Guaranteed Performance Nonlinear Observer for Simultaneous Localization and Mapping

Abstract

A geometric nonlinear observer algorithm for Simultaneous Localization and Mapping (SLAM) developed on the Lie group of \mathbb{SLAM}_{n}\left(3\right) is proposed. The presented novel solution estimates the vehicle's pose (i.e. attitude and position) with respect to landmarks simultaneously positioning the reference features in the global frame. The proposed estimator on manifold is characterized by predefined measures of transient and steady-state performance. Dynamically reducing boundaries guide the error function of the system to reduce asymptotically to the origin from its starting position within a large given set. The proposed observer has the ability to use the available velocity and feature measurements directly. Also, it compensates for unknown constant bias attached to velocity measurements. Unit-qauternion of the proposed observer is presented. Numerical results reveal effectiveness of the proposed observer. Keywords: Nonlinear filter algorithm, Nonlinear observer for Simultaneous Localization and Mapping, Nonlinear estimator, nonlinear SLAM observer on manifold, nonlinear SLAM filter on matrix Lie Group, observer design, asymptotic stability, systematic convergence, Prescribed performance function, pose estimation, attitude filter, position filter, feature filter, landmark filter, gradient based SLAM observer, gradient based observer for SLAM, adaptive estimate, SLAM observer, observer SLAM framework, equivariant observer, inertial vision unit, visual, SLAM filter, SE(3), SO(3).