Image Jacobian estimation using structure from motion on a centralized point

Image based visual servoing (IBVS) has become increasingly common in automated systems. IBVS control systems are dependent on the accuracy of an image Jacobian, which requires the knowledge of the internal and external parameters of the system. In most systems, some or all of these parameters are unknown. A centralized motion algorithm (CMA) is proposed to compute the image Jacobian with fast convergence and low iterations. Centralized motion is defined as a motion where a single feature point does not change its pixel coordinate value through the camera's motion. Therefore, the CMA is an algorithm that exploits the fact that the chosen feature point will have little to no changes in pixel coordinates. As a result, the CMA requires only a single stationary feature point, along with a minimum of two more feature points that will be dynamic, in the image to compute the image Jacobian. Using a Whole-Arm Manipulation (WAM) IBVS system, it was shown that an image Jacobian with an average condition number of 45, converges in an average of 4 iterations from 6 different starting positions. Experiments show that the CMA is a fast and effective online calibration algorithm.