Optimal Strategies for a Class of Multi-Player Reach-Avoid Differential Games in 3D Space

A multi-player reach-avoid differential game with autonomous aerial robots in the three dimensional space is studied. Two pursuers form a team to guard a target against an evader with the same speed as the pursuers. This letter provides the complete solution of this differential game that resides within a high-dimensional state space. The Barrier surface is characterized and the saddle-point strategies are synthesized and verified. Degeneration of the two-pursuer one-evader game into the one-on-one case is addressed and the corresponding strategies are obtained. Finally, several examples illustrate the robustness properties and the guarantees provided by the saddle-point strategies obtained in this letter.