An Observer Design for Visual Simultaneous Localisation and Mapping with Output Equivariance

TL;DR

This paper introduces a new observer design for VSLAM that leverages output equivariance, resulting in a simple, robust, and computationally efficient algorithm suitable for embedded robotic systems.

Contribution

It presents a novel fully non-linear gradient-based observer exploiting symmetry in VSLAM with inverse depth measurements, achieving stability and efficiency improvements.

Findings

Achieves almost global asymptotic and local exponential stability.

Demonstrates similar accuracy to Extended Kalman Filter.

Offers significant processing time gains and robustness improvements.

Abstract

Visual Simultaneous Localisation and Mapping (VSLAM) is a key enabling technology for small embedded robotic systems such as aerial vehicles. Recent advances in equivariant filter and observer design offer the potential of a new generation of highly robust algorithms with low memory and computation requirements for embedded system applications. This paper studies observer design on the symmetry group proposed in previous work by the authors, in the case where inverse depth measurements are available. Exploiting this symmetry leads to a simple fully non-linear gradient based observer with almost global asymptotic and local exponential stability properties. Simulation experiments verify the observer design, and demonstrate that the proposed observer achieves similar accuracy to the widely used Extended Kalman Filter with significant gains in processing time (linear verses quadratic bounds with respect to number of landmarks) and qualitative improvements in robustness.