Graph Optimality-Aware Stochastic LiDAR Bundle Adjustment with Progressive Spatial Smoothing

TL;DR

This work tackles robust, efficient, and scalable LiDAR Bundle Adjustment (LBA) in GNSS-denied, large-scale environments by introducing PSS-GOSO. The approach combines Progressive Spatial Smoothing (PSS) for robust LiDAR feature associations via a polynomial smoothing kernel with Graph Optimality-aware Stochastic Optimization (GOSO) to sparsify the relation graph, cluster edges stochastically, and marginalize the graph for subproblem solving. The method is validated across ground-based, aerial, and proprietary cross-platform datasets, showing improved Absolute Pose Error (APE) over pose-graph baselines and competitive runtimes. The results demonstrate strong applicability to long-range mapping and automatic last-mile delivery, with future work including integrating image data to further enhance accuracy.

Abstract

Large-scale LiDAR Bundle Adjustment (LBA) to refine sensor orientation and point cloud accuracy simultaneously to build the navigation map is a fundamental task in logistics and robotics. Unlike pose-graph-based methods that rely solely on pairwise relationships between LiDAR frames, LBA leverages raw LiDAR correspondences to achieve more precise results, especially when initial pose estimates are unreliable for low-cost sensors. However, existing LBA methods face challenges such as simplistic planar correspondences, extensive observations, and dense normal matrices in the least-squares problem, which limit robustness, efficiency, and scalability. To address these issues, we propose a Graph Optimality-aware Stochastic Optimization scheme with Progressive Spatial Smoothing, namely PSS-GOSO, to achieve \textit{robust}, \textit{efficient}, and \textit{scalable} LBA. The Progressive Spatial Smoothing (PSS) module extracts \textit{robust} LiDAR feature association exploiting the prior structure information obtained by the polynomial smooth kernel. The Graph Optimality-aware Stochastic Optimization (GOSO) module first sparsifies the graph according to optimality for an \textit{efficient} optimization. GOSO then utilizes stochastic clustering and graph marginalization to solve the large-scale state estimation problem for a \textit{scalable} LBA. We validate PSS-GOSO across diverse scenes captured by various platforms, demonstrating its superior performance compared to existing methods. Moreover, the resulting point cloud maps are used for automatic last-mile delivery in large-scale complex scenes. The project page can be found at: \url{https://kafeiyin00.github.io/PSS-GOSO/}.

Figures (16)

• Figure 1: Graph optimality-aware stochastic optimization with progressive spatial smoothing for a robust, efficient, and scalable LBA. The Progressive Spatial Smoothing (PSS) module extracts robust LiDAR feature association exploiting the prior structure information obtained by the polynomial smooth kernel. The Graph Optimality-aware Stochastic Optimization (GOSO) module first satisfies the graph according to optimality for an efficient optimization. GOSO then utilizes stochastic clustering and graph marginalization to solve the large-scale state estimation problem for a scalable LBA.
• Figure 2: System overview of the proposed LBA approach. (a) Progressive Spatial Smoothing (PSS); (b) Graph Optimality-aware Stochastic Optimization (GOSO).
• Figure 3: Surface fitting within a smoothing kernel. (a) Points in the world frame. (b) Points in the kernel space for polynomial fitting.
• Figure 4: Example of stochastic clustering. (a) The sparsified graph of an example bundle adjustment problem; (b),(c), and (d) illustrates the different stochastic clustering results from three optimization steps. The random colors illustrate different clusters.
• Figure 5: Graph marginalization.

Theorems & Definitions (4)

• Theorem 1: mirzasoleiman2015lazier
• Theorem 2: nemhauser1978analysis
• Theorem 3: nemhauser1978analysis
• Remark 1