Distributed Relative Localization for Homogeneous Multi-Robot Systems through UWB Ranging and Limited Communications
Authors: Zhiqiang Cao, Ran Liu, Billy Pik Lik Lau, Chau Yuen, U-Xuan Tan
Organizations: Engineering Product Development, Singapore University of Technology and Design, Singapore 487372 · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
Accurate and reliable relative localization is crucial for multi-robot applications like exploration, search, and rescue missions. LiDAR-based solutions offer high accuracy in localizing surrounding objects; however, distinguishing homogeneous robots with similar appearances remains challenging due to the lack of distinctive identification features. In this paper, we propose a fully distributed relative pose estimation approach by integrating LiDAR, UWB, and odometry measurements, allowing each robot to accurately and continuously localize its teammates without external infrastructure. Specifically, potential anonymous teammate robot clusters from LiDAR scans are tracked by a dynamic tracker. We then identify teammate robots from these tracked anonymous clusters using a joint matching strategy, ensuring reliable data association between robots and clusters. Finally, by combining the corresponding LiDAR observations, UWB ranging, and odometry measurements, each robot precisely localizes others while minimizing data exchange. The system requires only odometry data exchange through onboard UWB, eliminating the need for additional communication infrastructure like WiFi routers or mesh networks. Extensive simulation and real-world experiments demonstrate the effectiveness and reliability of the proposed relative localization approach.
Figures & tables
Fig. 1: Illustration of the relative localization problem considered in this paper, from Robot 1’s perspective. Robot 1 attempts to localize others in its local frame under the following conditions: unknown initial pose correspondence, anonymous LiDAR clusters, and possible occlusions during movement. Additionally, data transmission relies solely on the UWB communication network, mounted on the robot, without any external communication devices. Each robot in the multi-robot system independently executes the same relative localization procedure.
Work
Sensors
Markers
Data Exchanged
Initial Pose
[ 19 ]
LiDAR + Camera + IMU
N/A
Ego state, Feature descriptors
Unknown
[ 20 ] [ 21 ]
Camera + IMU
N/A
Ego state
Known
[ 13 ]
LiDAR + IMU
Reflective taps
Ego state, Mutual observations
Unknown
[ 23 ]
Camera + UWB + IMU + IR LEDs
LED coded boards
IMU, Mutual observations
Unknown
[ 24 ]
LiDAR + UWB
N/A
UWB ranging meas.
Unknown
[ 25 ] [ 26 ]
Four UWBs
N/A
N/A
Unknown
TABLE I: Comparison of related works on relative localization in multi-robot systems.
Fig. 2: Architecture of the proposed fully distributed relative localization approach, comprising five core modules. The data preprocessing module eliminates outlier UWB and LiDAR observations. The dynamic tracker module tracks the anonymous LiDAR clusters. The extrinsic transformation estimation and teammate identification module addresses the unknown initial pose correspondence and data association problem. The teammate tracker module enables continuous localization of teammate robots by fusing UWB, LiDAR, and odometry data. All the communications among robots rely solely on the UWB communication network module.
Fig. 3: Illustration of raw and filtered UWB ranging data, as measured by Robot 1 . (a) UWB ranging measurements of Robot 2 . (b) UWB ranging measurements of Robot 3 .
Fig. 4: Illustration of the teammate tracker based on pose graph optimization, demonstrating how Robot i localizes Robot j within its own global frame. The constraints include odometry measurements of two robots (black line), UWB ranging measurements (red line), and LiDAR detection (blue line). An initial guess is used to determine the initial poses of Robot j ’s trajectory for each optimization.
Fig. 5: The message structure employed in the UWB communication network. Only odometry information is broadcasted within our multi-robot system.
Fig. 6: Three mobile robots moved randomly in the environment with a size of 17.1m × 6.2m, and the initial correspondence among them is unknown. The box is used for controllable LiDAR detection, ensuring a more systematic performance evaluation. Notably, only a single LiDAR scan channel is used for 2D perception.
Fig. 7: Ground truth and odometry measurements of three different robots in the experiment.
Approach
Robot 2
Robot 3
No. of Inliers
No. of Outliers
Trans. error (m)
No. of Inliers
No. of Outliers
Trans. error (m)
Distance matching
1579
80
0.15
806
259
1.08
Trajectory matching
1579
0
0.08
806
279
1.01
Joint matching ( Ours )
1579
0
0.08
806
0
0.13
TABLE II: Evaluation of teammate identification under different teammate identification methods from Robot 1’s perspective: number of identified teammates and translational error (in meters).
Fig. 8: Evaluation of teammate identification using various joint dissimilarity thresholds λ .
Fig. 9: The estimated trajectory of Robot 2 and Robot 3 with respect to Robot 1, generated by the teammate tracker with an initial guess based on the latest extrinsic transformation for each optimization under different combinations of constraints (dark blue line: odom; purple line: odom+UWB; pink line: odom+UWB+LiDAR).
Odom constraints
Odom + UWB constraints
Odom + UWB + LiDAR constraints
Trans. error
Rot. error
Time (ms)
Trans. error
Rot. error
Time (ms)
Trans. error
Rot. error
Time (ms)
mean
std
mean
std
mean
std
mean
std
mean
std
mean
std
Robot 2
0.15
0.13
3.82
2.73
33.1
0.11
0.07
3.76
2.22
49.5
0.09
0.05
2.95
1.39
50.5
Robot 3
0.31
0.18
4.72
2.29
34.3
0.21
0.13
3.34
1.99
50.4
0.14
0.06
3.20
1.50
51.1
TABLE III: Evaluation of the teammate tracker with different constraint conditions from Robot 1’s perspective: relative translational error (in meters), relative rotational error (in degrees), and average computational time (in milliseconds). mean is the average value, and std represents the standard deviation value.
Fig. 10: Evaluation of different approaches with identical communication requirements: the average relative translational error (in meters) and relative rotational error (in degrees) in our experiment.
What should be received
What has received
Loss rate (%)
# of packets
Size (KB)
# of packets
Size (KB)
Robot 1
9597
76.776
9536
76.288
0.64%
Robot 2
9595
76.760
9564
76.512
0.32%
Robot 3
9596
76.768
9551
76.408
0.47%
TABLE IV: Packet loss rate in our experiment using the UWB communication network. One packet corresponds to one message consisting of 8 Bytes.
Fig. 11: Three mobile robots moved randomly in a 14.2m × 14.2m unstructured environment containing dynamic and static obstacles.
Fig. 12: Visualization of pose estimation from different observing robots’ viewpoints. Trajectories are obtained by transferring the estimated relative pose to the ground truth of the observing robot.
Fig. 13: Simulation environment and trajectories of ten robots. (a) Gazebo-based simulation environment with a size of 16m × 16m. (b) Ground truth and odometry trajectories.
Average relative translational error (in meters) and rotational error (in degrees) with respect to Robot 1
Trial 1
Trial 2
Trial 3
Trial 4
Robot 2
Trans. error
0.09±0.05
0.11±0.09
0.11±0.09
0.14±0.09
Rot. error
2.86±2.58
2.34±1.64
2.48±1.97
2.01±1.35
Robot 3
Trans. error
0.18±0.12
0.16±0.11
0.16±0.10
0.21±0.13
Rot. error
3.10±2.01
2.78±1.88
2.78±1.60
3.47±2.10
Robot 4
Trans. error
-
0.08±0.05
0.08±0.05
0.08±0.04
TABLE V: Relative pose estimation accuracy (i.e., translational error and rotational error) of our approach from Robot 1’s perspective. Trials 1–4 correspond to teams of 3, 5, 7, and 10 robots, respectively. ’-’ denotes robot absent from the trial.
Engineering Product Development, Singapore University of Technology and Design, Singapore 487372 · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China. · Huzhou Institute of Zhejiang University, Huzhou, China. · University of Michigan, Ann Arbor, MI, USA. +1
Department of Industrial Engineering, University of Trento, Trento, Italy · Department of Information Engineering and Computer Science, University of Trento, Trento, Italy