基于随机概率的机器人工作空间及其面积求解

Generation of manipulator workspace boundary geometry using the probabilistic method and its area computation

采用随机概率的蒙特卡罗方法得到了平面机器人的工作空间。由于此方法不用对机器人进行逆 解计算,也不必直接对奇异值进行计算,所以非常适于工作空间边界曲线的绘制。本文的另一 个目的在于扩展一种简单快速的方法,更有效地确定一般平面机器人工作空间的面积。由于工 作空间是由一系列的直线或圆弧曲线构成的封闭图形,所以可以采用矢量法对边界点予以表示, 并用窄矩形对面积进行近似计算。最后,对一个平面机构的实例进行了面积计算和比较分析。 本文介绍的方法不但简单而且在工程中非常实用。

The Monte Carlo method based on random probability is used to generate the workspaces of manipulators. The method does not use any inverse calculations, and no directcompu- tation of points ofsingularity is required,so it is naturally suitable for graphicalpresentation of the geometry of the boundary surfaces. Another contribution of this work is to further develop apracticalapproachin orderto determine thearea ofa generalplanermanipulator?s workspace more effectively.The boundary surfaces of workspace is closed consisting of a series ofstraightline and arc segments,soits boundary points can be represented by close sets, and its area can be approached by narrow rectangles. Finally, the area of a planar robotmanipulators iscalculatedand investigatedbycomparing withactualresult.Themethod of this paper was shown to be simple and readily implemented in practice.