Quaternion-based visual servo control in the presence of camera calibration error

Visual servo control systems use information from images along with knowledge of the optic parameters (i.e. camera calibration) to position the camera relative to some viewed object. If there are inaccuracies in the camera calibration, then performance degradation and potentially unpredictable response from the visual servo control system may occur. Motivated by the desire to incorporate robustness to the camera calibration, different control methods have been developed. Previous adaptive/robust controllers (especially for six degree-of-freedom camera motion) rely heavily on properties of the rotation parameterization to formulate state estimates and a measurable closed-loop error system. All of these results are based on the singular axis-angle parameterization. Motivated by the desire to express the rotation by a non-singular parameterization, efforts in this paper address the question: Cart state estimates and a measurable closed-loop error system be crafted in terms of the quaternion parameterization when the camera calibration parameters are unknown? To answer this question, a contribution of this paper is the development of a robust controller and closed-loop error system based on a new quaternion-based estimate of the rotation error. A Lyapunov-based analysis is provided which indicates that the controller yields asymptotic regulation of the rotation and translation error signals given a sufficient approximate of the camera calibration parameters. Simulation results are provided that illustrate the performance of the controller for a range of calibration uncertainty. Copyright (C) 2009 John Wiley & Sons, Ltd.