PEBO-SLAM: Observer design for visual inertial SLAM with convergence guarantees

TL;DR

This paper presents a novel observer design for visual inertial SLAM that reformulates the problem into a linear least squares framework, providing global convergence guarantees without the need for persistent excitation.

Contribution

It introduces a PEBO-based observer for VI-SLAM that achieves global convergence without traditional observability conditions, using a new linear parameterization on nonlinear manifolds.

Findings

Reformulates VI-SLAM as a linear least squares problem.

Provides almost global asymptotic stability of the observer.

Eliminates the need for persistent excitation or uniform observability.

Abstract

This paper introduces a new linear parameterization to the problem of visual inertial simultaneous localization and mapping (VI-SLAM) -- without any approximation -- for the case only using information from a single monocular camera and an inertial measurement unit. In this problem set, the system state evolves on the nonlinear manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully to generate invariant foliations, such that the problem can be reformulated into online \emph{constant parameter} identification, then interestingly with linear regression models obtained. It demonstrates that VI-SLAM can be translated into a linear least squares problem, in the deterministic sense, \emph{globally} and \emph{exactly}. Based on this observation, we propose a novel SLAM observer, following the recently established parameter estimation-based observer (PEBO) methodology. A notable merit is that the proposed observer enjoys almost global asymptotic stability, requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with provable stability but can hardly be assured in many practical scenarios.