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

TL;DR

<3-5 sentence high-level summary> LIMOncello introduces a 6-DoF LiDAR–Inertial Odometry system that propagates motion on the $\mathrm{SGal}(3)$ manifold within the IKFoM iterated error-state Kalman filter to improve robustness in geometrically degenerate and low-observability scenarios. It pairs this novel state representation with a lightweight $i$-Octree mapping backend, replacing traditional kd-tree structures to enable real-time updates with modest memory growth. The approach is validated across multiple public datasets, showing competitive accuracy and superior stability in tunnel-like and feature-poor environments, and is released as an extensible open-source implementation. By tightly coupling space-time dynamics and providing an efficient incremental map, LIMOncello offers a practical, robust LIO-SLAM solution for resource-constrained platforms.

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 $\mathrm{SO}(3)\times\mathbb{R}^6$, 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.

Figures (5)

• Figure 1: Commutative diagram of the mappings between $\mathbb{R}^m$, the Lie algebra $\mathfrak{m}$, and the manifold $\mathcal{M}$, including the shortcuts $\mathrm{Exp}=\exp(\tau^\wedge)$ and $\mathrm{Log}=\log(\mathcal{X})^\vee$.
• Figure 2: System overview. Unlike most LIO systems, motion compensation is done first, allowing the whole point cloud to be later used for fine-grained perception on a global map as detailed as possible.
• Figure 3: Qualitative comparison of accumulated trajectories in the feature-degenerate tunnel segment of City02, using only the left-facing LiDAR. Top: Map reconstructed by LIMO, showing both the start and end points of the tunnel. Bottom: Trajectories projected onto the x–y plane and compared against ground truth during the tunnel traversal, where FAST-LIO2 exhibits an early, non-recoverable divergence. RESPLE, in contrast, continues through the tunnel but also undergoes non-recoverable drift, deviating severely from the ground truth, including descent below the ground surface. Meanwhile, LIMO is the only method that traverses the tunnel under stable conditions.
• Figure 4: Per-frame computation time on the ntu_day_01 sequence in a simulation setup where three IESKF iterations are executed for every LiDAR frame. Under these conditions, the octree-based methods sustain real-time performance, whereas ikd–Tree exhibits substantially higher and more variable processing times.
• Figure 5: Geometric interpretation of the $\oplus$ operation on $S^2$. The tangent basis $[\mathbf{b}_1,\mathbf{b}_2]$ at $\mathbf{x}$ spans the plane $T_\mathbf{x} S^2$, where the increment $\boldsymbol{\tau}$ is defined. The updated point $\mathbf{y} = \mathbf{x} \oplus \boldsymbol{\tau}$ is obtained by mapping $\boldsymbol{\tau}$ to a 3-dimensional tangent vector via $\mathbf{B}(\mathbf{x})$ and rotating $\mathbf{x}$ by this vector, interpreted as an angle–axis rotation.