Recently, the robotics community has regained interest in radar-based perception and state estimation. A 2D imaging radar provides dense 360deg information about the environment. Despite the radar antenna's cone of emission and reception, the collected data is generally assumed to be limited to the plane orthogonal to the radar's spinning axis. Accordingly, most methods based on 2D imaging radars only perform SE(2) state estimation. This paper presents 3DRO, an extension of the SE(2) Direct Radar Odometry (DRO) framework to perform state estimation in SE(3). While still assuming planarity of the data through DRO's 2D velocity estimates, it integrates 3D gyroscope measurements over SO(3) to estimate SE(3) ego motion. While simple, this approach provides lidar-level odometry accuracy as demonstrated using 643km of data from the Boreas-RT dataset.
Figures & tables
Fig. 1: Imaging radars collect data by sweeping radio waves around and analyzing the returned signal. Due to the narrow cone of emission, this type of device is generally considered as a 2D sensor. (b) and (c) present typical data obtained with a 2D imaging radar in raw/polar and Cartesian forms, respectively. In this work, we investigate the problem of SE(3) state estimation using a 2D imaging radar in combination with a 3-DoF gyroscope. Our experiments suggest that such a sensor suite can provide lidar-level odometry accuracy.
Fig. 2: Illustration of the misalignment between the radar sensing plane and the plane of motion. Note that the angle αi is amplified for clarity. In reality, this angle is close to zero.
Fig. 3: Example of odometry trajectories obtained with 3DRO and the various baselines of our SE(3) performance analysis.
Seq. type
LTR w/ gyro [ 13 ]
2Fast-2Lamaa [ 29 ]
DRO [ 2 ]
3DRO No vz
3DRO (ours)
suburbs
0.29 / 0.09
0.22 / 0.08
1.38/0.58
0.55/ 0.09
0.31/ 0.09
industrial
0.25 / 0.09
0.20 / 0.07
1.41/0.63
0.66/0.13
0.49/0.13
urban
0.49 / 0.20
0.38 / 0.10
1.54/0.66
1.01/0.32
0.92/0.32
forest
0.70/ 0.11
0.47 /0.18
3.04/1.22
0.51/ 0.08
0.34 / 0.08
farm
0.44 / 0.12
0.36 / 0.10
1.09/0.48
0.62/0.15
0.54/0.15
regional
0.35 / 0.09
0.20 / 0.08
1.19/0.49
0.63/ 0.08
0.39/ 0.08
TABLE I: Per-route average SE(3) odometry accuracy on the Boreas-RT dataset ( best and second best ).
Seq. type
3DRO No vz
3DRO (ours)
RMSE
Avg. err.
RMSE
Avg. err
suburbs
0.063
0.041
0.042
-0.003
industrial
0.056
0.029
0.044
-0.007
urban
0.041
0.019
0.030
-0.002
forest
0.094
0.069
0.063
-0.016
farm
0.083
0.054
0.060
-0.013
TABLE II: Per-route vertical body velocity errors [m/s] with and without the proposed approximation ( best ).
Fig. 4: Per-axis velocity estimates obtained with 3DRO on three different sequences of the Boreas-RT dataset.
Sequence type
RTR w/
OG
DRO
3DRO
gyro [ 13 ]
[ 32 ]
[ 2 ]
(ours)
suburbs
0.36/0.05
0.25/ 0.04
0.20 / 0.04
0.18/0.03
industrial
0.45/0.08
0.28 / 0.05
0.34/ 0.05
0.33 / 0.03
urban
1.10/0.16
0.44 / 0.11
0.65/ 0.11
0.63 / 0.10
forest
0.57/ 0.06
0.38/ 0.06
0.28 / 0.06
0.18/0.02
TABLE III: Per-route average SE(2) odometry results on the Boreas-RT dataset ( best and second best ).
Sequence type
ID
LTR w/ gyro [ 13 ]
2Fast-2Lamaa [ 29 ]
3DRO (ours)
suburbs
2024-12-03-12-54
0.30/0.10
0.24/0.08
0.35/0.11
2024-12-05-14-25
0.29/0.09
0.21/0.08
0.34/0.10
2025-01-08-10-59
0.30/0.09
0.23/0.08
0.32/0.10
2025-01-08-11-22
0.28/0.09
0.21/0.07
0.26/0.07
2025-01-08-12-28
0.26/0.08
0.21/0.08
0.37/0.08
TABLE IV: Per-sequence SE(3)odometry results on the Structured and Rural sequences of the Boreas-RT dataset.
Sequence type
ID
LTR w/ gyro [ 13 ]
2Fast-2Lamaa [ 29 ]
3DRO (ours)
regional
2024-12-03-13-13
0.34/0.09
0.18/0.07
0.47/0.09
2024-12-03-13-34
0.34/0.09
0.20/0.08
0.36/0.08
2024-12-10-12-07
0.34/0.09
0.20/0.08
0.34/0.07
2024-12-10-12-24
0.35/0.10
0.21/0.08
0.30/0.08
2024-12-10-12-38
0.32/0.08
0.18/0.08
0.34/0.07
TABLE V: Per-sequence SE(3) odometry results on the Highway sequences of the Boreas-RT dataset.
Robotics Institute University of Toronto. · Department of Computer, Control, and Management Engineering “Antonio Ruberti”, Sapienza University of Rome.