This paper develops a novel analytical framework for system kinematic reliability sensitivity analysis of robotic manipulators, which can provide the analytical results of local and global reliability sensitivity defined on the pose and position errors. First, uncertainty analysis of the pose error of the end-effector is accomplished by virtue of the second-order closed-form error propagation formula on motion groups. Then, the system kinematic reliability, namely the probability of the system kinematic error located within the prescribed safe boundary, is analytically calculated. Specifically, the non-central chi-square approximation and expectation propagation technique are employed to compute the system kinematic reliability defined on the position and pose errors, respectively. On this basis, the local and global system kinematic reliability sensitivity of robotic manipulators are analytically obtained. Finally, the effectiveness of the proposed method is validated by comparison with the Monte Carlo simulation and Kriging modeling method. The results indicate the proposed method has good efficacy and efficiency in system kinematic reliability sensitivity analysis for robotic manipulators.

本文为机器人机械手的系统运动学可靠性灵敏度分析开发了一种新的分析框架，该框架可以提供定义在位姿和位置误差上的局部和全局可靠性灵敏度的分析结果。首先，利用运动群上的二阶闭式误差传播公式完成末端执行器位姿误差的不确定性分析。然后，对系统运动学可靠性，即系统运动学误差位于规定安全边界内的概率进行解析计算。具体而言，采用非中心卡方近似和期望传播技术分别计算定义在位置和姿态误差上的系统运动学可靠性。在此基础上，分析获得机器人机械手的局部和全局系统运动学可靠性灵敏度。最后，通过与蒙特卡罗模拟和克里金建模方法的对比，验证了所提方法的有效性。结果表明，该方法在机器人机械手系统运动学可靠性灵敏度分析中具有良好的有效性和效率。