Multiplexed joint method for determining the inverse kinematics of an n DOF serial link manipulator

This paper presents an approach to solving the inverse kinematics problem for an n degree-of-freedom (dof) serial link manipulator; regardless of the manipulator's kinematic configuration or whether it is redundant or nonredundant. As opposed to other proposed methods, this method is computationally efficient, especially for large n. The method, referred to as the `multiplexed joint' method is based on moving joints individually in such a manner as to minimize the weighted norm of the resultant linearized location error transformation. A higher level joint scheduling algorithm controls which joints are to be moved. The simplest form of this joint scheduling algorithm would be to cyclicly sequence through all of the joints - hence the analogy to the multiplexor operation. An improvability condition is investigated which shows that the weighted norm of the linearized location error after movement of joint `i' can be reduced iff the ith joint's Jacobian is not orthogonal to a virtual force scaled by the kinematic error. An approximate inverse Jacobian matrix is also derived based on the multiplexed joint method and is shown to be a `weighted Jacobian transpose.' Simulation results are presented for the case of a 3 dof planar redundant manipulator which corroborates the theory. Finally, the computational complexity for the basic method combined with a simple joint scheduling algorithm is shown to grow only linearly with the number of joints given the Jacobian and kinematic error.