Dynamic BFGS method for uncalibrated visual servoing

Based on the dynamic BFGS (Broyden-Fletcher-Goldfarb-Shanno) method, an uncalibrated visual servoing control approach was presented for the real time tracking of a moving targets. The method directly estimated, global Hessian matrix containing the residual (the Hessian matrix of an object function), thus reducing the cost of computation. Meanwhile, it solved the singularity problem of the Hessian matrix. According to the approximate affine model of the mapping relations between the joint variables map and the image plane, an estimation of the image Jacobian matrix was obtained, which increased the robustness in tracking a dynamic target. Based on the Matlab Robotools, a mechanical arm visual tracking system with three degrees of freedom was constructed. By means of simulation experiments, the presented method was compared with the direct computing method of the residual term and the D-DFP method. The results verify the good tracking performance of the D-BFGS method.