In this paper, a novel encirclement guaranteed cooperative pursuit problem involving N pursuers and a single evader in an unbounded two-dimensional game domain is studied. Throughout the game, the evader’s action is unavailable to the pursuers. Moreover, 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 mainly addresses the unavailability issue of the evader’s actions. Despite the reformulation, the resulting RMPC problem involves a bilinear constraint due to the encirclement requirement. To further address such a bilinear constraint, a novel encirclement guaranteed partitioning scheme is devised, which in turn helps simplifying 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 explicit consideration of the encirclement condition significantly improves the chance of successful capture of the evader in various scenarios.