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.

翻译：本文提出了一种方法，以避免多智能体自主机器人系统（MARS）中分布式碰撞避免的控制障碍函数（CBF）出现“无解”情形。MARS由分布式自主移动机器人组成，预计能有效执行诸如特定区域搜索等协作任务。因此，在实际部署MARS时必须考虑碰撞避免问题。CBF可有效解决碰撞避免问题，但在大量机器人聚集于同一位置的极端条件下，确保机器人间安全距离的CBF约束可能被违反。我们从理论上证明该问题在特定情况下会发生，并引入了一种用于CBF不等式约束的不对称设计。我们利用机器人的绝对速度，通过权重函数实现了不等式约束的不对称分散化，使其他机器人能够在极端条件下接管该机器人的约束。在多个机器人聚集于同一位置的二维场景中，我们验证了所提出方法的有效性，并在实际机器人上实现了该方法，进一步证实了该理论的可行性。