机器人工作空间求解的蒙特卡洛法改进

摘要

The principle, the algorithm, and the applicable scope of the Monte Carlo method were analyzed. The non-uniform feature of the distribution of random points in workspace was analyzed, as well as the different signification between the points within the workspace and the points on the boundary. The error resulted from spatial workspace slicing was summarized. In order to optimize the boundary accuracy, based on the continuity of the mapping from joint space to workspace, by generating new random joint values in a sufficiently small neighborhood of the existed random joint values corresponding to the boundary points extracted before, new random points in workspace were generated, which distributed around the corresponding old boundary points. Then, from the newly generated points, more accurate boundary points could be extracted. The approach demonstrated to be effective to improve the boundary precision. To reduce the error caused by the slice thickness, in each slice interval, only a thin layer of points were used. A large number of tests illustrate that the algorithm works well.%对机器人工作空间求解的蒙特卡洛法的基本原理、算法流程、适用范围等进行了研究,分析了蒙特卡洛法中随机点分布的不均匀性以及内部随机点和边界随机点的不同作用,并总结了立体工作空间随机点分层处理时引起的误差情况.针对传统算法边界处随机点分布不理想的问题,强调边界点的重要性,根据关节空间到工作空间映射的连续性,在先期搜索到的边界点的小邻域内重新生成随机点,从而有效改善了边界处随机点的分布状况,提高了边界点的精确度.针对立体工作空间随机点分层处理带来的误差,采用二次分层的方法,通过减小统计层厚度提高边界点的统计精度.大量的试验证明了算法的有效性.