并联机器人可操作度分析的蒙特卡罗方法

Monte Carlo Method for Manipulability Analysis of Parallel Manipulators

对蒙特卡罗法生成的并联机器人工作空间上的随机点分布不均匀性进行了研究,基于多维随机变量函数的分布密度公式,推导出蒙特卡罗法生成的并联机器人工作空间点概率密度与雅可比行列式的关系式,建立了输出空间概率密度与并联机器人可操作度之间的关系。以平面两自由度5R并联机器人为研究对象,采用蒙特卡罗法分析了其工作空间上的可操作度,并根据工作模式将输入空间划分成4个子空间,指出了子空间交界处的逆向奇异性。仿真结果表明,蒙特卡罗法是分析并联机器人可操作度和逆向奇异的一种有效方法。

Nonuniform distribution characteristics of random points generated by Monte Carlo method in the workspace of parallel manipulators were discussed. Based on the density of distribution of the multiple random variable function, the relationship between Jacobian matrix and the probability density function of workspace points generated by Monte Carlo method was deduced, and the relationship between the probability density of the output space and the manipulability of the parallel manipulator was also constructed. The manipulability of a 2-DOF 5R parallel manipulator was analyzed based on the Monte Carlo method. According to the working mode of the robot, the input space was divided into four subspaces, and the inverse singularity occurred in the boundary among different subspaces was pointed out. Simulation experiment illustrated that the Monte Carlo method could work well for manipulability analysis of parallel manipulators.