The purpose of this study is to propose an inverse geodesic optimization algorithm based on manifold principle to solve the problems of low precision and low efficiency of inverse kinematics of 7-DOF robots. This approach offers a significant improvement over traditional analytical and numerical methods.
The MD-H method is used for the forward kinematics analysis of the 7R redundant robot. Within the confines of the Riemannian manifold, the robot’s workspace is partitioned into three distinct spaces: position, attitude and moment. Each space is assigned specific Riemannian metrics. The inverse kinematics solutions for the 7R redundant robot are derived by constructing and resolving geodesic equations. A case study was conducted using the KUKA robot, followed by simulation experiments.
The Riemannian manifold-based geodesic optimization algorithm for the 7R robot yields a global mean square error of 0.6009 mm2, accompanied by a standard deviation of 0.7752 mm. The average end position error is recorded at 1.8853 mm. In contrast, the root mean square errors for the Jacobi pseudo-inverse, quintic polynomial interpolation and Bezier curve methods are 0.4379, 6.2994 and 7.2229 mm2. The average end position errors for these methods stand at 2.4352, 5.8699 and 6.1807 mm, respectively. The data derived from the inverse solution optimization algorithm, which uses geodesics on the Riemannian manifold, surpasses that of the Jacobi pseudo-inverse, quintic polynomial interpolation and Bezier curve methods. The robot’s deviation from the anticipated trajectory is notably minimal, demonstrating superior smoothness and enhanced trajectory accuracy.
This paper presented an inverse solution algorithm designed to address the complexities and low precision inherent in the inverse kinematics problem for 7R robots. This is achieved by leveraging geodesic equations within Riemannian manifolds. Furthermore, a reverse solution model specifically for 7R robots is proposed.
