On-line Joint/Cartesian Optimal Control of Redundant Robot Manipulators Without Inverse Kinematics

This article presents a novel on-line optimal control for redundant robot manipulators for which inverse kinematics is not required. The controller considers a Cartesian PID control that yields stability of the closed loop, but presents poor performance unless using high gains. A joint space dynamic optimal control based on the gradient flow approach is introduced to improve the performance of the robot. 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 control solves 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 fulfill the optimization index. The paper presents experimental results with a three degree of freedom (dof) planar manipulator, showing that the optimal control part highly improves the performance of the closed loop system.