Inverse attitude solution of manipulator based on improved quaternion

Abstract

Typically, quaternions or rotational matrices are used to establish kinematic equations and produce inverse kinematic solutions for the attitude of 6R decoupled manipulators. These approaches have certain drawbacks, such as duplicate equations and manual solution processes that cannot be eliminated automatically. In this study, we introduce the Ju-Gibbs quaternion to establish the kinematic equations, which are isomorphic to the Euler quaternion and share the same mathematical characteristics. Using this modeling method, one can create non-redundant kinematic equations wherein the number of equations equals the number of unknowns. A novel Dixon elimination method is then used to resolve the multilinear problem. Since no division operations are involved in the solution process, the solution has the advantage of being free of computation singularity issues. The experiment verifies that the proposed method can accomplish the autonomous modeling and elimination solution process of 6R manipulators with low computation complexity and high precision.