Robots have become indispensable parts for the industrial automated workshop. The distance calculation between the industrial robot and obstacles is a fundamental problem for the robotic collision-free motion control. But existing methods for this problem have the disadvantage that the accuracy and execution efficiency cannot be guaranteed at the same time. In this paper, a pseudo-distance algorithm is presented based on the convex-plane-polygons-based representation to solve this problem. In this algorithm, convex plane polygons (CPPs) and cylinders are utilized to represent obstacles and the manipulator, respectively. The spatial relationship between each CPP and each cylinder is discussed through defining condition parameters, and is divided into six conditions including three special conditions when the contact happens, and the other three conditions when there exists a certain distance between the CPP and the cylinder. The distance is modelled under different relations based on the theory of mathematics and geometry. The pseudo distance is determined through selecting the smallest value from distances between CPPs and cylinders. The numerical experiment is performed based on the proposed and two previous algorithms to estimate the shortest distance between an industrial robot and a groove-shape obstacle. And an application example is performed to show the significance of this work on the robotic motion control. Results indicate that the proposed algorithm is more efficient than previous algorithms under a certain precision requirement, and can be effectively applied in the robotic motion control.

机器人已成为工业自动化车间必不可少的部分。工业机器人与障碍物之间的距离计算是机器人无碰撞运动控制的基本问题。但是，针对该问题的现有方法具有不能同时保证准确性和执行效率的缺点。本文提出了一种基于凸面多边形表示的伪距离算法来解决这个问题。在该算法中，凸平面多边形（CPP）和圆柱体分别用于表示障碍物和操纵器。通过定义条件参数来讨论每个CPP和每个气缸之间的空间关系，并将其分为六个条件，包括发生接触时的三个特殊条件，CPP与圆柱体之间有一定距离时的其他三个条件。距离是根据数学和几何学理论在不同关系下建模的。通过从CPP和圆柱之间的距离中选择最小值来确定伪距离。基于所提出的算法和先前的两种算法进行了数值实验，以估算工业机器人与凹槽形障碍物之间的最短距离。并通过一个应用实例说明了这项工作对机器人运动控制的重要性。结果表明，在一定精度要求下，该算法比以前的算法具有更高的效率，可以有效地应用于机器人运动控制中。