An Analytically Stable Structure and Motion Observer Based on Monocular Vision

Abstract

This paper presents a novel nonlinear sliding-mode differentiator-based complete-order observer for structure and motion identification with a calibrated monocular camera. In comparison with earlier work that requires prior knowledge of either the Euclidean geometry of the observed object or the linear acceleration of the camera and is restricted to establishing stability and convergence from image-plane measurements of a single tracked feature, the proposed scheme assumes partial velocity state feedback to asymptotically identify the true-scale Euclidean coordinates of numerous observed object features and the unknown motion parameters. The dynamics of the motion parameters are assumed to be described by a model with unknown parameters that incorporates a bounded uncertainty, and a Lyapunov analysis is provided to prove that the observer yields exponentially convergent estimates that converge to a uniform ultimate bound under a generic persistency of excitation condition. Numerical and experimental results are obtained that demonstrate the robust performance of the current scheme in the presence of model error and measurement noise.