Asymptotic position control of robot manipulators using uncalibrated visual feedback

Abstract

To implement a visual feedback controller, it a's necessary to calibrate the homogeneous transformation matrix between the robot base frame and the vision frame besides the intrinsic parameters of the vision system. The calibration accuracy greatly affects the control performance. We address the problem of controlling a robot manipulator using visual feedback without calibrating the transformation matrix. It is assumed that the vision system can measure the 3D position and orientation of the robot in real-time. Based on the fact that the visual Jacobian matrix can be represented in a linear form of elements of the transformation matrix, we propose a simple adaptive algorithm to estimate the unknown matrix on-line. This visual feedback controller greatly simplifies the implementation process of a robot-vision workcell and is especially useful when a pre-calibration is not possible, such as when a robot works with an active vision system carried by a mobile robot. It is proved by the Lyapunov approach that the robot position approaches asymptotically to the desired one and the estimated matrix is bounded under the control of this visual feedback controller. The performance has been confirmed by simulations and experiment.