Kinematic Modeling of 7-DOF Cable-Driven Manipulators Based on Damped Least-Squares Method and Gradient Projection Algorithm

Abstract In order to solve the singularity problem of the Jacobian matrix in the numerical solution of the inverse kinematics of the 7-DOF line-driven manipulator (hereinafter referred to as the LDM7 manipulator), a new forward and inverse kinematics algorithm for the LDM7 manipulator was proposed. This paper first introduces the model design of the LDM7 manipulator. The manipulator consists of a 3-DOF shoulder joint, a 1-DOF elbow joint and a 3-DOF ball wrist joint. Then, the forward kinematics model of the manipulator based on the virtual coupled joints and the inverse kinematics model of the LDM7 manipulator based on the least damped square method and the gradient projection algorithm are established. Then, the simulation experiment of forward and inverse kinematics is carried out in this paper, and the simulation results verify the effectiveness of the algorithm. According to the kinematics model, the range of motion of the elbow joint and wrist joint is calculated, and the overall and local working space is obtained by Monte Carlo random sampling algorithm simulation. In addition, this paper verifies the inverse kinematics algorithm from four aspects, including the verification of the inverse kinematics algorithm based on coordinate points, the comparative experiment compared with the traditional algorithm, the comparative experiment of different optimization indexes λ, and the trajectory planning based on the helix equation. The experimental results show that the calculated inverse kinematics results are the most effective when λ=0.06, and the error can be controlled within 0.001. Based on the above derivation and experimental verification, it is shown that the inverse kinematics algorithm proposed in this paper not only effectively solves the singular value problem of the robotic arm with 7-DOF virtual coupling joints, but also reduces the error of the inverse kinematics results.