Distributed Relative Localization Based on Ultra-WideBand and LiDAR for Multi-robot with Limited Communication
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
Relative localization is crucial for a multi-robot system to collaboratively perform tasks, such as exploration and formation. However, this is highly challenging for homogeneous robots with similar appearance in GPS-denied and communication-limited environments. In this paper, we propose a fully distributed relative position estimation approach for a team of robots based on onboard UWB and LiDAR sensors, in which LiDAR is utilized to obtain the position of anonymous objects in Line-of-Sight (LOS), and UWB is used for ranging between robots. We construct two graphs, namely UWB connection graph and LiDAR connection graph, to represent the spatial relationship among objects (robots and obstacles) based on UWB and LiDAR measurements. Identification and relative position estimation are formulated as a common subgraph matching problem. A falsely-matched robot identification approach is designed to recognize the falsely-matched results caused by obstacle blockage in LiDAR field of view. These robots are then localized by leveraging the well-matched robots and the UWB ranging measurements in the UWB connection graph. We conducted experiments to evaluate the performance of our approach. The results show that the proposed approach is capable of achieving satisfactory positioning accuracy for a team of robots in a distributed manner with only exchanging limited information.
Figures & tables
Fig. 1: Overview of the proposed distributed relative localization system using Robot1 as an example. Each robot is equipped with one UWB node to measure the distances to nearby robots and broadcast a small amount of UWB ranging data. The robot also carries LiDAR to estimate the position of the surrounding objects (robots and obstacles) in LOS. The proposed relative localization approach independently runs in a distributed manner.
Fig. 2: The architecture of the proposed distributed relative localization approach.
Method
Platform
Sensors
Data exchanged
Appraoch
[ 20 ]
UGV
Visual
3D points+Ctrl cmd.
EKF
[ 21 ]
UAV
Visual+IMU
3D features+Odom.
EKF
[ 24 ]
UGV+UAV
Visual+IMU+ UWB+LEDs
Mutual meas. +Odom.
ESKF
[ 22 ]
UAV
Visual+IMU
N/A
Machine learning
[ 31 ]
UGV
Four UWBs
N/A
Non-linear optimization
TABLE I: Review of the related work on relative localization.
Notation
Description
N
The number of robots in the team.
Guwb
UWB connection graph.
Glidar
LiDAR connection graph.
L(vi)
Label sequence of vertex vi in Guwb .
L(ul)
Label sequence of vertex ul in Glidar .
Luwb
Set of label sequences of unmatched vertices in Guwb .
TABLE II: The critical notations used in this paper.
Fig. 3: The illustration of the UWB and LiDAR connection graphs. (a) constructed by utilizing UWB ranging directly measured by itself (blue solid line) and those shared by peer robots (blue dotted line) based on the customized UWB communication protocol, as depicted in Section IV-A . (b) constructed by using the distance between each pair of clusters (aqua solid line) generated by the adaptive clustering algorithm [ 14 ] . The robot that is not detected by LiDAR will not be considered as a vertex.
Fig. 4: The UWB communication protocol for different communication rates.
Fig. 5: The experimental setups in an indoor environment with 6m × 17m, including 8 robots and several obstacles. Robot 1 is NLOS to Robot 3 and Robot 4 (aqua dotted line). Note that paper wrapping only provides a controllable LiDAR detection for performance evaluation.
Fig. 6: The experimental results obtained from the optimal vertex correspondences disclosure based on common subgraph matching module (Section III-B ) with different distance threshold λ in Robot1’s perspective. ”-” denotes the robot was not estimated.
The solution rate (%) to localize nearby robots at different dissimilarity threshold ϵ with respect to Robot1
Robot2
Robot3
Robot4
Robot5
Robot6
Robot7
Robot8
ϵ=0.0
100%
0%
0%
100%
100%
100%
97.7%
ϵ=0.2
100%
0%
0%
100%
100%
100%
100%
ϵ=0.5
100%
0%
0%
100%
100%
100%
100%
ϵ=0.7
100%
0%
0%
100%
100%
100%
100%
ϵ=1.0
100%
0%
0%
100%
100%
100%
100%
TABLE III: Experimental evaluation of the proposed falsely-matched robot identification module (see Section III-C ) at different dissimilarity threshold ϵ . We aim to remove all falsely-matched results for Robot4 (a solution rate of 0%) and retain the results for other robots (a solution rate of 100%).
Fig. 7: Visualization of experimental results: (a) results of the optimal vertex correspondences disclosure based on common subgraph matching module (Section III-B ), (b) results with the falsely-matched robot identification module (Section III-C ), (c) results with the positioning unestimated robots module (Section III-D ). ”-” denotes the robot was not estimated.
Comm. rate
0%
14%
43%
71%
100%
Comm. cost (Bytes)
0
2
6
10
14
Comp. time (Seconds)
0.038
0.056
0.175
0.372
0.382
TABLE IV: The communication cost per robot and the average time consumption of the proposed approach (Module 2 + Module 3 + Module 4) under different communication rates.
Approach
Comm. Rate
Average relative position error (in meters) with respect to Robot1 and solution rate (%)
Robot2
Robot3
Robot4
Robot5
Robot6
Robot7
Robot8
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Optimal vertex correspondences disclosure based on common subgraph matching module (Module 2)
Optimal vertex correspondences disclosure based on common subgraph matching module (Module 2)
14%
3.31
100%
-
0%
6.42
98.32%
0.16
100%
0.19
100%
0.26
100%
0.26
100%
TABLE V: Evaluation of the proposed approach under different communication rates: relative position error (in meters) and solution rate (in %) of each robot with respect to robot1. ”-” denotes the robot was not estimated.
Protocols
Comm. Rate
Average relative position error (in meters) with respect to Robot1 and solution rate (%)
Robot2
Robot3
Robot4
Robot5
Robot6
Robot7
Robot8
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Rel. error
Sol. rate
Fixed
0%
3.33
100%
-
0%
6.44
97.18%
0.65
100%
0.19
100%
0.26
100%
1.14
100%
Random
3.33
100%
-
0%
6.44
97.18%
0.65
100%
0.19
100%
0.26
100%
1.14
100%
Fixed
14%
3.31
100%
20.58
98.32%
6.42
98.32%
0.16
100%
0.19
100%
0.26
100%
0.26
100%
Random
1.41
99.34%
9.97
38.41%
4.86
76.82%
0.29
99.34%
0.32
100%
0.72
100%
0.56
99.34%
TABLE VI: Evaluation of the proposed approach (Module 2 + Module 3 + Module 4) under different UWB communication protocols: relative position error (in meters) and solution rate (in %) of each robot with respect to robot1. ”-” denotes the robot was not estimated.
Fig. 8: The simulation setups in a 15m × 15m environment with different numbers of robots.
Fig. 9: Evaluation of the positioning accuracy of each robot relative to Robot1, with different numbers of robots.
N
6
8
10
12
Comm. cost (Bytes)
7
10
13
16
Comp. time (Seconds)
0.107
0.207
1.03
1.725
TABLE VII: The communication cost per robot and the average time consumption of the proposed approach with different numbers of robots.
Fig. 10: Robot1 is controlled to move along the rectangle path. When Robot1 moves to the rightmost position, both Robot2 and Robot3 are out of Robot1’s LiDAR range.
Fig. 11: The relative position error of each robot relative to Robot1 when Robot1 moves along the rectangle path.
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.
Zhiqiang Cao, Ran Liu, Billy Pik Lik Lau +2
Engineering Product Development, Singapore University of Technology and Design, Singapore 487372 · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
Relative localization is essential for cooperation in autonomous multi-robot systems. Existing approaches either rely on shared environmental features or inertial assumptions, or they degrade under pairwise non-line-of-sight conditions and outliers in complex environments. Robustly and efficiently fusing inter-robot bearings, distances, and inertial measurements for tens of robots remains challenging. We present CREPES-X (Cooperative RElative Pose Estimation System with multiple eXtended features), a hierarchical relative localization framework that enhances speed, accuracy, and robustness under challenging conditions, without requiring any global information. The hardware packs infrared (IR) LEDs, an IR camera, an ultra-wideband module, and an IMU into a cube no larger than 6cm on each side. On this hardware, a two-stage hierarchical estimator meets different latency, accuracy, and robustness requirements. The single-frame estimator returns instantaneous relative poses from a closed-form solution with bearing outlier rejection. The multi-frame estimator then refines these poses with IMU pre-integration under robocentric relative kinematics, using loosely- and tightly-coupled optimization. Extensive simulations and real-world experiments validate the effectiveness of CREPES-X, demonstrating robustness of up to 90% bearing outliers, resilience in challenging conditions, and RMSE of 7.0cm and 2.2∘ in real-world datasets.
Zhehan Li, Jiadong Lu, Zheng Wang +6
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
The ability to localise teams of robots is essential for applications ranging from robotic fleets in unstructured environments to cooperative control and navigation tasks. In such contexts, fixed infrastructure is often unavailable, deployments must be fast and flexible, and system requirements must be minimal. We present a decentralised cooperative localisation algorithm that addresses all these challenges at once. The method is anchor-less, fully decentralised, and, unlike most existing approaches, does not require controlling the robots motion to ensure team observability. It relies only on local odometry, sparse inter-agent ranging measurements, and short-range communication, all of which are widely available in practice. The algorithm adopts a multi-hypothesis Bayesian framework that maintains the entire set of feasible solutions, ensuring robustness under transient unobservable conditions. Moreover, through information sharing, each agent benefits from the estimates of the entire group, even in partially connected conditions.
Paolo Golinelli, Tommaso Faraci, Daniele Fontanelli
Department of Industrial Engineering, University of Trento, Trento, Italy · Department of Information Engineering and Computer Science, University of Trento, Trento, Italy