The cable-driven redundant manipulator (CDRM) is characterized by its lightweight, low inertia, and inherent compliance, enabling a wide range of applications in fields such as home services and medical rehabilitation. However, due to its complicated cable drive and transmission mechanism, compared with traditional redundant manipulator, the additional coupling cable kinematics is introduced into the inverse kinematics. Further, as the number of coupled equivalent joints of CDRM increases, it becomes challenging to obtain an efficient as well as stable inverse kinematics solution. In this paper, we propose an efficient geometry-informed inverse kinematics method by combining the geometry-based analytical approach and gradient-based numerical approach. First, the CDRM with 11 equivalent kinematic joints is reconstructed into a 7-DOF manipulator without joint offset. Based on the geometric characteristics, the analytical inverse kinematics of the reconstructed offset-free manipulator is derived to provide physically explainable iterative initial values in approximate solution space for numerical approach. Several numerical calculation results demonstrate that our method inherits the advantages of analytical approach, achieving accurate IK solutions, and improving the computational efficiency and the number of feasible solutions. Additionally, it also addresses the divergence issue resulting from irrational selection of initial values in numerical approach. Furthermore, the solution space can be comprehensively exploited by intuitively adjusting the arm-shape parameters and optimizing the manipulator’s configuration, in order to avoid surrounding obstacles, and optimize cable-tension distribution.
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