On Line Optimal Control of Robots for Tracking without Inverse Kinematics Control Optimo en Línea de Robot para Seguimiento sin Cinemática Inversa

This article presents a novel on-line optimal control for tracking tasks on 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 this proposal the joint space optimal controller determines on line the required joint variables to achieve the Cartesian task, without using the inverse kinematics of the robot, thus an explicit inverse kinematics model of the robot is not needed. The paper presents experimental results with a two degree of freedom (dof) planar manipulator, showing that the optimal control part highly improves the tracking performance of the closed loop system.