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RAGNAROK: Radar-Aided Gravity-Normalized Alignment for Robust Open Keyframe-based Radar-Visual-Kinematic-Inertial SLAM

Hanjun Kim, Chiyun Noh, Sangwoo Jung, Jaehyung Jung, Simon Boche, Cedric Le Gentil, Stefan Leutenegger, Ayoung Kim

arXiv:2610.11531v1cs.RO

TL;DR

Legged-robot estimators face rough-terrain proprioceptive corruption, yaw drift in radar-aided systems, and underexplored failure-aware multimodal fusion. RAGNAROK combines radar-aided proprioception with visual SLAM and adaptive fusion; the authors report stronger performance than SOTA baselines in low-light and high-vibration scenarios.

  • Problem

    Proprioceptive estimators are vulnerable on rough terrain, while radar-aided methods have limited yaw observability and failure-aware fusion for adverse environments remains underexplored.

    Source: §I · pp. 1–2

  • Method

    RAGNAROK combines radar-aided B-spline proprioceptive estimation with slip- and rolling-contact-aware leg factors, kinematics-aware radar weighting, degradation-aware visual enhancement, and adaptive fusion.

    Source: §I · p. 2, D. Factor Graph Optimization · p. 3, B. Spatial-Feature-Aware Image… · p. 4

  • Results

    RAGNAROK achieves more robust performance than SOTA baselines in low-light and high-vibration scenarios.

    Source: §V · p. 8

  • Takeaways & Limitations

    The work releases an open legged-robot dataset combining multiple radars, RGB and stereo IR cameras, LiDAR, proprioceptive sensors, and an IMU.

    Source: §I · p. 2

Abstract

from arXiv · show

Legged robots offer superior mobility in unstructured environments, but reliable operation in such conditions requires robust state estimation. To address the vulnerability of proprioceptive estimators in rough terrain, recent methods have incorporated radar to provide velocity measurements. However, their limited yaw observability still leads to drift, and failure-aware fusion for adverse environments remains underexplored. In this letter, we present RAGNAROK, the first radar-visual-kinematic-inertial SLAM designed for robust operation in challenging environments. It integrates slip- and rolling-contact-aware leg velocity estimation, a kinematics-aware radar factor, and degradation-aware image enhancement. We further incorporate a B-spline-based radar-aided proprioceptive backbone, adaptive weighting, and online extrinsic calibration. Extensive experiments on public and self-collected datasets demonstrate that RAGNAROK achieves robust performance under challenging conditions and outperforms state-of-the-art baselines. The source code and dataset are available at https://github.com/hanjun815/RAGNAROK.

I. INTRODUCTION

Legged-robot state estimation remains vulnerable to rough-terrain interactions, while radar-aided methods face yaw drift and limited mapping and loop-closure support. RAGNAROK combines radar, visual, kinematic, and inertial estimation with failure-aware fusion and is evaluated in challenging environments.

I. INTRODUCTION

  • Proprioceptive estimators are vulnerable to contact impacts, vibrations, and foot slippage, while radar-aided methods retain yaw drift and limited loop-closure and mapping support.The paper identifies failure-aware visual fusion with radar-aided gravity estimation as underexplored.Source: §I · pp. 1–2
  • RAGNAROK is presented as a radar-visual-kinematic-inertial SLAM framework with degeneracy-aware adaptive fusion for robust operation in challenging environments.The authors describe it as the first system of this type designed for these conditions.Source: §I · p. 2
  • The framework combines slip- and rolling-contact-aware leg estimation, a kinematics-aware radar factor, and spatial-feature-aware image enhancement.It also uses adaptive sensor weighting, radar-enhanced place recognition, and a continuous-time radar-aided proprioceptive backbone.Source: §I · p. 2
  • RAGNAROK is validated across outdoor, low-light, glare, and slippage conditions, with superior performance reported in forested terrain, stair traversal, and self-similar corridors.The authors also report evaluations on public and self-collected datasets.Source: §I · p. 2

II. PROPRIOCEPTIVE-BASED STATE ESTIMATOR

The proprioceptive estimator optimizes B-spline representations of velocity, rotation, and local gravity, then supplies relative-motion constraints at visual keyframe times. Its leg factor accounts for rolling contact and slip while deriving velocity from leg kinematics.

II. PROPRIOCEPTIVE-BASED STATE ESTIMATOR

  • The estimator optimizes B-spline representations of ego-centric velocity, rotation, and local gravity, and queries the resulting motion at visual keyframe timestamps.The queried spline provides relative-motion constraints to the exteroceptive estimator.Source: §II · p. 2

B. Slip & Rolling-Contact-Aware Leg Velocity Factor

  • The leg factor imposes its kinematic constraint at the terrain-normal support point, directly accounting for contact velocity induced by rolling motion.It uses the analytical joint-velocity relation and retains trajectory-dependent angular coupling rather than injecting raw gyroscope measurements.Source: B. Slip & Rolling-Contact-Aware Leg… · p. 2
  • A two-dimensional velocity bias is embedded in the stance-contact tangent plane to model shared support-plane slip.Leg reliability is downweighted after touchdown, abrupt contact changes, or inconsistent velocity estimates.Source: B. Slip & Rolling-Contact-Aware Leg… · p. 3

C. Kinematics-Aware Radar Velocity Factor

The radar velocity factor uses an orthogonal dual-radar configuration and makes Doppler uncertainty depend on the radar’s directional uncertainty and the robot’s motion.

C. Kinematics-Aware Radar Velocity Factor

  • The system uses forward-facing and 90°-rolled radars to address radar’s asymmetric angular resolution.The radar targets provide radial velocity measurements used in the multi-radar velocity residual.Source: C. Kinematics-Aware Radar Velocity… · p. 3
  • The factor projects 3D directional covariance onto the scalar Doppler axis using egovelocity, yielding a state-dependent Doppler variance.This accounts for how directional uncertainty affects the radial measurement under the robot’s instantaneous motion.Source: C. Kinematics-Aware Radar Velocity… · p. 3

D. Factor Graph Optimization

The factor-graph optimization combines leg and radar residuals over an active window, with robust losses and online extrinsic calibration. Radar weighting accounts for radar placement and motion.

D. Factor Graph Optimization

  • The radar-aided proprioceptive spline is optimized over the active window W_i at each iteration.The residual set includes newly introduced leg, radar, and calibration terms alongside residuals following GaRLILEO.Source: D. Factor Graph Optimization · pp. 3–4
  • A Cauchy loss suppresses dynamic radar outliers, while a calibration residual enables online multi-sensor extrinsic calibration.The formulation describes the Cauchy loss as enabling stable velocity estimation without costly RANSAC.Source: D. Factor Graph Optimization · p. 3
  • Kinematics-aware radar weights account for radar placement and motion, including lower Doppler residual weights under harsh motion.The information matrix is diagonal, and increased positional uncertainty lowers radar Doppler residual weights.Source: D. Factor Graph Optimization · p. 3, Figure 3 · p. 4

III. EXTEROCEPTIVE-BASED STATE ESTIMATOR

The exteroceptive estimator defines a state at each camera timestamp, including IMU pose, velocity, and sensor biases.

III. EXTEROCEPTIVE-BASED STATE ESTIMATOR

  • The exteroceptive estimator has a distinct state definition from the proprioceptive estimator, in which accelerometer bias is observable.The passage contrasts its state model with Section II-A, where accelerometer bias is structurally unobservable.Source: A. State Definition and Notation · p. 4
  • At each camera timestamp, the estimator tracks global-frame IMU position, orientation, and velocity, plus gyroscope and accelerometer biases.The accelerometer bias is modeled as a random walk, while the gyroscope bias remains neglected.Source: A. State Definition and Notation · p. 4

B. Spatial-Feature-Aware Image Enhancement

Image enhancement combines AGCWD and CLAHE, with parameters optimized online to support dense, spatially uniform visual features. Its utility incorporates feature quality, and the method avoids the over- or under-correction seen with the compared enhancement methods.

B. Spatial-Feature-Aware Image Enhancement

  • Bayesian optimization tunes AGCWD weighting and CLAHE clip-limit parameters, then fuses their outputs using image mean and histogram entropy.The CLAHE tile-grid size is fixed.Source: B. Spatial-Feature-Aware Image… · p. 4
  • SFA-EWG uses a positive entropy-weighted gradient score, saturation penalties, and BRISK feature count and spatial uniformity.The formulation ensures the positive EWG score is nonnegative and aligns the objective with feature-based visual SLAM.Source: B. Spatial-Feature-Aware Image… · p. 4

USFA-EWG (E(Ic

  • The enhanced image has more extracted features distributed more uniformly than the unenhanced image.The passage describes the enhanced features as dense and spatially uniform.Source: Figure 4 · p. 4, USFA-EWG (E(Ic · p. 4
  • USFA-EWG scales the positive EWG utility by feature-count and spatial-uniformity quality, with parameters optimized by maximizing the objective.The next sample is selected by expected improvement from the updated Gaussian process.Source: USFA-EWG (E(Ic · p. 4
  • BO enhancement avoids AGCWD bright-region over-enhancement and CLAHE dark-region under-enhancement, providing stable enhancement without over- or under-correction.BO is triggered only when raw-image utility changes sufficiently; otherwise, previous parameters are reused.Source: USFA-EWG (E(Ic · p. 4

C. Visual Frontend

The visual frontend uses proprioceptive estimates to manage keyframes, orient visual descriptors, initialize landmarks, and reject motion-inconsistent matches. Its backend adds proprioceptive motion constraints to OKVIS2-X.

1) Zero-Velocity Detection:

  • Near-static intervals detected from proprioceptive estimates suppress keyframe insertion, reducing redundant processing and maintaining a well-distributed sliding window.Source: 1) Zero-Velocity Detection · p. 4

2) Gravity-Enhanced Keypoint Extraction:

3) Matching and Initialization:

  • New landmarks are initialized by stereo triangulation across keyframes or between the live frame and selected keyframes, with relative pose initialized by dead reckoning.Dead reckoning uses proprioceptive velocity and rotation estimates.Source: 3) Matching and Initialization · p. 4

4) Motion-Inconsistent Landmark Rejection:

D. Visual-Inertial SLAM

  • The exteroceptive estimator extends the OKVIS2-X backend with proprioceptive relative-pose and velocity factors.These factors inject proprioceptive motion constraints.Source: D. Visual-Inertial SLAM · p. 5

1) Proprioceptive Relative-Pose Factor:

The proprioceptive spline supplies time-aligned relative poses and ego-centric velocities to the exteroceptive estimator. Loop closure and joint factor-graph optimization complement these factors; retaining the IMU residual empirically improves estimation.

1) Proprioceptive Relative-Pose Factor:

  • The spline provides the time-aligned relative transform between camera timestamps, defining the proprioceptive relative-pose factor through an SE(3)-to-se(3) logarithm map.The transform is computed between camera states k−1 and k.Source: 1) Proprioceptive Relative-Pose Factor · p. 5

2) Velocity Factor:

  • The velocity factor compares proprioceptive ego-centric velocity with the exteroceptive estimator’s velocity state.Source: 2) Velocity Factor · p. 5

3) Loop Closure:

  • Loop closure ranks candidates using DBoW2 and radar-scan polar-BEV cross-correlation, then accepts matches only after 3D-2D RANSAC verification.Verified matches recover pose-graph edges as landmarks and observations, and add observations between matched and current frames.Source: 3) Loop Closure · p. 5

E. Factor Graph Optimization

  • The factors are jointly estimated with nonlinear least squares, and retaining the IMU residual empirically improves estimation performance.The objective includes visual reprojection and IMU residuals, among others.Source: E. Factor Graph Optimization · p. 5

F. Adaptive Weighting

Adaptive weighting shifts information toward proprioception as visual tracking quality falls and suppresses unreliable visual constraints during fallback. The paper also describes a Spot dataset and its ground-truth construction.

F. Adaptive Weighting

  • RAGNAROK adapts nominal factor information weights online according to visual reliability, using visual tracking quality and fallback conditions to adjust sensor contributions.Source: F. Adaptive Weighting · p. 5
  • Lower visual quality increases the proprioceptive contribution up to 1/Qmin, while fallback prioritizes proprioception and suppresses unreliable visual constraints.The quality threshold or the USFA-EWG threshold triggers visual fallback.Source: F. Adaptive Weighting · p. 5

A. Dataset

  • The authors collected a Spot dataset because existing legged-robot datasets lacked either radar or camera data, and generated ground truth with PALoc and Leica RTC360 TLS maps.The reported TLS bundle errors are 0.002–0.006 m, and the initial pose was refined using ICP; the proprioceptive estimator was also evaluated on GaRLILEO and Co-RaL.Source: A. Dataset · p. 5

B. Experimental Setup

On challenging outdoor sequences, RAGNAROK-SLAM reports a lower average translational APE than RAGNAROK-Odom, while results also cover public datasets and component ablations. The setup compares sensor configurations and evaluates odometry with translational and rotational APE RMSE.

B. Experimental Setup

  • The evaluation includes RVI, RKI, VKI, full Odom, and full SLAM configurations, with odometry accuracy measured by translational and rotational APE RMSE.The SLAM configuration adds submapping, loop closure, and bundle adjustment; component-level ablations and SOTA comparisons are also performed.Source: B. Experimental Setup · p. 6

D. Performance on Co-RaL and GaRLILEO Datasets

  • RAGNAROK-RKI outperforms existing methods on Co-RaL and achieves the best performance on GaRLILEO, including MoCap sequences designed to induce leg failures.The rolling-contact and kinematics-aware covariance ablations both improve overall accuracy on Co-RaL.Source: D. Performance on Co-RaL and GaRLILEO… · p. 6

E. Ablation Study

  • On Overpass, S, G, M, and O reduce APEt by 4.5%, 9.2%, 24.3%, and 31.8%; I and A reduce average APEt by 59.7% and 87.7% on visually degraded sequences.Effects of S, G, M, and O are limited on the more stable TerraceLoop and Atrium sequences.Source: E. Ablation Study · p. 6

C. Performance on Self-Collected Dataset

F. Runtime Analysis

The runtime analysis reports per-frame processing and loop-closure costs across Terrace and FloorGyre; the conclusion reports more robust performance than SOTA baselines in low-light and high-vibration scenarios.

F. Runtime Analysis

  • 49.5 ms/frame on Terrace sustains 15 Hz camera input with one dropped frame; FloorGyre averages 64.8 ms/frame and 589.3 ms per loop closure.Source: F. Runtime Analysis · p. 7, Figure 11 · p. 7
  • Proprioceptive optimization takes 7.3 ms on Terrace and 8.2 ms on FloorGyre; enhancement takes 1.1 ms and 0.8 ms, respectively, with BO triggered by significant illumination changes.Source: F. Runtime Analysis · p. 7
  • Terrace loop closures average 110.7 ms without blocking real-time estimation; 105.5 ms end-to-end latency does not limit frame rate because the frontend proceeds in parallel.Source: F. Runtime Analysis · p. 7
  • Configurable parameters offer faster operation at a small cost in accuracy.Source: F. Runtime Analysis · p. 7

V. CONCLUSION

  • RAGNAROK achieves more robust performance than SOTA baselines in low-light and high-vibration scenarios.Source: §V · p. 8
  • The architecture combines slip- and rolling-contact-aware leg estimation, kinematics-aware multi-radar factors, degradation-aware enhancement, radar-enhanced place recognition, and adaptive weighting.Source: §V · pp. 7–8
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