DRT&R: Direct Radar Teach & Repeat

I. INTRODUCTION

• FMCW spinning radar offers a 360° viewpoint, weather resilience, and long range, but radar teach-and-repeat degrades in fully off-road scenarios.Earlier radar work generally extracted sparse point clouds, and performance in unstructured off-road settings could degrade to failure.Source: §I · p. 1
• Repeatable radar artifacts can provide localization information, and teach-and-repeat helps preserve similar sensor viewpoints between mapping and repeat runs.Point-cloud methods avoid extracting artifact points, while direct methods often smooth or remove artifact pixels; local maps can instead encode these repeatable features.Source: §I · p. 1
• DRT&R combines direct radar odometry and localization into a topometric navigation approach evaluated in closed loop on a Clearpath Warthog.The evaluation compares localization with direct globally consistent mapping and path tracking with an existing point-cloud method; lidar-based ground truth is used where GNSS performs poorly.Source: §I · pp. 1–2
• 344 km of on-road data and 20 km of off-road data yield SOTA radar localization results; closed-loop off-road tracking exceeds 10 km with 6 cm RMS error.The reported tracking performance is on par with lidar-based methods.Source: §I · p. 2

II. RELATED WORK

• Sparse radar representations rely on reflective objects and environmental structure, assumptions often violated by off-road foliage and sparse human-made features.Direct methods use the full intensity return rather than downsampling according to assumptions about reliable returns.Source: §II · p. 2
• DRO and its extensions showed robustness and performance on-road, while direct global localization had not been studied off-road.Earlier radar odometry and localization methods based on ICP were observed to fail on off-road datasets.Source: §II · p. 2
• Global maps can remove pose-specific measurement biases, whereas topometric maps retain locally consistent metric maps linked along paths.Prior radar T&R systems used point clouds; Xiao et al. used lidar maps with 4D radar localization, and Hilger et al. stored point maps with oriented normals.Source: §II · p. 2
• Prior closed-loop radar T&R performance depended on off-road structure, while this approach reports improved offline localization and closed-loop tracking without degradation in unstructured environments.The cited prior closed-loop radar T&R systems are Xiao et al. and Qiao et al..Source: §II · p. 2

III. METHOD

• Teach-and-repeat first creates a topometric map during manual traversal, then autonomously navigates its taught paths using odometry and localization against nearby submaps.Odometry links the submaps along locally consistent paths, and successful localization and odometry guide submap switching during repeats.Source: §III · p. 2
• Submaps preserve perspective-dependent multipath reflections and viewpoint-specific geometry that are re-observed at similar locations during repeat runs.The figure contrasts these local features with the globally aligned Dr-BA map, where such features are averaged out.Source: Figure 2 · p. 3
• DRT&R roots odometry, submaps, and localization in dense FMCW radar scans rather than sparse point representations.The method uses local submaps to encode perspective-dependent features that a globally aligned map can average out.Source: §III · p. 3, Figure 2 · p. 3

A. Radar Formulation

• Each radar scan is stored as an N × M image, with azimuth measurements by row and range-bin intensities represented across each row.The stored data also includes measurement times and the corresponding range-bin positions.Source: A. Radar Formulation · p. 3

1) Odometry:

• DRO estimates each frame’s body-centric velocity and intra-frame orientation change, then integrates velocity to compute the relative pose between frames.A gyroscope provides additional interoceptive information; when available, DRO preintegrates orientation from heading measurements.Source: 1) Odometry · p. 3
• DRO estimates motion by maximizing cross-correlation between the live dense scan and a short history of dense scans.The history is a motion- and Doppler-undistorted Cartesian image transformed into the current scan; live-return coordinates are corrected for motion distortion and Doppler before bilinear interpolation.Source: 1) Odometry · p. 3
• Gradient ascent maximizes the cross-correlation over velocity and, optionally, intra-frame orientation, recomputing corrected return coordinates at each iteration.Source: 1) Odometry · p. 3
• After optimization, DRO updates the smoothed scan pixel-wise with an exponential moving average using the current undistorted intensity scan.DRT&R sets β = 0.25.Source: 1) Odometry · p. 4

2) Submaps:

• DRT&R uses individual locally smoothed scans as submaps rather than globally bundle-adjusted scans, to avoid averaging out perspective-dependent radar measurements.The stored submaps are further smoothed and down-sampled into a regularly spaced voxel grid.Source: 2) Submaps · p. 4
• Teach-and-repeat can make artifact bias in the live scan and submap roughly cancel when localization occurs from a state matching the teach.The submap-frequency choice trades variance reduction from larger maps against retaining artifacts in smaller, more frequent maps.Source: 2) Submaps · p. 4
• A new submap is created when the similarity score with the most recent submap falls below τ; DRT&R uses τ = 0.95.The score proxies overlap of non-zero intensity measurements, and submaps are intended to capture unique viewpoints and consistent radar artifacts.Source: 2) Submaps · p. 4

C. Repeat

• Direct radar localization estimates pose by comparing the live smoothed scan with the nearest voxelized submap.DRO runs on every frame to provide an initial guess and prior for the localization optimization.Source: C. Repeat · p. 4
• Repeat frames approximately follow the teach path, with greater overlap in viewpoint-dependent features between paired scans than in the averaged Dr-BA map.Source: C. Repeat · p. 4
• When closed-loop control is available, an MPC uses localization-derived relative pose to guide the robot toward the taught path.The controller is identical to the one used in.Source: C. Repeat · p. 4

IV. EVALUATION

• 344 km of on-road data and 20 km of off-road data are used to establish DRT&R as a state-of-the-art spinning-radar localization approach.The on-road evaluation uses Boreas-RT; the off-road evaluation uses newly collected Clearpath Warthog data.Source: §IV · pp. 4–5
• 58 km of Boreas-RT data are used for teach mapping and 286 km for repeat localization, using the baseline dataset split.Source: §IV · p. 4
• 20.1 km of Warthog data cover four off-road sequences, with manual and autonomous runs and deliberately varied manual paths.The manual runs include nominal, left/right-offset, and low- and high-frequency oscillating paths.Source: §IV · p. 5, Figure 3 · p. 5
• Off-road pose evaluation uses synchronized Ouster lidar scans localized with 2Fast-2Lamaa as ground truth.The Warthog GNSS system has significant position errors under tree cover and other multipath effects.Source: §IV · p. 5
• Offline localization is compared with Dr-BA, while closed-loop tracking is compared with RT&R and lidar teach-and-repeat.Source: §IV · p. 5

V. RESULTS

• 74.9% lower position error on Farm is the largest improvement over previous radar methods, while DRT&R achieves state-of-the-art radar localization across on-road routes.A locally re-observed ground strike and a perspective-dependent tree view provide cues omitted from Dr-BA’s global map.Source: §V · pp. 5–6, Figure 4 · p. 6
• Local submaps improve translational localization in Farm and Skyway examples through ground-strike and perspective cues or better overlap in road visibility.Source: Figure 4 · p. 6, §V · p. 6
• 50% better orientation estimates than other radar methods are reported in Tunnel, where multiple wall reflections provide longer-range features.The reflections are nonphysical, and DRO also leverages Doppler information for longitudinal position estimates.Source: §V · p. 6
• 50% lower average position error and 32.2% lower average orientation error than Dr-BA are reported off-road, with the largest improvement of 68.5% on Campus.Topologically distant but physically close revisits can make Dr-BA’s global maps imprecise; the topometric submaps do not share information across those places.Source: §V · p. 6

A. Effect of Submap Frequency on Localization

• More submaps lead to more accurate localization, while topometric-map storage grows with submap count.In Garage, gains from 40 to 400 submaps are small despite requiring 10 times the disk space.Source: A. Effect of Submap Frequency on… · p. 6
• Similarity-based submapping is superior to distance-based submapping when thresholds yield few submaps.The comparison covers Industrial, Tunnel, and Garage environments.Source: Figure 5 · p. 6
• Similarity scoring captures abrupt transitions such as tunnel entrance occlusion, where distance thresholding misses the change and localization suffers.In Garage, similarity-based submaps also cluster around the outside transition and changing radar ground strike as the robot climbs.Source: A. Effect of Submap Frequency on… · p. 6

B. Effect of Path Following on Localization

• Within 4 m of lateral offset from the taught path, localization position error has no observed correlation with distance from the path.The Warthog manual runs include deliberately offset and oscillating paths.Source: B. Effect of Path Following on… · p. 6

C. Closed-Loop Path Tracking

• The closed-loop evaluation integrates the full stack on a Warthog over 10.6 km of repeats at 1 m/s across five routes.Source: C. Closed-Loop Path Tracking · p. 6
• 44% average reduction in path-tracking error is reported with DRT&R compared with RT&R.DRT&R localization RMSE remains around 3.5 cm and path-tracking RMSE ranges from 3.8 cm to 6.2 cm.Source: C. Closed-Loop Path Tracking · p. 7, Table IV · p. 7
• 6.2 cm RMS path-tracking error is reported over an additional 6.5 km of autonomous Campus repeats.The maximum path-tracking error also decreases in all sequences, with the largest reduction of 35 cm in Woody.Source: C. Closed-Loop Path Tracking · p. 7
• Over 10.3 km of autonomous repeating, DRT&R path-tracking errors are within 1 cm of LT&R and tracking handles three-dimensional terrain and indoor-outdoor transitions.The comparison uses an identical MPC controller across the three cases.Source: C. Closed-Loop Path Tracking · p. 7
• Both RT&R and DRT&R run faster than the 4 Hz radar frame rate on the tested laptop.In Woody, DRT&R takes 107.67 ms for odometry and 55.58 ms for localization; code optimization of DRO is left for future work.Source: C. Closed-Loop Path Tracking · p. 7

• DRT&R achieves state-of-the-art localization on 344 km of on-road data and 20 km of off-road data.Source: §VI · p. 8
• 6 cm RMS path-tracking errors over more than 10 km in closed loop were accompanied by a 44% lower average error than using point clouds.The evaluation used a Clearpath Warthog off-road.Source: §VI · p. 8
• Small local maps preserve state-dependent artifacts, including multi-path reflections and ground strikes, that improve localization.Source: §VI · p. 8
• A submap-creation method based on incoming-scan similarity increases density at transitions and saves storage in consistent environments.Source: §VI · p. 8