LIMOncello: Revisited IKFoM on the SGal(3) Manifold for Fast LiDAR-Inertial Odometry

2025-12-22

AI Summary

In sparse-geometry, low-observability environments, conventional SO(3)×ℝ⁶-based LiDAR-inertial odometry suffers from numerical instability, large drift, and poor robustness. To address these issues, this paper proposes a tightly coupled LiDAR–IMU odometry formulated on the SGal(3) Lie group manifold. Our key contributions are: (1) the first adaptation of the Incremental Kalman Filter on Manifolds (IKFoM) framework to SGal(3), enabling numerically stable discrete-time propagation of motion states; and (2) a lightweight, local-search-free incremental i-Octree mapping mechanism that ensures real-time performance and bounded memory growth. Extensive experiments demonstrate that our method significantly improves localization accuracy and robustness in geometrically sparse scenarios while maintaining real-time operation. A complete open-source implementation is publicly available on GitHub.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This work introduces LIMOncello, a tightly coupled LiDAR-Inertial Odometry system that models 6-DoF motion on the $mathrm{SGal}(3)$ manifold within an iterated error-state Kalman filter backend. Compared to state representations defined on $mathrm{SO}(3) imesmathbb{R}^6$, the use of $mathrm{SGal}(3)$ provides a coherent and numerically stable discrete-time propagation model that helps limit drift in low-observability conditions. LIMOncello also includes a lightweight incremental i-Octree mapping backend that enables faster updates and substantially lower memory usage than incremental kd-tree style map structures, without relying on locality-restricted search heuristics. Experiments on multiple real-world datasets show that LIMOncello achieves competitive accuracy while improving robustness in geometrically sparse environments. The system maintains real-time performance with stable memory growth and is released as an extensible open-source implementation at https://github.com/CPerezRuiz335/LIMOncello.

Problem

• Develops a LiDAR-inertial odometry system using SGal(3) manifold for stable motion modeling
• Introduces an incremental i-Octree mapping backend for efficient memory and update speed
• Aims to improve robustness and accuracy in geometrically sparse environments

Innovation

• Uses SGal(3) manifold for stable motion modeling
• Implements lightweight incremental i-Octree mapping backend
• Combines LiDAR-inertial odometry in iterated Kalman filter