A differential game approach to intrinsic encirclement control

This paper investigates the encirclement control problem involving two groups using a non-cooperative differential game approach. The active group seeks to chase and encircle the passive group, while the passive group responds by fleeing cooperatively and simultaneously encircling the active group. Instead of prescribing an expected radius or a predefined path for encirclement, we focus on the whole formation manifold of the desired relative configuration, two concentric circles, by allowing permutation, rotation, and translation of players. The desired relative configurations arise as the steady state resulting from Nash equilibrium strategies and are achieved in an intrinsic way by designing the interaction graphs and weight function of each edge. Furthermore, the asymptotic convergence to the desired manifold is guaranteed. Finally, numerical simulations demonstrate encirclement and counter-encirclement scenarios, verifying the effectiveness of our strategies.