Asymptotic trajectory tracking of manipulators using uncalibrated visual feedback

To implement a position-based visual feedback controller for a manipulator, it is necessary to calibrate the homogeneous transformation matrix between its base frame and the vision frame besides intrinsic parameters of the vision system. The accuracy of such a calibration greatly affects the control performance. Substantial efforts must be made to obtain a highly accurate transformation matrix. In this paper, we propose an adaptive visual feedback controller for manipulators when the homogeneous transformation matrix is not calibrated. It is assumed that the vision system can measure the 3D position and orientation of the manipulator in real-time. Based on an important observation that the unknown transformation matrix can be separated from the visual Jacobian matrix, we propose an adaptive algorithm, similar to the model-based adaptive algorithm, to estimate the unknown matrix online. The use of the proposed visual feedback controller greatly simplifies the implementation of a manipulator-vision workcell. This controller is especially useful when such a pre-calibration is not possible. It is proved by Lyapunov approach that the motion of the manipulator approaches asymptotically to the desired trajectory. Simulations and experimental results are included to demonstrate performance of this adaptive visual feedback controller.