An Analytical Quaternion and its Applications to Inverse Kinematics of 6R Manipulators

In order to solve the real-time and high-precision inverse kinematics problem of 6R manipulators, a new analytical quaternion is proposed, which is used for inverse kinematics modelling and solutions of 6R manipulators. The coordinate system and axis vectors of 6R manipulators are established. An analytical quaternion which is isomorphic to the traditional unit quaternion and a quasi-direction cosine matrix isomorphic to the direction cosine matrix are proposed to establish a non-redundant and second-order inverse kinematics model of 6R manipulators. Based on the structural vectors’ decomposition, the general method for modelling 6R decoupling manipulators is proposed, and the decoupling conditions are analyzed, which can be used to derive the analytical inverse kinematics solution of 6R manipulators with three-axis decoupling, offset decoupling and orthogonal decoupling mechanisms. The simulation results show that the solution speed of the proposed method is less than 5.7 ms, the position accuracy is better than 10‒15 m, and the direction accuracy is better than 10‒8(°). This work is done to effectively deal with the complex configuration of spatial 6R manipulators and meet the requirements of high precision and efficiency. © 2022 Editorial Office of Chinese Journal of Mechanical Engineering. All rights reserved.