an encirclement guaranteed partition (EGP) based on angle-based Regions that guarantees encirclement when each region contains at least one pursuer, reducing the problem to decentralized linear tube MPC subproblems solvable via QP. Simulations show the framework effectively achieves encirclement and capture, outperforming baseline strategies, and highlight practical guidance such as assigning four pursuers to encirclement in larger teams.

Abstract

This paper studies a novel encirclement guaranteed cooperative pursuit problem involving $N$ pursuers and a single evader in an unbounded two-dimensional game domain. Throughout the game, the pursuers are required to maintain encirclement of the evader, i.e., the evader should always stay inside the convex hull generated by all the pursuers, in addition to achieving the classical capture condition. To tackle this challenging cooperative pursuit problem, a robust model predictive control (RMPC) based formulation framework is first introduced, which simultaneously accounts for the encirclement and capture requirements under the assumption that the evader's action is unavailable to all pursuers. Despite the reformulation, the resulting RMPC problem involves a bilinear constraint due to the encirclement requirement. To further handle such a bilinear constraint, a novel encirclement guaranteed partitioning scheme is devised that simplifies the original bilinear RMPC problem to a number of linear tube MPC (TMPC) problems solvable in a decentralized manner. Simulation experiments demonstrate the effectiveness of the proposed solution framework. Furthermore, comparisons with existing approaches show that the explicit consideration of the encirclement condition significantly improves the chance of successful capture of the evader in various scenarios.

Figures (6)

• Figure 1: Red triangles represent pursuers and blue circle represents evader. Blue line represents angle-based Partition. (a) Encirclement condition. (b) Satisfaction of the encirclement condition with four pursuers. (c) Angle based partition. (d) Example of angle-based partition that is not an Encirclement Guaranteed Partition.
• Figure 2: Red circle represents pursuer. Colored line represents EGP. Blue star represents evader. Column (a): EGP with $7$ randomly generated pursuers and $4$ partitions; (b): EGP with $7$ randomly generated pursuers and $5$ partitions; (c): EGP with $7$ randomly generated pursuers and $6$ partitions; (d): Cases where no EGP exists.
• Figure 3: Simulation snapshots with the proposed TMPC-based method.
• Figure 4: Simulation snapshots with Voronoi partition methodhuang2011guaranteedzhou2016cooperative
• Figure 5: Simulation snapshots with Direct Charge (DC) methodMac17RAL

Theorems & Definitions (11)

• Definition 1: Encirclement Condition
• Definition 2: Capture Condition
• Remark 1
• Definition 3: Angle-based Partition
• Definition 4: Encirclement Guaranteed Partition
• Remark 2
• Theorem 1
• proof
• Corollary 1
• Remark 3