Analytical inverse kinematics of a class of redundant manipulator based on dual arm-angle parameterization

The arm-angle was often used to parameterize the self-motion of S-R-S (Spherical-Revolute-Spherical) redundant manipulators when solving the inverse kinematics. However, there were some shortcomings for previous works: existing algorithm singularity or not suitable for configuration control. In this paper, we proposed an analytical resolution method based on dual arm-angle parameterization. Using two orthogonal vectors to define two absolute reference planes, we got two arm-angles which satisfy a specific condition. Since there is always at least one arm angle to represent the redundancy, the algorithm singularity problem does not exist. The “dual arm-angle” method keeps the advantages of “arm-angle”, and overcomes the shortcomings of the traditional methods. Another contribution of this paper is that we derived the absolute reference elbow attitude matrix ⁰R₃^ψ=0, which is the key for the analytical inverse kinematics resolution but was not addressed in the previous paper. Simulation results for a general case and an algorithm singularity case verified the presented method.