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Efficient Continuous-Time SLAM for 3D Lidar-Based Online Mapping
David Droeschel, Sven Behnke
TL;DR
High-rate 3D laser scanners make online SLAM difficult because immediate state estimates can leave measurements misaligned. The paper introduces hierarchical continuous-time SLAM with local multiresolution mapping and graph-based refinement, and reports improved map quality and sharper maps in experiments.
Problem
Online 3D laser SLAM must handle high data rates while avoiding misalignments caused by committing to scan estimates immediately or initializing from sparse information.
Method
The method combines surfel-registered local multiresolution maps, a hierarchical graph for allocentric mapping, scan-level sub-graphs, and continuous-time trajectory interpolation.
Results
Evaluation shows that the approach increases map quality and leads to sharper maps, with qualitative correction of misaligned scans and entropy-based map-quality measurement.
Takeaways & Limitations
The approach supports online mapping while refining previously acquired sensor data and correcting drift or misalignments as more information becomes available.
Abstract
from arXiv · showhide
Modern 3D laser-range scanners have a high data rate, making online simultaneous localization and mapping (SLAM) computationally challenging. Recursive state estimation techniques are efficient but commit to a state estimate immediately after a new scan is made, which may lead to misalignments of measurements. We present a 3D SLAM approach that allows for refining alignments during online mapping. Our method is based on efficient local mapping and a hierarchical optimization back-end. Measurements of a 3D laser scanner are aggregated in local multiresolution maps by means of surfel-based registration. The local maps are used in a multi-level graph for allocentric mapping and localization. In order to incorporate corrections when refining the alignment, the individual 3D scans in the local map are modeled as a sub-graph and graph optimization is performed to account for drift and misalignments in the local maps. Furthermore, in each sub-graph, a continuous-time representation of the sensor trajectory allows to correct measurements between scan poses. We evaluate our approach in multiple experiments by showing qualitative results. Furthermore, we quantify the map quality by an entropy-based measure.
I. INTRODUCTION
The paper addresses efficient online 3D laser SLAM while allowing previously registered measurements to be reassessed and corrected as more information becomes available.
- High-rate laser sensing makes online SLAM computationally challenging, while recursive estimation can commit to misaligned measurements.
- Earlier local multiresolution mapping was efficient and robust for sparse laser scans but could not reassess previously aggregated measurements after registration errors.
- The proposed method models individual 3D scans as sub-graphs in a hierarchical graph, enabling map refinement when more information is available.
- The system combines local multiresolution maps, allocentric graph mapping, and a continuous-time trajectory representation to address sparse-measurement alignment problems.
II. RELATED WORK
Prior work balances efficiency, accuracy, and motion compensation in laser-based mapping, but the paper combines hierarchical optimization with local sub-maps and continuous-time trajectories.
- Existing laser-mapping methods can create accurate maps under certain conditions but generally lack efficient assessment and refinement.
- Rolling shutter artifacts deform scans acquired during motion and can degrade map quality and sensor-pose estimation when scans are treated as rigid bodies.
- Some continuous-time methods model sensor trajectories with splines to interpolate poses between measurements and compensate for motion effects.
- The proposed approach uses a hierarchical graph to optimize simplified problem parts independently, local sub-maps to overcome laser sparsity, and continuous-time trajectories for rolling-shutter effects.
III. SYSTEM OVERVIEW
The system builds local multiresolution surfel maps, links them into an allocentric pose graph, and refines selected scans while mapping continues.
- Measurements are aggregated in robot-centric multiresolution grid maps whose cells store occupancy probabilities and surfels summarizing points by mean and covariance.
- Surfel-based registration aligns each acquired 3D scan with the aggregated map before adding it to the local map.
- Local maps are registered into an allocentric pose graph, with nearby-map edges supporting loop closure and drift minimization.
- The refinement process reassesses scan alignment and optimizes trajectories locally and globally, enabling online mapping while previously acquired data is refined.
IV. HIERARCHICAL REFINEMENT
A hierarchical graph represents local-map poses, scan poses, and scan-line poses, allowing efficient independent refinement and continuous-time interpolation within local sub-graphs.
- The coarsest graph level represents local maps, each aggregating consecutive scans and the robot’s vicinity at a view pose.
- Registration edges constrain both relative poses between local maps and scan poses relative to local maps.
- Scan lines are the smallest optimization elements, but their measurements are assumed too sparse for robust registration.
- A continuous-time trajectory interpolates scan-line acquisition poses, while sub-graph optimization estimates scan and local-map poses efficiently.
- Sub-graphs are refined in parallel, and full-graph optimization is triggered selectively after significant local changes or loop-closure constraints.
A. Local Sub-Graph Refinement
The method selectively refines scans within each local sub-graph, using uncertainty and newly added constraints to target likely alignment errors before optimizing the local trajectory.
- A. Local Sub-Graph Refinement: Selected 3D scans are realigned with their local map, producing refined spatial constraints while avoiding refinement of every scan.Selecting only some scans supports fast convergence with similar map quality.
- A. Local Sub-Graph Refinement: Scan refinement is guided by spatial constraints and their information matrices, whose inverse covariance indicates pose uncertainty.The uncertainty measure selects the scan with the largest expected alignment error.
- A. Local Sub-Graph Refinement: After refinement, local graph optimization infers the trajectory from relative pose observations, and optimized sub-graph results are incorporated into the allocentric pose graph.The local sub-graph is optimized independently before higher-level graph optimization.
- A. Local Sub-Graph Refinement: Figure 4 shows odometry-derived scan-line poses being refined through interpolation from a continuous-time trajectory built from scan poses.The trajectory representation is constructed within the local sub-graph.
B. Local Window Alignment
The local optimization window grows when additional measurements can resolve missing information, while a continuous-time spline models motion during each scan acquisition.
- B. Local Window Alignment: Realignment can improve map quality only after additional scans provide previously unknown information, ideally from different view poses.The method therefore increases the local optimization window by adding scans.
- B. Local Window Alignment: Long 3D laser acquisitions make a single discrete scan pose produce artifacts, but finely discretizing poses would make the state intractable.This motivates continuous-time trajectory modeling.
- B. Local Window Alignment: The sensor trajectory is represented as a smooth cubic B-spline in SE(3) with local support, enabling interpolation between discrete scan nodes.The spline is parameterized with cumulative basis functions in the Lie algebra.
- B. Local Window Alignment: Scan nodes and their acquisition times serve as spline control points, assuming consecutive scans have a uniform temporal distribution.The pose of each scan node is used as a trajectory control pose.
- B. Local Window Alignment: Four control points interpolate the trajectory between scan nodes, and the resulting spline updates scan-line poses within that interval.The cumulative basis, logarithmic map, and normalized time parameter define the interpolation.
- B. Local Window Alignment: The resulting 3D map uses color to encode height from the ground.Figure 5 depicts a map from an indoor/outdoor environment.
D. Loop-Closure and Global Optimization
The back-end adds candidate map-node constraints based on distance and alternates information flow between local sub-graphs and global pose-graph optimization.
- D. Loop-Closure and Global Optimization: After adding a local map, the system checks for a new constraint between the current reference map node and other map nodes.The candidate constraint is selected using a probability dependent on linear distance between view poses.
- D. Loop-Closure and Global Optimization: When a new spatial constraint is added, the highest-level pose graph is optimized globally and changes propagate down to the affected sub-graph.Significant sub-graph changes can trigger global optimization again.
V. EXPERIMENTS
The experiments evaluate refinement on two datasets with different sensor setups, using mean map entropy and iterative refinement behavior to assess map quality and runtime.
- V. EXPERIMENTS: Two datasets evaluate refinement: MAV data from a Velodyne VLP-16 and Deutsches Museum data provided by the Google Cartographer team.New map nodes are added using a 5 m distance threshold.
- V. EXPERIMENTS: Mean map entropy is computed from the resulting map points to quantify map quality.The evaluation uses local covariance within radius r = 0.5 m and averages entropy over all map points.
- V. EXPERIMENTS: Lower entropy indicates higher map quality because the measure represents map crispness or sharpness.The entropy is based on the sample covariance of mapped points in a local neighborhood.
- V. EXPERIMENTS: Post-processing experiments refine one scan per sub-graph per iteration, optimize local sub-graphs in parallel, and perform global optimization afterward.Entropy is plotted against iteration count to assess convergence behavior.
- V. EXPERIMENTS: Runtime measurements are averaged over 10 runs on an Intel Core i7-6700HQ quad-core CPU with 32 GB of RAM.The processor runs at 2.6 GHz.
A. Courtyard
The Courtyard experiment evaluates refinement on MAV lidar data, comparing map entropy and point-cloud quality while measuring refinement runtime.
- A. Courtyard: The data set was recorded during MAV flight with a Velodyne VLP-16 lidar and IMU in a building courtyard.The lidar provides approximately 300,000 range measurements per second across 16 horizontal scan rings.
- A. Courtyard: Map entropy was compared with and without continuous-time trajectory interpolation (CT).
- A. Courtyard: 2000 scans were recorded during a 200 s flight, producing a graph with 16 map nodes and 27 edges.
- A. Courtyard: The proposed method corrects misaligned 3D scans and increases map quality relative to the previous method.The comparison uses resulting point clouds, while map entropy is evaluated across refinement iterations.
- A. Courtyard: Refinement required 54 ms per iteration for one map node and 380 ms per iteration for all 16 map nodes in parallel.
B. Deutsches Museum
The Deutsches Museum evaluation uses backpack-mounted dual lidars, tests calibration refinement, and compares convergence and map entropy across multiple mapping methods.
- B. Deutsches Museum: The data set contains horizontal and vertical Velodyne VLP-16 scanners mounted on a backpack carried through the Deutsches Museum.Some portions include dynamic objects such as moving persons, and the provided inter-sensor calibration is refined using additional graph constraints.
- B. Deutsches Museum: Table I reports resulting best mean map entropies (MME) for the Deutsches Museum data set.
- B. Deutsches Museum: Covariance-based scan selection leads to faster convergence in the evaluated method.Convergence is compared with and without covariance-based scan selection using entropy measurements.
- B. Deutsches Museum: The presented method is compared with the previous method, Google’s Cartographer, and a continuous-time SLAM method.The results are summarized for each method in Table I.
VI. CONCLUSIONS
The paper concludes with a hierarchical, continuous-time 3D SLAM approach combining efficient local mapping with graph-based refinement of scan alignments.
- VI. CONCLUSIONS: The method aggregates lidar measurements in local multiresolution maps using surfel-based registration and represents local maps in a graph for allocentric mapping.
- VI. CONCLUSIONS: Individual scans form sub-graphs whose optimization accounts for drift and misalignments in local maps.
- VI. CONCLUSIONS: A continuous-time trajectory representation interpolates measurements between discrete scan poses.
- VI. CONCLUSIONS: Evaluation shows increased map quality and sharper maps.