Planar Image Based Visual Servoing as a Navigation Problem

We describe a hybrid planar image-based servo algorithm which, for a simplified planar convex rigid body, converges to a static goal for all initial conditions within the workspace of the camera. This is achieved using the sequential composition of a palette of continuous image based controllers. Each subcontroller, based on a specified set of collinear feature points, is shown to converge for all initial configuations in which the feature points are visible. Furthermore, the controller guarantees that the body will maintain a “visible” orientation, i.e. the feature points will always be in view of the camera. This is achieved by introducing a change of coordinates from SE(2) to an image plane measurement of three points, and imposing a navigation function in that coordinate system. Our intuition suggests that appropriately generalized versions of these ideas may be extended to SE(3).