A Fast Damped Least-squares Solution To Manipulator Inverse Kinematics And Singularities Prevention

摘要

In this article the inverse kinematics problem for robot manipulators is considered under an inexact context; and a fast procedure for its solution and pseudoinverse robustness is presented. The approach is based on solving the linear system based on the symmetric matrix JJT+pl (where, J and I are the Jacobian and the identity matrix respectively, and p is a damping factor) by a Gaussian elimination process that takes into account the matrix symmetry, and automatically evaluating some simple parameters. These parameters are used in either one of two original schemes, which are theoretically justifiable, that are also proposed for the appropiate evaluation of the damping factor. In the first scheme an upper bound for the condition number of the matrix JJT+pl, in terms of some of the calculated parameters is used. Alternatively, in the second scheme the sufficiency condition for the rank preservation of the Jacobian developed in [5] is considered. First, an upper bound for the pseudoinverse matrix p, in terms of some of the evaluated parameters is found. Then, it is easily shown that the sufficiency condition for rank preservation can be established in terms of this bound and on the 00 norm of the Jacobian rate of change matrix. Furthermore, and as important, here it is also shown how to properly implement these schemes, in particular the one based on an upper bound for the pseudoinverse, in conjuction with a recently developed approach [4] for the singularities prevention of redundant manipulators. The developed algorithms are tested on the simulation of a planar redundant manipulator. From the results obtained it is observed that the proposed approach (in terms of efficiency, robustness and ability to prevent large joint speeds) compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure. 2. The inverse Linematics problem.