PEBO-SLAM: Observer Design for Visual Inertial SLAM With Convergence Guarantees

Abstract

In this article, we introduce a new parameterization for the problem of visual inertial simultaneous localization and mapping (VI-SLAM), i.e., for a robot only equipped with a single monocular camera and an inertial measurement unit. In this problem, the system state evolves on the nonlinear manifold <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathit{SE}(3)\times \mathbb {R}^{3\mathit{n}}$</tex-math></inline-formula>, on which we design dynamic extensions such that the deterministic VI-SLAM problem can be reformulated—without any approximation—into online <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constant parameter</i> identification, expressed as a linear regression. This demonstrates that deterministic VI-SLAM can be translated into a linear least squares problem <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">globally</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">exactly</i>. Based on this observation, we propose a novel SLAM observer, following the recently established parameter estimation-based observer methodology. A notable merit of the proposed observer is its almost global asymptotic stability. Unlike most existing methods, its convergence does not rely on persistency of excitation or uniform complete observability—assumptions commonly used in stability proofs that can be challenging to satisfy in real-world applications.