Inverse kinematic solution of 6R robot manipulators based on screw theory and the Paden–Kahan subproblem
Inverse kinematic solution of 6R robot manipulators based on screw theory and the Paden–Kahan subproblem
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DOI：
10.1177/1729881418818297
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发表时间：
2018-11
影响因子：
2.3
通讯作者：
Rongbo Zhao;Zhiping Shi;Yong Guan;Zhenzhou Shao;Qianying Zhang;Guohui Wang
中科院分区：
文献类型：
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作者：
Rongbo Zhao;Zhiping Shi;Yong Guan;Zhenzhou Shao;Qianying Zhang;Guohui Wang
传统的Denavit-Hatenberg方法是一种比较成熟的机器人运动学建模方法。然而，它有一个明显的缺点，即Denavit-Hatenberg模型的参数是不连续的，导致相邻关节轴平行或接近平行时出现奇点。因此，该模型不适合进行运动学标定。在本文中，为了避免奇异性问题，采用基于螺旋理论的指数积方法进行运动学建模。此外，结合Paden-Kahan子问题和矩阵理论，采用解析法、几何法和代数法求解6R机器人机械手的运动学逆解。分析了Denavit-Hatenberg模型及其乘积的运动参数，并说明了这两种模型的奇异性。最后，得到了8个反运动学解，验证了本文算法的正确性和较高的精度。该算法为具有三个相邻并联关节的机器人的运动学逆解提供了参考。
The traditional Denavit–Hatenberg method is a relatively mature method for modeling the kinematics of robots. However, it has an obvious drawback, in that the parameters of the Denavit–Hatenberg model are discontinuous, resulting in singularity when the adjacent joint axes are parallel or close to parallel. As a result, this model is not suitable for kinematic calibration. In this article, to avoid the problem of singularity, the product of exponentials method based on screw theory is employed for kinematics modeling. In addition, the inverse kinematics of the 6R robot manipulator is solved by adopting analytical, geometric, and algebraic methods combined with the Paden–Kahan subproblem as well as matrix theory. Moreover, the kinematic parameters of the Denavit–Hatenberg and the product of exponentials-based models are analyzed, and the singularity of the two models is illustrated. Finally, eight solutions of inverse kinematics are obtained, and the correctness and high level of accuracy of the algorithm proposed in this article are verified. This algorithm provides a reference for the inverse kinematics of robots with three adjacent parallel joints.