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Voxgraph: Globally Consistent, Volumetric Mapping using Signed Distance Function Submaps

Victor Reijgwart, Alexander Millane, Helen Oleynikova, Roland Siegwart, Cesar Cadena, Juan Nieto

arXiv:2004.13154v1cs.RO

TL;DR

Dense mapping can provide geometry needed beyond localization, but maintaining global consistency can exceed the resources available on small robots. Voxgraph aligns overlapping SDF submaps with efficient, correspondence-free constraints; field experiments report better trajectory-error performance than comparison systems, and simulation shows subsampling improves efficiency without dramatically affecting reconstruction accuracy.

  • Problem

    Dense SDF maps are useful beyond localization, but global optimization becomes intractable as data grows, while many existing approaches are limited to small environments or repeated raw-data processing.

    Source: §I · p. 1

  • Method

    Voxgraph represents the environment as overlapping SDF submaps and uses ESDF-based, correspondence-free registration constraints to optimize their global alignment.

    Source: §I · p. 1, §IX · p. 7

  • Results

    Field experiments report that Voxgraph outperformed a state-of-the-art visual SLAM system and a top-performing LiDAR system on trajectory error; simulation found subsampling boosted computational efficiency without dramatically impacting reconstruction accuracy.

    Source: §IX · pp. 7–8

  • Takeaways & Limitations

    The system creates consistent large-scale maps in real time on a lightweight computer, with global optimization enabled regularly by efficient registration constraints.

    Source: §IX · p. 7

Abstract

from arXiv · show

Globally consistent dense maps are a key requirement for long-term robot navigation in complex environments. While previous works have addressed the challenges of dense mapping and global consistency, most require more computational resources than may be available on-board small robots. We propose a framework that creates globally consistent volumetric maps on a CPU and is lightweight enough to run on computationally constrained platforms. Our approach represents the environment as a collection of overlapping Signed Distance Function (SDF) submaps, and maintains global consistency by computing an optimal alignment of the submap collection. By exploiting the underlying SDF representation, we generate correspondence free constraints between submap pairs that are computationally efficient enough to optimize the global problem each time a new submap is added. We deploy the proposed system on a hexacopter Micro Aerial Vehicle (MAV) with an Intel i7-8650U CPU in two realistic scenarios: mapping a large-scale area using a 3D LiDAR, and mapping an industrial space using an RGB-D camera. In the large-scale outdoor experiments, the system optimizes a 120x80m map in less than 4s and produces absolute trajectory RMSEs of less than 1m over 400m trajectories. Our complete system, called voxgraph, is available as open source.

I. INTRODUCTION

Dense volumetric maps are useful beyond localization, but maintaining global consistency as data grows is computationally challenging. Voxgraph represents the world as overlapping SDF submaps and aligns them through efficient geometric constraints, targeting globally consistent mapping on a CPU.

I. INTRODUCTION

  • Dense volumetric maps support tasks beyond localization, but global optimization becomes intractable as data grows, limiting many approaches to small environments or repeated raw-data processing.Sparse feature maps are of limited use for recovering surface shape and connectivity.Source: §I · p. 1
  • Voxgraph estimates globally consistent submap poses from the dense map itself, using overlapping SDF submaps rather than computing the full sensor trajectory.The system formulates alignment as graph optimization with odometry and loop-closure constraints.Source: §I · p. 1
  • ESDF-based registration uses level-set points and constraint subsampling to generate efficient geometric constraints between submaps.The introduction also identifies global loop closures from traditional methods as complementary constraints for wide-baseline revisits.Source: §I · pp. 1–2
  • The system is applied to dynamic MAV flight in a large-scale environment and released with a challenging dataset from a sensor-equipped hexacopter flying through an artificial disaster site.The dataset includes visual, inertial, LiDAR, and RTK GPS sensors.Source: §I · p. 2

II. RELATED WORK

Prior dense-mapping approaches trade map completeness, global consistency, and computational cost. Voxgraph builds on submap-based mapping with direct geometric alignment, while its formulation uses gravity-aligned frames when odometry makes gravity observable.

II. RELATED WORK

  • Dense maps represent free and occupied space, but SDF systems can lose raw observations during fusion, complicating global correction after loop closures.Other dense representations may not explicitly distinguish free space from unknown space.Source: §II · p. 2
  • BundleFusion stores raw data and repeatedly re-integrates globally optimized trajectories, while later keyframe methods improve efficiency but retain a monolithic map.Submap approaches avoid raw-data storage and reintegration, though simultaneous tracking across submaps can be costly without a GPU.Source: §II · p. 2
  • Voxgraph extends map-centric submap alignment with correspondence-free ESDF constraints, weighted subsampling, and loop closures for wide-baseline loops.The paper evaluates the approach with both RGB-D and LiDAR MAV setups.Source: §II · p. 2

III. PRELIMINARIES

  • Transformations map points between coordinate frames and concatenate across frames; the logarithmic map sends rotations to the corresponding Lie algebra around identity.The paper parameterizes frame transformations using SE(3).Source: §III · p. 2
  • When odometry makes gravity fully observable, several framework transformations can be represented in R^3 × SO(2) rather than SE(3).Source: §III · p. 2

IV. PROBLEM STATEMENT

The mapping problem is reduced to estimating globally consistent poses for locally built SDF submaps, rather than relying on a single map built from drifting odometry. Voxgraph’s front end creates submaps and registration data for a back end that aligns the collection.

IV. PROBLEM STATEMENT

  • Because odometry accumulates error, the reconstruction is represented as contiguous sensor-data submaps whose world poses and SDFs define the map to be aligned.The SDF stores distance to the nearest observed surface and a weighting or confidence measure.Source: §IV · p. 3

V. SYSTEM

  • The front end converts sensor measurements into submaps and constraints, while the back end maintains constraints and estimates the most likely submap alignment.Source: §V · p. 3

A. Submap Creation

  • Contiguous pointclouds are ray-cast into spatially hashed voxel grids, with new submaps created at a fixed frequency under an assumption of slowly accumulating odometry error.The sensor trajectory is also stored as submap-relative poses during construction.Source: A. Submap Creation · p. 3
  • After submap completion, the front end computes an ESDF from the TSDF and extracts isosurface points with marching cubes for later registration.The ESDF extends distance lookups beyond the TSDF truncation band.Source: A. Submap Creation · p. 3

B. Constraint Generation

The back end receives odometry, loop-closure, and registration constraints to optimize the submap collection. The front end forms these constraints from odometry estimates, externally supplied loop closures, and overlapping submaps.

B. Constraint Generation

1) Odometry:

  • Odometry constraints penalize deviations between successive submaps’ estimated relative pose and the transformation concatenated from intervening sensor odometry.The estimate is passed to the back end to constrain the corresponding submap frames.Source: 1) Odometry · p. 3

2) Loop Closure:

  • External loop closures link sensor frames at different times; the front end identifies their containing submaps and uses submap-relative poses to pass the relation to the back end.The system is agnostic to the loop-closure source; the paper tests DBoW2.Source: 2) Loop Closure · p. 3

3) Registration:

  • Registration constraints are generated for every overlapping submap pair, with overlap detected using world-aligned AABBs bounding each submap’s OBB.The OBB is computed once after pointcloud integration from the maximal dimensions of allocated voxel blocks.Source: 3) Registration · pp. 3–4

VII. BACK END

The back end aligns the submap collection by minimizing the total error of its pose-graph constraints. Odometry residuals penalize deviations from front-end estimates of relative poses between submaps.

VII. BACK END

  • The back end minimizes the total error of all pose-graph constraints over the submap poses.The poses are optimized on a nonlinear manifold using increments in the corresponding Lie algebra.Source: §VII · p. 4

A. Odometry Residuals

  • Odometry residuals compare the relative pose between submap base frames with the front-end odometry estimate.For successive submaps, the odometry constraint uses the front-end-estimated relative pose.Source: A. Odometry Residuals · p. 4

B. Loop Closure Residuals

Loop-closure residuals constrain relative poses using sensor frames within two submaps. Registration constraints align submaps without explicit point correspondences by evaluating iso-surface points in another submap’s ESDF.

B. Loop Closure Residuals

  • Loop-closure residuals constrain relative poses of points within two submaps using sensor frames that need not coincide with the submap frames.The sensor poses are expressed with respect to their respective submap frames.Source: B. Loop Closure Residuals · p. 4

C. Registration Constraints

  • Registration constraints avoid correspondence search by reading the target submap’s ESDF at transformed source iso-surface points and summing squared distances.The points lie on the source submap’s zero-level surface; the residual’s Jacobian is differentiated over submap x, y, z, and yaw coordinates.Source: C. Registration Constraints · p. 4
  • Figure 3 depicts transformed red iso-surface points evaluated in the ESDF, with red arrows showing gradients of the resulting cost.The second triangle is offset in z for clarity.Source: Figure 3 · p. 5
  • The ESDF-distance derivative is obtained from trilinear interpolation, while the relative submap transformation moves source points through the target submap.The derivative of the interpolation function is computed as a byproduct of the distance lookup.Source: C. Registration Constraints · pp. 4–5

D. Registration constraint sub-sampling

To reduce the cost of evaluating many iso-surface residuals, the method approximates pairwise registration error with a sampled subset at each solver iteration.

D. Registration constraint sub-sampling

  • Each solver iteration approximates pairwise registration error using a random subset of iso-surface residuals, reducing the computation required for large surface-point sets.The method draws samples with replacement, with selection probability proportional to voxel weights.Source: D. Registration constraint sub-sampling · p. 5

VIII. EXPERIMENTS

The experiments are designed to evaluate whether the system efficiently generates globally consistent SDF maps. They include simulation, outdoor MAV mapping assessed through trajectory accuracy, and qualitative RGB-D mapping of an industrial space.

VIII. EXPERIMENTS

  • The evaluation targets efficient generation of globally consistent SDF maps and includes simulation experiments with access to ground-truth geometry.The supplied passage introduces the simulation experiments but does not report their results.Source: §VIII · p. 5
  • Outdoor MAV experiments assess reconstruction performance using trajectory accuracy as a proxy while mapping a large scene.The passage describes this evaluation setup but gives no trajectory accuracy values.Source: §VIII · p. 5
  • An RGB-D-equipped MAV is used to produce qualitative mapping results in an industrial space.The supplied passage states the scenario and qualitative evaluation, without reporting a specific outcome.Source: §VIII · p. 5

A. Simulation Experiments

The simulation evaluates reconstruction error under constraint subsampling while introducing drift into a LiDAR-equipped MAV trajectory. Weighted subsampling to about 5% reduces optimization runtime without observable error changes in the tested range.

A. Simulation Experiments

  • The simulated LiDAR-equipped MAV flew a 242 s trajectory around a multi-story building, with odometry drifted by biased Gaussian noise to a final error of 9.88 m.The noise produced accumulating position and yaw errors.Source: A. Simulation Experiments · p. 5
  • Reconstruction error is measured by comparing the fused global map’s SDF with a ground-truth SDF over observed voxels, excluding the ground plane.The ground plane is excluded because its simple geometry is well reconstructed by all systems and tends to dominate average error.Source: A. Simulation Experiments · p. 5
  • Across 120 experiments, the study varied subsampling from 100% to 0.01% and compared weighted sampling with two uniform-sampling alternatives.The alternatives either retained sample weights in residuals or discarded them; weighted sampling yielded more reliable results at high downsampling ratios.Source: A. Simulation Experiments · pp. 5–6
  • From 100% to about 5% weighted subsampling, reconstruction and position errors show no observable change while pose-graph optimization runtime decreases linearly.The reported result is specific to the simulated experiments; weighted sampling is more reliable at high downsampling ratios.Source: Figure 4 · p. 6, A. Simulation Experiments · p. 6

B. Field Experiments

Field experiments evaluate voxgraph on a hexacopter carrying LiDAR or RGB-D sensors, with RTK-GNSS used for trajectory evaluation in the outdoor disaster-area flight. On the four LiDAR trajectories, voxgraph outperformed the compared trajectory-estimation systems while running on the onboard CPU.

B. Field Experiments

  • Onboard experiments used an Intel i7-8650U-class processor, with LiDAR and RGB-D sensor suites and time-synchronized camera-IMU odometry.The LiDAR data came from an Ouster OS1 and the RGB-D data from an Intel RealSense D415.Source: B. Field Experiments · p. 6

1) Lidar-based Mapping:

  • The disaster-area flight used RTK-GNSS for trajectory ground truth, while the map-centric system projected submap-relative odometry through optimized submap poses to obtain an evaluation trajectory.The system does not compute an optimal sensor trajectory.Source: 1) Lidar-based Mapping · p. 6
  • Voxgraph ran on fewer than three CPU threads, although its total CPU use exceeded the compared frameworks because it also computed a volumetric map.Discounting T- and ESDF computation, its optimization time was comparable to or less than the comparison systems.Source: 1) Lidar-based Mapping · p. 6
  • Voxgraph achieved RMSE drift of 0.83 m, 0.59 m, 0.94 m, and 0.52 m on four trajectories, substantially outperforming comparison systems across datasets.The table compares voxgraph with VINS-Mono, LOAM, and ROVIO; ROVIO represents front-end-only performance, and a dash denotes estimator divergence.Source: 1) Lidar-based Mapping · p. 6, Table I · p. 7
  • Global optimization used 44% of one CPU core, and its maximum runtime across the four trajectories was about 4 s.The CPU breakdown covers point-cloud integration, ESDF computation, pose-graph optimization, LiDAR undistortion, and ROVIO odometry.Source: 1) Lidar-based Mapping · pp. 6–7, Figure 6 · p. 7

2) RGB-D-based Mapping:

In industrial RGB-D mapping, adding submap-relative loop-closure constraints corrects gross map distortions. The conclusion reports consistent large-scale mapping on lightweight hardware and better trajectory-error performance than two comparison systems.

2) RGB-D-based Mapping:

  • Adding submap-relative loop-closure constraints corrects gross distortions in the industrial RGB-D map.The visual-inertial-only and registration-only configurations show significant distortion when the MAV revisits a location with an inconsistent pose estimate.Source: 2) RGB-D-based Mapping · p. 7, Figure 9 · p. 8

IX. CONCLUSION

  • Voxgraph represents scenes as overlapping SDF submaps and aligns them geometrically to maintain global consistency.It uses ESDFs and zero-level iso-surface points to form correspondence-free registration constraints, with random residual subsampling to reduce optimization cost.Source: §IX · p. 7
  • Constraint subsampling boosts computational efficiency without dramatically affecting reconstruction accuracy, supporting consistent large-scale mapping in real time on lightweight computers.The conclusion reports these effects in simulation and describes the resulting system as real-time on a lightweight computer.Source: §IX · p. 7
  • The proposed system outperforms a state-of-the-art visual SLAM system and a top-performing LiDAR system on trajectory error alone.The conclusion notes this despite not explicitly estimating an optimal trajectory and spending most computation on the global volumetric map.Source: §IX · p. 8

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