  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.
