同伦算法在6R机器人运动学逆解上的应用
党磊，熊瑞平，唐静莹，孙飞
（四川大学 制造科学与工程学院，四川 成都 610065）
摘要：针对一般6R机器人运动学的逆解问题，提出了一种自适应同伦算法的求解方法。利用SolidWorks对机器人进行结构建模，根据D-H坐标法建立了相应的坐标系，建立机器人运动学模型后得到含六个未知变量的六个非线性运动学方程。在定点同伦和牛顿同伦的基础上，引入自适应参数构造自适应的同伦算法，避免了运动学逆解的雅可比矩阵逆阵奇异。再结合求解常微分方程初值问题的的四阶Runge-Kutta法和Matlab编程，最终得到机器人运动学逆解的全部解。该算法简单易行，计算效率高，为一般型机器人运动学逆解的研究提供了一种有效的方法。
关键词：6R机器人；同伦算法；D-H坐标法；四阶Runge-Kutta法；Matlab
中图分类号：O311 文献标志码：A doi：10.3969/j.issn.1006-0316.2017.04.002
文章编号：1006－0316 (2017) 04－0005－05
Application of Homotopy Algorithm to Inverse Kinematics of 6R Manipulators
DANG Lei，XIONG Ruiping，TANG Jingying，SUN Fei
( School of Manufacturing Science and Engineering, Sichuan University, Chengdu 610065, China )
Abstract：Aiming at the inverse kinematics problem of general 6R manipulators, an adaptive homotopy algorithm is proposed. The structure of the manipulators is modeled with SolidWorks, and the corresponding coordinate system is established according to the D-H coordinate method. Six nonlinear kinematics equations with six unknown variables are obtained after the manipulators kinematics model is established. On the basis of fixed - point homotopy and Newton homotopy, an adaptive homotopy algorithm is constructed by introducing adaptive parameters, which avoids the singularity of inverse Jacobian matrix in inverse kinematics. Combined with the fourth-order Runge-Kutta method to solve the initial value problem of ordinary differential equation and using Matlab programming, the final solution of the inverse kinematics of the manipulators is obtained. The algorithm is simple and efficient, and it provides an effective method for the inverse kinematics of the general manipulators.
Key words：6R manipulators；homotopy algorithm；D-H coordinate method；the fourth order Runge-Kutta method；Matlab
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收稿日期：2016－11－17
作者简介：党磊（1991－），男，湖北荆州人，硕士研究生，主要研究方向为工业机器人误差分析。
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