Constructive Barrier Feedback for Collision Avoidance in Leader-Follower Formation Control

This paper proposes a novel constructive barrier feedback for reactive collision avoidance between two agents. It incorporates this feature in a formation tracking control strategy for a group of 2nd-order dynamic robots defined in three-dimensional space. Using only relative measurements between neighboring agents, we propose an elegant decentralized controller as the sum of a nominal tracking controller and the constructive barrier feedback for leader-follower formations under a directed single-spanning tree graph topology. The key ingredient is the use of divergent flow as a dissipative term, which slows down the relative velocity in the direction of the neighboring robots without compromising the nominal controller's performance. Compared to traditional barrier function-based optimization controllers, the proposed constructive barrier feedback avoids feasibility issues and results in more computationally efficient control algorithms with systematic equilibrium analysis. Simulations are provided to validate the effectiveness of the proposed control method.