基于Brent算法的轴偏置虎克铰型Hexapod平台位置反解

Inverse kinematics of Hexapod platform with axis offset Hooke joint based on Brent’s method

针对Newton-Raphson算法求解轴偏置虎克铰型并联六自由度Hexapod平台位置反解时高精度计算会降低平台响应速度的问题,提出了一种新的基于Brent算法的位置反解求解方法。首先,根据平台几何特性和轴偏置虎克铰结构运动特性,建立了基于空间圆辅助模型的运动学模型;接着,提出了基于空间圆距离求解方法的位置反解算法,并针对丝杠螺母副产生的衍生运动,提出了补偿方案;然后,介绍了Brent求根算法,并将Brent算法应用于位置反解算法;最后,通过实验验证了衍生运动误差补偿方案的必要性,同时与采用Newton-Raphson算法的位置反解进行了对比,并测试了该算法控制下的Hexapod平台的响应速度和精度。实验结果表明:在保证平台重复精度低于10μm和5″的工作需求下,基于Brent算法的位置反解与Newton-Raphson算法相比,综合响应速度提高了约0.5 s。因此,基于Brent算法的位置反解求解方法相对改善了Hexapod平台的响应速度。

When the Newton-Raphson algorithm is used to solve the inverse kinematics of a 6-degree-offreedom parallel Hexapod platform with axis offset Hooke joints,the high-precision calculation requirements can decrease the response speed of the platform.To solve this issue,a new method based on Brent’s method is proposed in this study.First,the kinematics model based on the space circle auxiliary model is established by considering the geometric characteristics of the platform and motion characteristics of the axis offset Hooke joint structure.Subsequently,an inverse kinematics algorithm based on the space circle distance solution method is proposed,along with a compensation scheme for the derivative motion of the screw–nut pair.Subsequently,Brent’s method to determine roots is introduced and applied to the inverse kinematics algorithm.Finally,the experiment is used to verify the necessity of the derivative motion error compensation scheme,compare it with the inverse kinematics based on the Newton–Raphson algorithm,and test the response speed and accuracy of the Hexapod platform controlled by the proposed algorithm.In the experimental results,a comparison of the inverse kinematics based on Brent’s method with those based on the Newton-Raphson algorithm indicates that the comprehensive response rate increases by approximately 0.5 s under the operating requirements of repeatability of less than 10μm and 5".Therefore,the inverse kinematics method based on Brent’s method improves the response speed of the Hexapod platform.