Simultaneous Localization and Mapping of Subterranean Voids with Gaussian Mixture Models

This paper presents a real-time viable method for Simultaneous Localization and Mapping (SLAM) using Gaussian mixture models (GMMs) for compute-constrained systems that operate in subterranean environments. The two contributions of this work are (1) a SLAM formulation that uses a GMM-based map representation for pose estimation, mapping and loop closure, and (2) an Expectation Maximization (EM) formulation that significantly reduces the time to learn a GMM from a sensor observation by exploiting the insight that although Gaussian distributions have infinite support, a substantial amount of the support is contained within a finite region. An on-manifold distribution-to-distribution registration approach is used to estimate the pose between consecutive GMMs, and the Cauchy–Schwarz divergence is employed to calculate the difference between the distributions to identify loop closures. The method is evaluated in mine and unstructured cave environments. The results demonstrate superior performance in leveraging the compact representation of the GMM as compared to traditional pose graph SLAM techniques that rely on point cloud-based methods. Further, exploiting the sparsity of the compact support significantly reduces training time toward enabling real-time viability.