Hierarchical Gaussian Distributions for Real-Time SLAM

Abstract

We present Gaussian distributions as structure primitives in a hierarchical multi-fidelity framework to enable accurate real-time Simultaneous Localization and Mapping (SLAM) using uncertain depth data.

Real-time mapping and localization capabilities are essential components of an autonomous system deployed in real-world environments. An autonomous system must be able to create an understanding of the world from the history of observed sensor information in unknown environments and operate appropriately in response. A typical state-of-the-art mobile robot has multiple perceptual processes operating concurrently on the incoming sensor information to enable various autonomy subsystems. Each subsystem processes the sensor data independently to obtain information suitable for its operation that is often unusable by other subsystems. Such a disjoint autonomy system creates redundancy in terms of data processing, and increases the computational load on the mobile system, the overall memory footprint, and the modes of failure. However, mobile robots deployed in real-world scenarios are Size Weight and Power (SWaP) constrained. SWaP constrained platforms impose constraints on the computational and memory resources available onboard thus introducing unique challenges in deploying such disjoint perceptual models in real-world. In this thesis, we propose a SLAM framework using a memory and computationally efficient map representation that can be utilized for various low level autonomy tasks and unify the perceptual architecture.
The real-time performance of active perception algorithms is dependent on the memory complexity of the used map representation. Higher memory footprint increases the computational complexity of active perception algorithms with marginal benefit to their performance. State-of-the-art SLAM techniques generate extremely high fidelity 3D reconstruction of the world. These 3D maps are often not suitable for active perception due to their high memory requirements. They must be post-processed, down-sampled and converted to a map representation more suitable for active perception such as voxel grids. Voxel grids provide high computational benefits and low memory footprint at the cost of loss of map accuracy and fidelity.

A family of generative map models have recently been proposed that compress point cloud data using hierarchical Gaussian Mixture Models (GMMs) by modeling the structural correlations evident in the input data. These generative models are more memory efficient and accurate than voxel based map representations. The generative nature of GMMs enable them to be elegantly converted to more commonly used map representations. Alongside dense 3D reconstruction, there is a wide range of work showing the utility of a GMM based map representation for scan matching, global and local pose estimation, collision avoidance, autonomous exploration and various other real-world robotic applications. However, the loss in mapping accuracy and map fidelity is not yet addressed and there is a significant gap between the quality of reconstruction obtained from state-of-the-art SLAM pipelines and generative mapping representations such as GMMs.

In this work, we combine the mathematical benefits of a generative map representation such as GMMs with the accuracy of reconstruction obtained from dense map representations such as surfels. Specifically, we create a hierarchical Gaussian distributions based map that is capable of reconstructing the world with high accuracy at lower hierarchical levels and retain the memory efficiency of GMMs at higher hierarchical levels. We propose a novel model fitting approach to raw point cloud data, that uses the projective constraints enforced by depth cameras to reduce the computational complexity of fitting a GMM to large scale data. Further, we propose a frame-to-model localization approach, that exploits the hierarchical structure of the map to obtain a more robust and reliable camera tracking performance. The reduced memory complexity of the proposed map representation enables deployment of our proposed
approach on SWaP constrained systems.

We demonstrate the superior qualitative and quantitative performance obtained by using the proposed map representation for applications such as SLAM, global localization and collision avoidance as compared to their respective state-of-the-art approaches. We also highlight the increased computational efficiency, reduced memory footprint and high reconstruction accuracy achieved using this map representation in simulated and real-world environments.