A Global Asymptotic Convergent Observer for SLAM

TL;DR

This paper introduces a novel hybrid observer for SLAM that guarantees global asymptotic convergence despite topological challenges, validated through Lyapunov stability and simulation comparisons.

Contribution

A new gradient-based hybrid observer is proposed to address topological obstructions in SLAM, ensuring global convergence on the non-contractible manifold SO(3).

Findings

The hybrid observer achieves global asymptotic convergence.

Simulation results show superior performance over smooth observers.

The approach effectively overcomes topological obstructions in SLAM.

Abstract

This paper examines the global convergence problem of SLAM algorithms, an issue that faces topological obstructions. This is because the state-space of attitude dynamics is defined on a non-contractible manifold: the special orthogonal group of order three SO(3). Therefore, this paper presents a novel, gradient-based hybrid observer to overcome these topological obstacles. The Lyapunov stability theorem is used to prove the globally asymptotic convergence of the proposed algorithm. Finally, comparative analyses of two simulations were conducted to evaluate the performance of the proposed scheme and to demonstrate the superiority of the proposed hybrid observer to a smooth observer.