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Distributed Relative Localization for Homogeneous Multi-Robot Systems through UWB Ranging and Limited Communications

Zhiqiang Cao, Ran Liu, Billy Pik Lik Lau, Chau Yuen, U-Xuan Tan

arXiv:2610.11308v1cs.RO

TL;DR

Relative localization for homogeneous robots is challenged by unknown correspondence, anonymous LiDAR detections, drift, and sensing or communication constraints. The paper combines LiDAR, UWB, and odometry in a distributed system that tracks and identifies teammates, reporting accurate localization with little data exchange.

  • Problem

    Unknown initial correspondence, anonymous detections, pose drift, and line-of-sight conditions complicate infrastructure-free relative localization of homogeneous robots.

    Source: §I · p. 1

  • Method

    The distributed approach tracks anonymous LiDAR clusters, identifies teammates through joint matching, and fuses LiDAR, UWB ranging, and odometry for continuous localization.

    Source: §I · p. 2, D. Teammate Tracker · p. 6

  • Results

    Approximately 0.12 m average relative translational error and 2.20° relative rotational error were achieved with 0.48 KB/s data exchange at 20 Hz in a three-robot system.

    Source: §VI · p. 10

  • Takeaways & Limitations

    The approach supports distributed localization of homogeneous robots using onboard UWB communication without prior initial correspondence or external communication infrastructure.

    Source: §I · p. 2, §VI · p. 10

    With only odometry constraints, tracker performance might degrade over time, though it can recover after the extrinsic transformation is periodically updated.

    Source: C. Evaluation of Teammate Tracker · p. 8

Abstract

from arXiv · show

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.

I. INTRODUCTION

Relative localization is needed for coordinated multi-robot tasks, but unknown initial correspondence, anonymous detections, sensor limitations, and constrained communications complicate it. The paper combines LiDAR, UWB, and odometry in a distributed approach and reports accurate localization with limited data exchange.

I. INTRODUCTION

  • Unknown initial pose correspondence, anonymous LiDAR detections, pose drift, and line-of-sight constraints complicate infrastructure-free relative localization.Feature matching may also require substantial computation and communication, while UWB ranging supplies identity but no bearing information.Source: §I · pp. 1–2
  • The approach tracks anonymous LiDAR clusters, identifies teammates through joint matching, then fuses LiDAR, UWB ranging, and odometry for continuous relative localization.Its onboard UWB network carries odometry messages of 8 Bytes per robot without external communication infrastructure.Source: §I · p. 2
  • 0.48 KB/s at 20 Hz in a three-robot system accompanied high relative localization accuracy with minimal data exchange.The system exchanges odometry through onboard UWB.Source: §I · p. 2

II. RELATED WORKS

  • Prior approaches trade communication and computation costs against assumptions or platform constraints: feature sharing is costly, some VIO methods assume known correspondence, and several association methods require customization or can fail in symmetric configurations.UWB-only methods may have limited accuracy or require multiple samples for an initial guess; one multimodal method exceeds UWB communication capacity.Source: §II · pp. 2–3

III. PROPOSED RELATIVE LOCALIZATION FRAMEWORK

The framework gives each robot an independent relative-localization procedure in its own global frame, without assuming known initial pose correspondence. Five modules process measurements, track anonymous clusters, identify teammates, estimate their poses continuously, and exchange odometry over UWB.

III. PROPOSED RELATIVE LOCALIZATION FRAMEWORK

  • The framework comprises preprocessing, anonymous-cluster tracking, extrinsic transformation estimation and teammate identification, teammate tracking, and a UWB communication network.The network broadcasts odometry to nearby robots within communication range.Source: §III · p. 3
  • Each robot carries LiDAR, UWB, and wheel odometry and maintains its own global and local frames; initial pose correspondence among robots is unknown.No universal world global frame is assumed; each robot's global frame is fixed at its initial point while its local frame follows its motion.Source: §III · p. 3

A. Data Preprocessing

Preprocessing rejects abnormal UWB ranges and LiDAR clusters before the main algorithm. For UWB ranges, a low-pass filter uses temporal variation and a robot-speed bound to screen and update measurements.

A. Data Preprocessing

  • Preprocessing is applied before the main algorithm to reduce the effect of severely noisy measurements.The section covers UWB ranging and LiDAR cluster outlier rejection.Source: A. Data Preprocessing · pp. 3–4

1) UWB outlier rejection:

  • Raw UWB ranges are smoothed and screened because multipath effects and electromagnetic interference can produce unpredictable outliers.Figure 3 illustrates raw and filtered measurements recorded by Robot 1 for Robots 2 and 3.Source: 1) UWB outlier rejection · p. 4, Figure 3 · p. 4
  • A low-pass filter initializes from a short-window mean only when variance is below a threshold; otherwise the data is discarded.After initialization, it updates only when the latest range lies within a bound determined by maximum robot speed, and it is reinitialized after an update-free period.Source: 1) UWB outlier rejection · p. 4

2) Potential teammate detection:

The method filters anonymous LiDAR clusters, tracks them over time, then estimates an extrinsic transformation to align teammate odometry with tracked-cluster trajectories. These steps prepare clusters for teammate identification despite unknown initial pose correspondence.

2) Potential teammate detection:

  • Clusters within the empirically chosen 1.0 m UWB-range difference and of robot-like size remain potential teammate candidates.The adaptive clustering algorithm supplies anonymous clusters with local positions and bounding-box sizes.Source: 2) Potential teammate detection · p. 4

B. Dynamic Tracker

  • Each anonymous cluster receives an independent tracker that predicts motion, associates nearby detections, corrects valid matches, and terminates after too many uncorrected steps.The tracker uses a random-velocity model and positions expressed in Robot i’s global frame.Source: B. Dynamic Tracker · p. 4

C. Extrinsic Transformation Estimation and Teammate Identification

  • Because initial pose correspondence is unknown, an extrinsic transformation aligns each teammate’s odometry trajectory with a tracked cluster’s trajectory and provides an initial guess for later optimization.The transformation includes a translation vector and rotation matrix.Source: C. Extrinsic Transformation Estimation… · p. 4

1) Extrinsic transformation estimation:

The method estimates an extrinsic transformation between a teammate’s odometry trajectory and a tracked LiDAR-cluster trajectory. It uses downsampled recent measurements and corrects rotation estimates that represent reflections.

1) Extrinsic transformation estimation:

  • Kabsch alignment minimizes root mean squared error over a fixed-length window of recent measurements, downsampled to s+1 evenly spaced samples.The transformation estimation procedure takes the tracked-cluster trajectory as input and returns an extrinsic transformation.Source: 1) Extrinsic transformation estimation · pp. 4–5
  • The algorithm centers trajectory points, computes a covariance matrix, applies singular value decomposition, then derives rotation and translation for the transformation.The translation is computed from the trajectories’ centroids and the estimated rotation.Source: 1) Extrinsic transformation estimation · p. 5
  • If the estimated rotation matrix has a negative determinant, the method treats it as a reflection and flips the second column of V before computing the rotation.This correction is intended to ensure the obtained rotation matrix is correct.Source: 1) Extrinsic transformation estimation · p. 5

2) Teammate identification:

Teammate identification compares tracked anonymous LiDAR clusters with teammate odometry and UWB ranging data. A joint dissimilarity threshold determines identification, while pose-graph optimization combines the corresponding measurements for localization.

2) Teammate identification:

  • Trajectory matching compares odometry and tracked-cluster trajectories using length-normalized dynamic time warping after alignment by the latest extrinsic transformation.The cost matrix accumulates costs for aligning trajectory points.Source: 2) Teammate identification · p. 5
  • Distance matching compares each teammate’s UWB ranging set with the distance sets of eligible tracked LiDAR clusters.The method computes distance dissimilarity recursively.Source: 2) Teammate identification · p. 5
  • A cluster is identified as Robot j when its minimum joint dissimilarity is below threshold λ; otherwise, it is not identified.The joint dissimilarity combines trajectory and distance matching.Source: 2) Teammate identification · pp. 5–6
  • The teammate tracker’s pose graph combines both robots’ odometry, UWB ranges, and LiDAR detections, using an initial guess for Robot j’s trajectory poses.The figure depicts Robot i localizing Robot j in Robot i’s global frame.Source: Figure 4 · p. 6

D. Teammate Tracker

Each identified teammate gets a pose-graph tracker in the observing robot’s global frame, initialized from transformed teammate odometry. A fixed recent-measurement window and robust constraints support pose estimation, including when LiDAR observations are occluded.

D. Teammate Tracker

  • A teammate tracker activates after identification and more than 2.5 m of cumulative displacement, then uses transformed teammate odometry to initialize pose-graph optimization.Each teammate has a separate tracker; the displacement threshold is chosen empirically, and the initial guess uses the latest extrinsic transformation.Source: D. Teammate Tracker · p. 6
  • To limit computation, the tracker retains a fixed-length recent-measurement window and sparsifies it to k evenly spaced measurements for optimization.The pose graph represents robot poses as vertices and measurement constraints as edges.Source: D. Teammate Tracker · p. 6
  • The tracker combines local and teammate odometry, LiDAR, and UWB constraints; it can continue using odometry and UWB when occlusion removes LiDAR constraints.Huber thresholds are 0.025 m for odometry, 0.5 m for LiDAR, and 1.0 m for UWB; the resulting teammate pose is transformed into a relative pose.Source: D. Teammate Tracker · p. 6
  • Inter-robot constraints provide no heading information because of the inherent limitations of LiDAR and UWB ranging measurements.Source: D. Teammate Tracker · p. 6

E. UWB Communication Network

Robots exchange odometry through the onboard UWB network without external communication devices. Each odometry measurement is encoded in 8 bytes, with fields suited to the system’s 2D state.

E. UWB Communication Network

  • Each robot broadcasts only odometry over UWB, with each measurement represented using 8 bytes to limit bandwidth while supporting localization.The UWB sensor has an approximately 100-byte maximum payload, which is insufficient for high-dimensional data such as point clouds or feature descriptors.Source: E. UWB Communication Network · p. 6, Figure 5 · p. 7
  • The message encodes 2D position and heading, using two bytes per value at approximately 0.004 resolution.Position spans −127.996 m to 127.996 m, and heading is expressed in radians over 0 to 2π.Source: E. UWB Communication Network · p. 7
  • The message structure uses its first and last bytes as start and end markers, respectively.Source: E. UWB Communication Network · p. 7, Figure 5 · p. 7

A. Experimental Setup

In experiments with three homogeneous robots, joint distance-and-trajectory matching outperformed either matching method alone. The evaluation also examined the threshold trade-off and reported translational errors under variable occlusion.

A. Experimental Setup

  • Three homogeneous TurtleBot2s moved randomly in a 17.1 m × 6.2 m indoor 2D experiment with unknown initial correspondence; their odometry drifted considerably.The evaluation used a controllable box for LiDAR detection and a single LiDAR scan channel for 2D perception.Source: A. Experimental Setup · p. 7, Figure 6 · p. 7

B. Evaluation of Teammate Identification

  • At λ = 0.005, outliers were fully excluded while the number of inliers remained virtually unaffected; stricter thresholds also discarded some valid associations.Higher thresholds produced more associations but a substantial proportion of outliers.Source: B. Evaluation of Teammate Identification · p. 7, Figure 8 · p. 8
  • Joint matching outperformed pure distance matching and pure trajectory matching in teammate identification.Table II summarizes identification counts and translational error from Robot 1’s perspective; distance matching does not require communication, while trajectory matching uses shared odometry.Source: B. Evaluation of Teammate Identification · p. 7, Table II · p. 8
  • Average relative translational error was 0.08 m for Robot 2 and 0.13 m for Robot 3, with variable occlusion producing different inlier counts.A teammate’s LiDAR cluster may be unavailable under occlusion, and random robot movement produced varying occlusion conditions.Source: B. Evaluation of Teammate Identification · p. 8

C. Evaluation of Teammate Tracker

The teammate tracker combines odometry, UWB, and LiDAR constraints to improve teammate pose estimates, while the proposed approach is compared with two representative methods. The evaluation reports the strongest translational accuracy for the proposed approach, with SLAM Toolbox providing higher rotational accuracy.

C. Evaluation of Teammate Tracker

  • Odometry-only tracking could degrade over time but recover after periodic extrinsic updates improved the optimization's initial guess.Adding UWB and LiDAR constraints improved accuracy; Table III reports relative errors and average computation time for varying constraint conditions.Source: C. Evaluation of Teammate Tracker · p. 8, Figure 9 · p. 8, Table III · p. 9
  • Independent teammate trackers run in parallel at approximately 50 ms per tracker, and estimates continue through occlusions.Each teammate's tracker starts after sufficient accumulated displacement, so initial estimates can occur at different times.Source: C. Evaluation of Teammate Tracker · p. 8

D. Comparison with Existing Approach

  • 0.126m average translational error gave the proposed approach the highest translational accuracy, while SLAM Toolbox achieved higher rotational accuracy.The proposed method's average rotational error was 2.275°; it significantly outperformed pure odometry and in rotational accuracy.Source: Figure 10 · p. 8, D. Comparison with Existing Approach · p. 9

E. Evaluation of Communication Efficiency

The paper evaluates communication, complex-environment performance, and scalability of its distributed relative localization approach. The reported results include approximately 0.12m translational error and 2.20° rotational error in three-robot experiments, and consistent accuracy in simulations scaling to ten robots.

E. Evaluation of Communication Efficiency

  • Three-robot experiments required 0.48KB/s of communication bandwidth at 20Hz, with an average packet loss rate of approximately 0.476%.Odometry broadcasting used the onboard UWB network without external communication devices; total exchange was 115.2KB over 240 seconds.Source: E. Evaluation of Communication… · p. 9, Figure 11 · p. 9

V. DISCUSSION

  • The discussion evaluates practicality in complex and unstructured scenarios and considers scalability through simulations.It situates these evaluations after prior results on accuracy and stability in a structured environment.Source: §V · p. 9

A. Evaluation in a Complex Environment

  • In the complex environment, the proposed approach achieved 0.11m average translational error and 2.12° rotational error, consistent with the previous experiment.The simulation used ten robots in a 16m×16m environment.Source: Figure 13 · p. 10

B. Scalability Analysis

  • Scaling simulations from 3 to 10 robots maintained consistent relative localization accuracy, while bandwidth rose from 0.48KB/s to 1.6KB/s and identification time from 6.3ms to 66.7ms.The paper attributes the increases to more robots participating in data exchange and more candidate associations to process; other modules were minimally impacted.Source: B. Scalability Analysis · p. 10, Table V · p. 10

VI. CONCLUSION AND FUTURE WORKS

  • Approximately 0.12m translational error and 2.20° rotational error were achieved with 0.48KB/s data exchange at 20Hz in a three-robot system.The paper reports these results from indoor experiments and describes the performance as robust.Source: §VI · p. 10
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