On-line free inverse kinematics joint/cartesian optimal control of redundant manipulators

This article presents a novel on-line optimal control for tracking tasks on redundant robot manipulators for which inverse kinematics is not required. The controller is composed by a stabilization Cartesian PID control plus a joint space optimal control, which is in charge of improving tracking performance. The joint space dynamic optimal control is based on the gradient flow approach with the robot dynamics as a constraint. The combination of both controllers is implemented in joint space, by considering the robot Jacobian, nonetheless for design of both controllers only direct kinematics and Cartesian errors are taken into account. Joint space controllers which are based on Cartesian errors commonly require the inverse kinematics of the robot, in our proposal the joint space optimal controller solves on line the inverse kinematics of the redundant robot by itself, thus an explicit inverse kinematics model of the robot is not needed. Furthermore the optimization control takes advantage of the redundancy of the robot to improve its performance. The paper presents experimental results with a three degree of freedom (dof) planar manipulator, showing that the optimal control part highly improves the tracking performance of the closed loop system.