An almost globally convergent observer for visual SLAM without persistent excitation

TL;DR

This paper introduces a novel visual SLAM observer using a monocular camera and IMU that guarantees almost global stability without needing persistent excitation, simplifying the stability conditions compared to existing methods.

Contribution

It presents a new observer design for visual SLAM on the manifold that achieves almost global convergence without persistent excitation or uniform observability.

Findings

Guarantees almost global asymptotic stability.

Does not require persistent excitation.

Simplifies stability conditions for visual SLAM.

Abstract

In this paper we propose a novel observer to solve the problem of visual simultaneous localization and mapping (SLAM), only using the information from a single monocular camera and an inertial measurement unit (IMU). The system state evolves on the manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully in order to generate an invariant foliation, such that the problem is reformulated into online \emph{constant parameter} identification. Then, following the recently introduced parameter estimation-based observer (PEBO) and the dynamic regressor extension and mixing (DREM) procedure, we provide a new simple solution. A notable merit is that the proposed observer guarantees almost global asymptotic stability requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with guaranteed stability.