Space manipulators which have a similar symmetrical structure with seven revolute joints, such as the space station remote manipulator system (SSRMS), can be called SSRMS-type space manipulators. The analytical inverse kinematics of an SSRMS-type manipulator can be solved by locking a single joint; the locked joint (joint 1, 2, 6, or 7) can be determined by configuration analysis. Although widely used in establishing the kinematics of SSRMS-type manipulators, the Denavit-Hartenberg (DH) method has a singular problem when two adjacent joint axes are nearly parallel. To avoid this problem, this paper proposes a novel analytical inverse kinematics method for SSRMS-type manipulators based on the product of exponentials (POE) formula and the Paden-Kahan subproblem. Because of the symmetrical structure, an SSRMS-type manipulator degrades to two kinds of 6-degree-of-freedom (DOF) manipulators when locking a single joint (joint 1, 2, 6, or 7). The analytical inverse kinematics of these two kinds of 6-DOF manipulators is solved by combining the Paden-Kahan subproblems and geometric and algebraic methods, respectively. The proposed approach is not only singularity free compared with the traditional DH-based methods but also more accurate than the POE-based numerical solution. The simulation results verify the efficiency of the proposed approach.

中文翻译：

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基于POE公式和Paden-Kahan子问题的SSRMS型空间机械臂的解析逆运动学方法

具有类似的对称结构和七个旋转关节的空间操纵器，例如空间站远程操纵器系统（SSRMS），可以称为SSRMS型空间操纵器。SSRMS型机械手的解析逆运动学可以通过锁定单个关节来解决。锁定的关节（关节1、2、6或7）可以通过配置分析确定。尽管广泛用于建立SSRMS型机械手的运动学，但Denavit-Hartenberg（DH）方法在两个相邻关节轴几乎平行时存在奇异问题。为了避免这个问题，本文提出了一种基于指数乘积（Paide-Kahan）和Paden-Kahan子问题的乘积的SSRMS型机械手的解析逆运动学方法。由于结构对称，当锁定单个关节（关节1、2、6或7）时，SSRMS型操纵器会退化为两种6自由度（DOF）操纵器。这两种6自由度机械臂的解析逆运动学分别通过将Paden-Kahan子问题与几何和代数方法相结合来解决。与传统的基于DH的方法相比，该方法不仅具有奇异性，而且比基于POE的数值解决方案更准确。仿真结果验证了该方法的有效性。与传统的基于DH的方法相比，该方法不仅具有奇异性，而且比基于POE的数值解决方案更准确。仿真结果验证了该方法的有效性。与传统的基于DH的方法相比，该方法不仅具有奇异性，而且比基于POE的数值解决方案更准确。仿真结果验证了该方法的有效性。