A numerical algorithm for solving robot inverse kinematics

Abstract

SUMMARYAn extension of the inverse kinematics algorithm by Gupta and Kazerounian is presented. The robot kinematics is formulated by using the Zero Reference Position Method. Euler parameters and the related vector forms of the spatial rotation concatenation have been used to improve the efficiency of the velocity Jacobian computation. The joint rates are formally integrated by using a modified predictor-corrector method particularized to robot inverse kinematics – it is a strict descending, p(1)c(0 – n), variable step algorithm. The definitions of the rotational error and overall error measure have been revised. Depending upon the convergence criteria used, these modifications reduce the overall computational time by 20%.

Speeding Up Robot Manipulators With Elastic Joints

“…Due to the nature of this method, small changes in the structure inherently correspond to small changes in the structure parameters. It has also proven its effectiveness and versatility in many works on both kinematic and dynamic analysis of robot manipulators [4], [5], [6], [7] and [8]. The joint coordinate systems in this method are not used.…”

“…They are converted to the current position as the manipulator moves. The current vector are derived from their zero-reference-position vectors as follows [4] Where Eoi, Eo,i+l , Ej and Ei+I are derived from the Euler-Rodrigues parameters and Rodrigues composition formula. These formulas eliminate the inefficiency due to the use of the regular rotation matrices.…”

A successive approximation algorithm for the inverse position analysis of serial manipulators

“…Numerical iterative schemes based on Newton-Raphson have been used to obtain some of the solutions of inverse kinematics. 12 However, this method is known to have quadratic convergence in the neighbourhood of a solution, but away from it either procedure may fail to converge. Angeles 13 proposed to apply a small enough condition number of the Jacobian and continuation method to overcome this failure.…”