cs.ROOct 8, 2026

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

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Abstract

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.
MethodPlatformSensorsData exchangedAppraoch
     
[ 20 ]UGVVisual3D points+Ctrl cmd.EKF
[ 21 ]UAVVisual+IMU3D features+Odom.EKF
[ 24 ]UGV+UAVVisual+IMU+ UWB+LEDsMutual meas. +Odom.ESKF
[ 22 ]UAVVisual+IMUN/AMachine learning
[ 31 ]UGVFour UWBsN/ANon-linear optimization
TABLE I: Review of the related work on relative localization.
NotationDescription
NNThe number of robots in the team.
Guwb\mathcal{G}_{uwb}UWB connection graph.
Glidar\mathcal{G}_{lidar}LiDAR connection graph.
L(vi)L(v_{i})Label sequence of vertex viv_{i} in Guwb\mathcal{G}_{uwb} .
L(ul)L(u_{l})Label sequence of vertex ulu_{l} in Glidar\mathcal{G}_{lidar} .
Luwb\textbf{L}_{uwb}Set of label sequences of unmatched vertices in Guwb\mathcal{G}_{uwb} .
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 ×\times 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\lambda in Robot1’s perspective. ”-” denotes the robot was not estimated.
 The solution rate (%) to localize nearby robots at different dissimilarity threshold ϵ\epsilon with respect to Robot1
Robot2Robot3Robot4Robot5Robot6Robot7Robot8
ϵ=0.0\epsilon=0.0100%0%0%100%100%100%97.7%
ϵ=0.2\epsilon=0.2100%0%0%100%100%100%100%
ϵ=0.5\epsilon=0.5100%0%0%100%100%100%100%
ϵ=0.7\epsilon=0.7100%0%0%100%100%100%100%
ϵ=1.0\epsilon=1.0100%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\epsilon . 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. rate0%14%43%71%100%
Comm. cost (Bytes)0261014
Comp. time (Seconds)0.0380.0560.1750.3720.382
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.
ApproachComm. RateAverage relative position error (in meters) with respect to Robot1 and solution rate (%)
Robot2Robot3Robot4Robot5Robot6Robot7Robot8
Rel. errorSol. rateRel. errorSol. rateRel. errorSol. rateRel. errorSol. rateRel. errorSol. rateRel. errorSol. rateRel. errorSol. rate
Optimal vertex correspondences disclosure based on common subgraph matching module (Module 2)0%3.33100%-0%6.4497.18%0.65100%0.19100%0.26100%1.14100%
+ Falsely-matched robot recognition module (Module 3)3.33100%-0%6.4497.18%0.65100%0.19100%0.26100%1.14100%
+ Unestimated robots positioning module (Module 4)3.33100%-0%6.4497.18%0.65100%0.19100%0.26100%1.14100%
Optimal vertex correspondences disclosure based on common subgraph matching module (Module 2)14%3.31100%-0%6.4298.32%0.16100%0.19100%0.26100%0.26100%
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.
ProtocolsComm. RateAverage relative position error (in meters) with respect to Robot1 and solution rate (%)
Robot2Robot3Robot4Robot5Robot6Robot7Robot8
Rel. errorSol. rateRel. errorSol. rateRel. errorSol. rateRel. errorSol. rateRel. errorSol. rateRel. errorSol. rateRel. errorSol. rate
Fixed0%3.33100%-0%6.4497.18%0.65100%0.19100%0.26100%1.14100%
Random3.33100%-0%6.4497.18%0.65100%0.19100%0.26100%1.14100%
Fixed14%3.31100%20.5898.32%6.4298.32%0.16100%0.19100%0.26100%0.26100%
Random1.4199.34%9.9738.41%4.8676.82%0.2999.34%0.32100%0.72100%0.5699.34%
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 ×\times 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.
NN681012
Comm. cost (Bytes)7101316
Comp. time (Seconds)0.1070.2071.031.725
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.
Figure 19
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