A Lie Group-Based Iterative Algorithm Framework for Numerically Solving Forward Kinematics of Gough–Stewart Platform

In this work, we began to take forward kinematics of the Gough–Stewart (G-S) platform as an unconstrained optimization problem on Lie group-structured manifold SE(3) instead simply relaxing its intrinsic orthogonal constraint when algorithms are updated six-dimensional local flat Euclidean space or adding extra unit norm orientation parts parametrized by a quaternion. With thought in mind, construct two kinds iterative problem-solving (Gauss–Newton (G-N) and Levenberg–Marquardt (L-M)) with mathematical tools from group algebra. Finally, case study for general G-S was carried out compare these corresponding that seven-dimensional quaternion-based parametrization space. Experiment results demonstrate those behave better than others convergence performance especially initial guess selection is near branch solutions.