Constructive barrier feedback for collision avoidance in leader-follower formation control

Abstract: 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.