Differential Geometric SLAM

TL;DR

This paper introduces DG-SLAM, a novel 3D SLAM algorithm using differential geometry that is proven to be asymptotically stable and demonstrates robustness in noisy simulations.

Contribution

The paper presents a differential geometric approach to SLAM that guarantees stability and robustness, differing from traditional EKF-based methods.

Findings

Successful localization and mapping in simulations

Proven asymptotic stability of the algorithm

Robust performance under measurement noise

Abstract

The simultaneous localization and mapping (SLAM) problem is considered in three dimensions. The proposed algorithm, differential geometric SLAM (DG-SLAM), employs methods from differential geometry to propagate the state and map estimates. Unlike EKF SLAM, the proposed filter is provably asymptotically stable under the assumption of no measurement noise or biases. The robustness of the DG-SLAM algorithm is assessed in simulation with measurement noise. The simulation demonstrates successful localization and mapping.