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.