An exponential class of model-free visual servoing controllers in the presence of uncertain camera calibration

In recent papers, a new class of model-free (i.e., the 3-dimensional task-space model of the object is unknown) visual servoing methods was proposed that are based on the estimation of the relative camera orientation between two views of an object. By utilizing homography-based techniques, the control problem is decoupled by separating the rotation and translation components. A single controller is used to control the rotation component, and the class members consist of various translation controllers. Each of the current class members has been proven to yield asymptotic regulation in the presence of uncertainty in the intrinsic and extrinsic calibration parameters. New control development and stability analysis techniques are crafted in this paper to develop a new translation controller that yields exponential rotation and translation regulation in the presence of uncertainty in the intrinsic and extrinsic calibration parameters. Extensions to this research can be used to yield exponential regulation by the other translation controllers in the asymptotic class presented.