Improved Stability Results for Visual Tracking of Robotic Manipulators Based on the Depth-Independent Interaction Matrix

As we know, the dynamic visual-tracking control, which is based on the depth-independent interaction matrix, has been proposed to cope with the general 3-D motion of robot manipulators. To deal with the unknown camera parameters, an adaptive law has been designed. It is noted, however, that the designed adaptive law uses a vector signal defined by the true depths of feature points, which are unavailable when the camera parameters are unknown. Nevertheless, such an adaptive law can still be implemented by replacing the exact depths with the estimated depths, since the estimated depths can be readily calculated by using the estimated values of the camera parameters. In this case, however, we cannot definitely say whether or not the robot system can be guaranteed to achieve asymptotical stability or even stable behavior. To overcome this problem, in this paper, we redefine the mentioned vector signal using the estimated depths and show that the design based on the new vector signal can make the robot system asymptotically stable. Additionally, the existing tracking control design based on the concept of depth-independent interaction matrix is initial-state dependent. Thus, in this paper, we also modify the existing design to obtain an initial-state-independent result. To show the performance of the proposed designs, simulation results based on a two-link planar manipulator are presented. In addition, preliminary experimental results using an industrial manipulator are also given.