An almost globally convergent observer for visual SLAM without persistent excitation

Abstract

This paper introduces a new linear parameterization to the problem of visual inertial simultaneous localization and mapping (VI-SLAM)-without anyapproximation-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)×R 3n , on which we design dynamic extensions carefully to generate invariant foliations, such that the problem can be reformulated into online 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, 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 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.

Identifiability Implies Robust, Globally Exponentially Convergent On-line Parameter Estimation: Application to Model Reference Adaptive Control

“…On the other hand, simulation evidence has shown that D+G has a more "erratic" dependence on λ, g, α, β, k and κ, hence the commissioning procedure of the former is "easier". In any case, a better understanding of their similarities/differences is needed, • In [57] a procedure to "mix" the estimates θg (t) and θ(t) that preserves the main properties of Proposition 2 is proposed. The advantages of this new modification are yet to be clarified.…”