Collision-Free Reach-Avoid Differential Game of Multiple Underactuated Autonomous Surface Vehicles via Control Barrier Functions

This paper investigates a reach-avoid differential game between two groups of underactuated autonomous surface vehicles (ASVs) in a complex marine environment. All ASVs are assumed with the same resultant velocity, and every two defending ASVs are assigned to intercept a single attacking ASV. An optimal safe reach-avoid differential game guidance strategy is proposed to enable the defending ASVs to capture the attacking ASVs that intend to enter a target area without collisions. Firstly, a geometric approach is used to calculate the optimal capture position, and optimal strategies are proposed for both teams of ASVs to reach the capture position based on the differential game theory. In particular, the defenders in the same group can decide whether to cooperate in defense with groupmate or intercept the attacker individually online according to a orthogonal-line-related condition, ensuring that the attackers can be captured with higher efficiency. Secondly, to guarantee the safety during the game process, a quadratic programming problem based on control barrier functions (CBFs) is formulated subject to velocity constraints of the ASVs. Finally, an optimal safe game guidance law is proposed based on an auxiliary variable technique such that an underactuated ASV is able to execute the optimal game strategy and achieve the target area protection task. Optimality and safety analyses indicate that the designed reach-avoid strategies are multilaterally optimal and ensures system safety. Simulation results validate the effectiveness of the optimal safe reach-avoid differential game guidance strategy for area protection tasks.