Rigid body visual servoing using navigation functions

Visual servo controllers in the literature rarely achieve provably large domains of attraction, and seldom address two important sensor limitations: (i) susceptibility to self-occlusions and (ii) finite field of view (FOV). In this paper, we tackle the problem of global, occlusion-free visual servoing of a fully actuated rigid body by recourse to navigation functions on a compact manifold which encode these restrictions as control obstacles. For occlusion free rigid body servoing, the manifold of interest is the " visible " set of rigid body configurations, that is, those for which the feature points are within the field of view and unoccluded by the body. For a set of coplanar feature points on one face of a convex polyhedron, we show that a slightly conservative subset of the visible set has a simple topology ammenable to analytical construction of a navigation function. We construct the controller via a closed form coordinate transformation from our problem domain into the topological model space and conclude with simulation results.