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

This paper introduces 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 (IMU). In this problem, the system state evolves on the nonlinear manifold
$\mathit{SE}(3)\times \mathbb {R}^{3\mathit{n}}$
, on which we design dynamic extensions such that the deterministic VI-SLAM problem can be reformulated—without any approximation—into online
constant parameter
identification, expressed as a linear regression. This demonstrates that deterministic VI-SLAM can be translated into a linear least squares problem
globally
and
exactly
. Based on this observation, we propose a novel SLAM observer, following the recently established parameter estimation-based observer (PEBO) 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.