Dynamic tracking of manipulators using visual feedback from an uncalibrated fixed camera

This paper presents a new controller for controlling a number of feature points on a robot manipulator to trace desired trajectories specified on the image plane of a fixed camera, provided that the intrinsic and extrinsic parameters of the camera are not calibrated. A new adaptive algorithm is developed to estimate the unknown parameters on-line based on three original ideas. First, we use the pseudo-inverse of the depth-independent interaction matrix, proposed in our earlier work, to map the image errors onto the joint space so that we can linearly parameterize the closed-loop dynamics of the system. Second, to guarantee existence of the pseudo-inverse, we introduce a potential force to drive the estimated parameters away from the values resulting in singular image interaction matrix. Third, to ensure that the estimated parameters are convergent to their true values up to a scale, we combine the Slotine-Li method with an on-line algorithm for minimizing the errors between the estimated projections and real image coordinates of the feature points. We have proved asymptotic convergence of the image errors by Lyapunov method and demonstrated the performance by experiments