针对传统的蒙特卡洛法求解机器人工作空间时精确度不够的问题, 提出了一种改进的蒙特卡洛法。用传统的蒙特卡洛法生成一个种子工作空间, 基于标准差动态可调的正态分布对种子工作空间进行扩展。在扩展过程中设定一个精度阈值, 确保得到的工作空间中每个位置都能被准确的描述。基于得到的工作空间, 提出了一种体元化算法求取工作空间的体积, 寻找到工作空间的边界部分和非边界部分, 通过对边界部分的不断细化, 降低了体积求取误差。为了验证算法的有效性和实用性, 以九自由度的超冗余串联机械臂为例, 对本文改进的蒙特卡洛法和提出的体积求取算法进行仿真分析。结果表明: 采样点数量相同时, 改进的蒙特卡洛法生成的工作空间边界光滑, “噪声小”; 得到精确的工作空间时改进方法需要的采样点数仅是传统方法的4.67%; 体积求取算法效率较高, 相对误差小于1%; 求得的工作空间体积可用于评估机械臂性能, 为后续机械臂构型优化奠定了理论基础。

This study proposes an improved Monte Carlo method, considering that the traditional method lacks precision while calculating the workspace of a robot. The improved Monte Carlo method comprises two stages. In the first stage, a seed workspace is generated using the traditional Monte Carlo method. In the second stage, the seed workspace is expanded based on the normal distribution, and each region in the obtained workspace can be accurately described by setting an accuracy threshold in the process of expansion. Taking into account the characteristics of the normal distribution, to improve the efficiency of the expansion, dynamically adjustable standard deviations are used. Based on the obtained workspace, a voxel algorithm is proposed to determine the volume of the workspace. The algorithm for searching the boundary has been designed to locate the boundary as well as the non-boundary of the workspace. Refining the boundary alone reduces the calculation time and the resulting error. In order to verify the validity and practicability of the algorithm, the improved Monte Carlo method and the proposed volumetric algorithm were simulated and analyzed using a 9-degrees-of-freedom super-redundant serial robot. The results show that when the number of sampling points is the same, the boundary of the workspace generated by the improved Monte Carlo method is smoother and the noise is smaller. When the accurate workspace is obtained, the number of sampling points needed by the improved method is only 4.67% that of the traditional method. The designed volumetric algorithm is also more efficient, with a relative error less than 1%. The volume of workspace thus obtained can be used to evaluate the performance of a serial robot, which lays a theoretical foundation for the subsequent optimization of serial robot configuration.