RMS: Redundancy-Minimizing Point Cloud Sampling for Real-Time Pose Estimation

TL;DR

RMS addresses the data bottleneck in real-time lidar-based ego-motion by introducing a deterministic, uninformed, single-parameter point-cloud sampling method that minimizes redundancy. It exploits the insight that linear and planar surfaces introduce high redundancy in iterative pose estimation by using a gradient-flow based geometric feature and entropy-maximizing selection to pick informative border points, without requiring normals. The method is designed to be environment-agnostic and easily integrable into dense or feature-based odometry pipelines, and it provides theoretical and practical guarantees that translational optima are preserved while reducing data volume. Empirically, RMS delivers faster convergence, lower drift in degenerate geometries, and better compression across diverse datasets (KITTI, Hilti-Oxford, UAV) and pipelines (KISS-ICP, LOAM), making real-time, resource-constrained robot operation more feasible.

Abstract

The typical point cloud sampling methods used in state estimation for mobile robots preserve a high level of point redundancy. This redundancy unnecessarily slows down the estimation pipeline and may cause drift under real-time constraints. Such undue latency becomes a bottleneck for resource-constrained robots (especially UAVs), requiring minimal delay for agile and accurate operation. We propose a novel, deterministic, uninformed, and single-parameter point cloud sampling method named RMS that minimizes redundancy within a 3D point cloud. In contrast to the state of the art, RMS balances the translation-space observability by leveraging the fact that linear and planar surfaces inherently exhibit high redundancy propagated into iterative estimation pipelines. We define the concept of gradient flow, quantifying the local surface underlying a point. We also show that maximizing the entropy of the gradient flow minimizes point redundancy for robot ego-motion estimation. We integrate RMS into the point-based KISS-ICP and feature-based LOAM odometry pipelines and evaluate experimentally on KITTI, Hilti-Oxford, and custom datasets from multirotor UAVs. The experiments demonstrate that RMS outperforms state-of-the-art methods in speed, compression, and accuracy in well-conditioned as well as in geometrically-degenerated settings.

Figures (6)

• Figure 1: A fast and noise-filtering 3D point cloud sampling can speed up real-time estimation pipelines. (a) An example of a single-frame sampling at the crossroad highlighted in (b) by each of the given methods (input point cloud in black). (b--c) Although sampling in the input space is uninformed about point-map correspondences, such sampling can improve performance if the sampling is fast and preserves the quality of the points (e.g., removes non-informative points). (b) Trajectory estimated by KISS-ICP vizzo2023KISSICPDefensePointtoPoint odometry on KITTI seq. #00 when preceded by one of the sampling methods (ground truth in black). Similarly, (c) shows trajectory estimated on-board a mav using LOAM zhang2014LOAMLidarOdometry odometry in a vertically self-symmetrical church in Stará Voda petracek2023NewEraCultural. In LOAM, the plane and line features are sampled instead of the points.
• Figure 2: Pipeline of an iterative pose estimation pipeline extended with (a) in-the-loop residual sampling and (b) a single-shot input data sampling. (a) The formulation (used in jiao2021GreedyBasedFeatureSelectionli2021KFSLIOKeyFeatureSelectiontuna2024XICPLocalizabilityAwareLiDAR) utilizes the full point cloud $\mathcal{P}$ and introduces a significant overhead in each iteration. (b) The proposed architecture includes a single-shot out-of-the-loop sampling, which lowers the overall complexity by reducing the input size.
• Figure 3: Simplistic case of point redundancy (Def. \ref{['def:obj_func']} and \ref{['def:pminus1_redundant_residuals']}) for a robot translating from the position $\mathbf{t}_{k-1}$ (points) to $\mathbf{t}_k$ (points). (a) The point-to-point metric generates identical residuals, which makes the residual rate constant for any positive number of residuals used, e.g., a single residual generates $\bar{\mathbf{r}}(\mathcal{P}) = \prescript{*\!}{}{\mathbf{r}^{\bullet}}$. (b) The point-to-hyperplane metrics generate identical residuals per surface (in this example, the surfaces comprise three planes and a single line). The minimized objective function remains constant if any positive number of points is sampled per each surface. In this case, using the minimum amount of samples yields the residual rate $\bar{\mathbf{r}}(\mathcal{P}) = \prescript{*\!}{}{\mathbf{r}_1^{|}} + \sum_{i=1}^{3}\prescript{*\!}{}{\mathbf{r}_i^{\square}}$. This example assumes perfect correspondences, which is unrealistic under noise and rotation. The point sampling method proposed in \ref{['sec:quantifying_redundancy']} is designed to be robust to cases where this assumption is not met.
• Figure 4: Proposed gfh for quantifying redundancy in a point set. (a) gfh is computed for each point in a voxelized point set $\mathcal{P}_{\nu}$. (b) Points on the perceived borders have generally non-zero $\Delta_{\mathbf{p}}$, whereas (c) corner points yield the maximum $\Delta_{\mathbf{p}}$ (herein thresholded by an abstract value $\epsilon_{\Delta}$). Keeping the max-$\Delta_{\mathbf{p}}$ subset (c) ensures that all directions remain constrained, as shown by the black axes representing which translational directions the points constraint.
• Figure 5: Output of KISS-ICP vizzo2023KISSICPDefensePointtoPoint 6-dof odometry when preceded by different point cloud sampling methods. Parametrization: best performing for each method, robot: multirotor mav, sensor range: 30m, sensor noise: none. (a) Shows areas of translational (A, C, F) and body-frame z-axis rotational (B, D, E, G) degeneracy. At D and G, the degeneracy arises (see low values of the $R_z$ eigenvalue) from large mav tilt, which orients the lidar such that its data are degenerate around the z-axis. At G, a "loop closing" emerges naturally (see APE). (b) Due to the high compression rate and by balancing the translational space, RMS samples points such that they yield the fastest optimization convergence. (c) RMS yields the lowest drift, removes the largest amount of points, produces stable and lowest runtime, and preserves the highest information rate for optimization (only $R_z$ shown).

Theorems & Definitions (10)

• Definition 1
• Remark 1
• Definition 2
• proof
• Remark 2
• Remark 3
• Definition 3
• proof
• Definition 4
• Remark 4