Distributed Safety-Critical Optimal Flocking Control Algorithm With Feasibility Enhancement of High-Order Control Barrier Function

This article proposes a distributed safety-critical optimal flocking control algorithm for the multiagent system. In general, safety (i.e., collision avoidance) could be guaranteed by the use of a control barrier function (CBF) as constraints in the optimal control problem. However, the existence of conflicting safety constraints from multiple agents could lead to a feasibility problem (i.e., the absence of a feasible control command) in distributed optimal flocking control algorithms. To deal with this issue, we propose two effective feasibility enhancement approaches. First, we develop a high-order CBF associated with the collision risk to alleviate the burden of distributed safety constraints on agents with a high risk of collision. Second, to enhance feasibility, a relaxation method is used to enlarge the allowable control space of agents. In particular, to decrease the number of optimization variables in the relaxation method, a selective strategy is adopted. This involves applying the relaxation method only to specific CBF based on the decision variable related to the overlap of admissible control spaces among agents. Numerical simulations demonstrate the superiority and validity of the proposed optimal flocking algorithm compared with existing approaches.