一种3-PRS并联机器人位姿误差的数值计算方法

Position and orientation error analysis of a 3-PRS parallel robot based on numerical method

精度是衡量并联机器人工作质量优劣最主要的指标之一,常采用运动学推导和全微分的方法进行分析。文中针对公式复杂及全微分省略高次项带来精度下降等问题,用数值方法求解末端实际位姿来计算误差。在理想(不包含误差)的情况下通过逆解计算理论输入等参数;然后加上误差,用逆解求出的参数作为初值进行正解非线性方程组迭代求解,求得末端实际位姿,进而计算误差;最后用算例验证了方法的有效性及可行性。正解非线性方程组迭代求解直接采用高级语言的非线性方程组求解函数,文中采用的初值设置方法总能保证收敛到真实解,编程方便,计算精度高。

The precision is one of key characters of parallel robot working quality, which has always been analyzed based on kinematics and perfect differential. Aiming at the problems of com- plicated formulas and precision decreasing resulting from neglecting higher-order terms in perfect differential method, the paper discusses the algorithm to compute the actual position and orientation and corresponding error. The parameter values of input and the angle are computed through backward kinematics in ideal situation （without errors）. The forward kinematics nonlinear equations are solved by using the initial value from backward kinematics, and the position and orientation error is computed. The effectiveness and feasibility are verified through computing examples finally. The functions to solve systems of nonlinear equations of several variables in high-level programming languages can be directly used to solve the forward kinematics nonlinear equations. The initial value setting method ensures that the reasonable solution can be gotten. The method in the paper has characters of easy programming and high accuracy.