A Null-Space Solution of the Inverse Kinematics of Redundant Manipulators Based on a Decomposition of Screws

In this paper, an approach for solving the inverse kinematics (velocity) problem for redundant open-chain manipulators is addressed. The solution is based upon finding a particular joint rate solution and identifying a joint velocity null-space basis through a decomposition of screw coordinates representing the joint axes. Optimal joint rate solutions are formulated in terms of the joint null-space basis. A specification of computational costs for numerical application is presented. The method is shown to be useful for analytical application through example derivations for two 7 revolute jointed manipulators and a platform mounted nonredundant manipulator.