Optimal Object Configurations to Minimize the Positioning Error in Visual Servoing

Image noise unavoidably affects the available image points that are used in visual-servoing schemes to steer a robot end-effector toward a desired location. As a consequence, letting the image points in the current view converge to those in the desired view does not ensure that the camera converges accurately to the desired location. This paper investigates the selection of object configurations to minimize the worst-case positioning error due to the presence of image noise. In particular, a strategy based on linear matrix inequalities (LMIs) and barrier functions is proposed to compute upper and lower bounds of this error for a given maximum error of the image points. This strategy can be applied to problems such as selecting an optimal subset of object points or determining an optimal position of an object in the scene. Some examples illustrate the use of the proposed strategy in such problems.