State estimation for systems on SE(3) with implicit outputs: An application to visual servoing

Abstract

Motivated by applications in visual servoing, we consider the state estimation problem for a class of systems described by implicit outputs and whose state lives in the special Euclidean group SE(3). We propose an observer in the group of motion SE(3) that preserves invariance and therefore takes explicitly into consideration the geometry of the problem. We discuss conditions under which the linearized state estimation error converges exponentially fast. Furthermore, we analyze the problem when the system is subject to disturbances and noises and show that the estimate converges to a neighborhood of the real solution. The size of the neighborhood increases/decreases gracefully with the bound of the disturbance and noise. We apply and illustrate these results through an application of position and attitude estimation of a rigid body using measurements from a camera attached to the rigid body.