Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm

Samy Labsir,Gaël Pages,Damien Vivet

doi:10.3390/rs14030571

Samy Labsir, Gaël Pages + Show 1 more

Open Access

https://doi.org/10.3390/rs14030571

Copy DOI

Abstract

This paper addresses the problem of monocular Simultaneous Localization And Mapping on Lie groups using fiducial patterns. For that purpose, we propose a reformulation of the classical camera model as a model on matrix Lie groups. Thus, we define an original-state vector containing the camera pose and the set of transformations from the world frame to each pattern, which constitutes the map’s state. Each element of the map’s state, as well as the camera pose, are intrinsically constrained to evolve on the matrix Lie group SE(3). Filtering is then performed by an extended Kalman filter dedicated to matrix Lie groups to solve the visual SLAM process (LG-EKF-VSLAM). This algorithm has been evaluated in different scenarios based on simulated data as well as real data. The results show that the LG-EKF-VSLAM can improve the absolute position and orientation accuracy, compared to a classical EKF visual SLAM (EKF-VSLAM).

Highlights

The results show that the Lie Group-Extended Kalman Filter (LG-EKF)-VSLAM can improve the absolute position and orientation accuracy, compared to aclassical EKF visual Simultaneous Localization And Mapping (SLAM) (EKF-VSLAM)
We evaluated the LG-EKF-VSLAM with real data obtained within our laboratory, since, to the best of our knowledge, there are no available public benchmarks with coded patterns
Our algorithm has been compared with aclassical EKF-VSLAM using aEuler parametrization on simulated data as well as on real-world data

Summary

Introduction

There is an identity element defined, so that each element of the group has an inverse; Due to its manifold structure, it is possible to compute the derivative and the integral of two elements, or the inverse of one element. The properties of Lie Groups allow us to define atangent vector space. It is possible to associate any point of TI G to any point of TX G, thanks to the operator called left tangent application (see Figure 3). The latter is defined, between two tangent spaces, by: LXL Y

Objectives

Methods

Results

Conclusion