A calibration free analytical solution to image points path planning that ensures visibility

This work deals with trajectory planning for image based eye-in-hand visual servoing applications. Trajectories for extracted feature points of a target object are computed directly in the projective image space such that they are compatible with rigid body displacements. To this end, one separately parameterizes for: (a) the collineation with respect to the plane at infinity (which can be viewed as a projective representation of the rotation); and (b) the projective representation of the translation. Parameterizing the collineation by the use of decomposition into its canonical form provides an easy way to plan for a geodesic displacement. Furthermore, different strategies are proposed to interpolate for the translation path. As a result, the most advanced strategy guarantees, by the use of a simple analytic criterion, that the points remain visible during the whole path. The method requires in general nothing more than the initial and final images and does not depend on intrinsic camera parameters.