A new approach to inverse kinematic solution for a partially decoupled robot

Abstract

Conventional D-H model based inverse kinematic solution algorithms have to hypothesize that d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> =0 at the end of the robot hand, or the joint variables of D-H based kinematic equations can hardly be isolated to be solved. In practical application, d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> ≠ 0 usually occurs, hence it is required for supplemental transformation between the last frame of the D-H models and real operation frame, which decreases the efficiency. In this paper, a new inverse kinematic solution without the hypothesis of d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> =0 is proposed. We found that the joint variables of the partially decoupled robot can be separated without great difficulty even though d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> ≠ 0. The new approach uses a new multiplication sequence of the inverse matrix for solving the variables of the kinematic equation of the robot. The inverse solution process is straightforward and computationally cheap. Last, some exemplifications are given to valid the accuracy of the proposed approach.