Asymmetric Design of Control Barrier Function for Multiagent Autonomous Robotic Systems

In this paper, we propose a method to avoid "no-solution" situations of the control barrier function (CBF) for distributed collision avoidance in a multiagent autonomous robotic system (MARS). MARS, which is composed of distributed autonomous mobile robots, is expected to effectively perform cooperative tasks such as searching in a certain area. Therefore, collision avoidance must be considered when implementing MARS in the real world. The CBF is effective for solving collision-avoidance problems. However, in extreme conditions where many robots congregate at one location, the CBF constraints that ensure a safe distance between robots may be violated. We theoretically demonstrate that this problem can occur in certain situations, and introduce an asymmetric design for the inequality constraints of CBF. We asymmetrically decentralized inequality constraints with weight functions using the absolute speed of the robot so that other robots can take over the constraints of the robot in severe condition. We demonstrate the effectiveness of the proposed method in a two-dimensional situation wherein multiple robots congregate at one location. We implement the proposed method on real robots and the confirmed the effectiveness of this theory.