A dynamic quasi-Newton method for uncalibrated visual servoing

Tracking of a moving target by uncalibrated model independent visual servo control is achieved by developing a new "dynamic" quasi-Newton approach. Model independent visual servo control is defined as using visual feedback to control a robot without precisely calibrated kinematic and camera models. The control problem is formulated as a nonlinear least squares optimization. For the moving target case, this results in a time-varying objective function which is minimized using a new dynamic Newton's method. A second-order convergence rate is established, and it is shown that the standard method is not guaranteed convergence for a moving target. The algorithm is extended to develop a dynamic Broyden update and subsequently a dynamic quasi-Newton method. Results for both one- and six-degree-of-freedom systems demonstrate the success of the algorithm and shows dramatic improvement over previous methods.