For safe operation of cooperative robots, we propose a real-time collision avoidance algorithm that is robust to kinematic singularities of serial robots. The main idea behind the algorithms is to generate control inputs that increase the directional manipulability of a robot along the object direction by reducing directional safety measures. While existing directional safety measures show undesirable behaviors in the vicinity of the kinematic singularities of the robot, the proposed geometric safety measure, which is a distance on the space of positive semi-definite matrices with rank one, robustly generates control input that drives the robot to safer posture, even at the kinematic singularities. By adding the control input from the geometric safety measure to the conventional repulsive input for collision avoidance, a hierarchical collision avoidance algorithm that is robust to kinematic singularity is implemented. The proposed method is demonstrated and validated with a set of numerical experiments that consist of manipulability tracking and collision avoidance examples for a serial manipulator.

为了安全地运行协作机器人，我们提出了一种实时碰撞避免算法，该算法对串行机器人的运动奇异性具有鲁棒性。算法背后的主要思想是生成控制输入，通过减少定向安全措施来增加机器人沿对象方向的方向可操作性。虽然现有的定向安全措施在机器人的运动奇异点附近显示出不良行为，但所提出的几何安全措施（即正一阶正定半确定矩阵的空间上的距离）可以可靠地生成驱动机器人的控制输入即使在运动学奇点下也可以保持更安全的姿势。通过将来自几何安全措施的控制输入添加到常规的排斥避免输入中，实现了对运动奇异性具有鲁棒性的分层碰撞避免算法。通过一系列数值实验对所提出的方法进行了演示和验证，该数值实验由串行操纵器的可操纵性跟踪和避免碰撞示例组成。