Asymptotic stability of robot control with approximate Jacobian matrix and its application to visual servoing

In order to describe a task for the robot manipulator, a desired path for the end effector is usually specified in task space such as Cartesian space. In the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end effector path by solving the inverse kinematics problem. In addition, the Jacobian matrix of the mapping from joint space to task space could not be exactly derived. In this paper, we present feedback control laws for setpoint control of robot with uncertain kinematics and Jacobian matrix from joint space to task space. Sufficient conditions for the bound of the estimated Jacobian matrix and stability conditions for the feedback gains are presented to guarantee the stability of the robot's motion. Simulation results are presented to illustrate the performance of the proposed controllers.