GBP-LOAM: Lidar odometry and mapping using Gaussian Belief Propagation

In Simultaneous Localisation and Mapping (SLAM), factor graphs represent one of the most mature back-end optimisation frameworks. However, most methods are centralised and constrained by computational resources and efficiency. Gaussian Belief Propagation (GBP) is a distributed probabilistic inference method for approximating the probability distribution of a system that can be represented by a Factor Graph. We hypothesise that GBP-based solutions could provide a distributed solution that can efficiently tackle the distributed SLAM challenges. However, there is no existing SLAM framework available based on the GBP solution. As a pilot exploration, this work introduces a new GBP-based 3D SLAM framework, demonstrating the feasibility of GBP-based SLAM in 3D. We construct a factor graph on the back-end of a Lidar Odometry and Mapping (LOAM) pipeline and execute GBP for system optimisation, validating the potential and stability of GBP in SLAM. Our algorithm is evaluated on public datasets and benchmarked against state-of-the-art centralised solvers. The results demonstrate that the GBP-based distributed solver attains accuracy comparable to centralised approaches. However, achieving robust convergence on the SE(3) Lie-group state space remains challenging. Finally, we analyse the convergence of GBP and show that incorporating damping factors and regularisation offers a reliable means to enhance convergence. This work provides valuable insights and foundations for future exploration into multi-robot collaborative SLAM implementations.