An asymmetric allocation rule of constraints derived from control barrier function for collision avoidance between autonomous robots

This paper addresses the challenge of collision avoidance in multi-agent autonomous robotic systems. To design the control input in a distributed manner, traditional methods using Control Barrier Functions (CBFs) for collision avoidance propose allocation rules of the constraints, which are about the control inputs and are derived from CBFs to avoid the collision. However, these methods sometimes suffer from the infeasibility of Quadratic-programming (QP)-based controllers and noise due to the need for relative velocity information. To overcome these limitations, we first derive the necessary conditions for the allocation rule that decouples constraints derived from CBFs to guarantee the collision avoidance. We then propose a novel allocation rule that asymmetrically decouples the constraints, that satisfies the derived conditions. This allocation rule can enhance the feasibility of controllers and eliminate the need for relative velocity information. Finally, we demonstrate its effectiveness through simulations and real-world experiments. The results show that the proposed method successfully ensures collision avoidance, maintaining safety distances without relying on relative velocity data. Our contributions include: (1) defining the conditions for the allocation rule, (2) proposing a constraint allocation rule excluding relative velocity, (3) validating the feasibility of controllers through simulations, and (4) demonstrating real-world applicability with experiments, thus offering a practical solution for autonomous robotic systems.