Inverse-free solution of Z1G1 type to acceleration-level inverse kinematics of redundant robot manipulators

In past decades, the online solution of inverse kinematics (IK) has always been a mathematically troublesome problem for redundant robot manipulators. Besides, the traditional IK approaches, such as the pseudo-inverse method, have to calculate the computationally expensive inverse (specifically, pseudo-inverse) of Jacobian matrix. To drastically and effectively avoid the Jacobian inversion and to obtain the accurate solution of the time-varying IK problem for redundant robot manipulators, a special type of inverse-free solution, namely of Z1G1 type, is thus proposed and investigated at the joint-acceleration level in this paper. In addition, we conduct the path-tracking simulations performed on three-link, four-link and five-link planar robot manipulators to substantiate the effectiveness and accuracy of such an inverse-free solution. Moreover, the experiment based on a six-link redundant robot manipulator hardware system illustrates the physical realizability of the proposed novel solution for handling the time-varying IK problem of the redundant robot manipulator(s) in an inverse-free manner.