Feedback control for robotic manipulator with an uncertain Jacobian matrix

Abstract

In most applications of robots, a desired path for the end-effector is usually specified in task space such as Cartesian space. One way to move the robot along this path is to solve the inverse kinematics problem to generate the desired angles in joint space. However, it is a very time consuming task to solve the inverse kinematics problem. Furthermore, in the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end-effector path and the Jacobian matrix of the mapping from joint space to task space. In this article, a feedback control law using an uncertain Jacobian matrix is proposed for setpoint control of robots. Sufficient conditions for the bound of the estimated Jacobian matrix and stability conditions for the feedback gains are presented to guarantee the stability and passivity of the robots. A gravity regressor with an uncertain Jacobian matrix is also proposed for gravitational force compensation when the gravitational force is uncertain. Simulation results are presented to illustrate the performance of the proposed controllers. ©1999 John Wiley & Sons, Inc.