在gauge函数的基础上提出一种描述凸多面体集间拓扑关系的数值指标,用来检测凸多面体集间相交、边界接触和非接触.该指标函数的值是线性规划问题的解,计算简便,可应用于机器人柔性路径规划方法中假设路径的无碰撞约束检验,并提供生成中间位姿的启发信息. Based on the gauge function, a numerical index describing the topological relations among convex polyhedrons is proposed to detect the intersection of convex polyhedrons, boundary contact and non-contact. The value of this index function is the solution to the linear programming problem. The calculation is simple, It can be applied to collision-free constraint checking of the assumed path in the robot’s flexible path planning method and provides heuristic information to generate intermediate pose.