MURP: Multi-Agent Ultra-Wideband Relative Pose Estimation with Constrained Communications in 3D Environments

TL;DR

This work tackles inter-agent relative localization in 3D without reliance on external positioning infrastructure by leveraging multiple UWB antennas per agent, a robust bias-corrected ranging model, and a priori altitude/roll/pitch constraints to enable an instantaneous, locally computed 3D pose. It introduces a constrained nonlinear least squares formulation over $oldsymbol{T}^{A}_{B} \in SE(3)$ with a learned state-dependent bias $\bar{d}^{A_i}_{B_j}(\boldsymbol{T}^{A}_{B})$, solved via trust-constr and a robust loss to produce accurate relative poses using only local UWB measurements. The key contributions include a detailed noise characterization for 3D UWB ranging, a 3D instantaneous localization approach with minimal communication, hardware experiments achieving $\text{APE}=0.24$ m and $\text{AHE}=9.5^\circ$, and a publicly released dataset spanning over 200 hours of pairwise measurements. The results demonstrate improved accuracy and scalability compared to similarly constrained methods, highlighting the practical potential for large swarms operating in communication-limited settings and setting the stage for integration into distributed SLAM pipelines.

Abstract

Inter-agent relative localization is critical for many multi-robot systems operating in the absence of external positioning infrastructure or prior environmental knowledge. We propose a novel inter-agent relative 3D pose estimation system where each participating agent is equipped with several ultra-wideband (UWB) ranging tags. Prior work typically supplements noisy UWB range measurements with additional continuously transmitted data (e.g., odometry) leading to potential scaling issues with increased team size and/or decreased communication network capability. By equipping each agent with multiple UWB antennas, our approach addresses these concerns by using only locally collected UWB range measurements, a priori state constraints, and event-based detections of when said constraints are violated. The addition of our learned mean ranging bias correction improves our approach by an additional 19% positional error, and gives us an overall experimental mean absolute position and heading errors of 0.24m and 9.5 degrees respectively. When compared to other state-of-the-art approaches, our work demonstrates improved performance over similar systems, while remaining competitive with methods that have significantly higher communication costs. Additionally, we make our datasets available.

Figures (6)

• Figure 1: Diagram of proposed system. Here three agents fly at different altitudes while performing real-time 3D relative pose estimation. Each agent is equipped with six ultra-wideband (UWB) antennas, each capable of performing pairwise relative ranging between all other agents' individual antennas. By using trilateration, an improved sensor model, and a priori state constraints about altitude/roll/pitch, agents can perform instantaneous estimation entirely with locally collected UWB measurements (i.e., without the need to continuously transmit other measurements, such as odometry). Additionally, each agent locally monitors its a priori constraints via downward facing LiDAR and IMU, enabling an event-based communication model that only transmits if said assumptions change or are violated. The pictured drone is used in the experiments outlined in Section \ref{['sec:uav-experiments']}.
• Figure 2: Plots demonstrating the UWB noise and geometry characteristics outlined in Section \ref{['sec:extensions-3d']}. (a) Histogram of our entire set of UWB measurements binned by range error. Demonstrates a non-zero mean and long tail (i.e., violates the zero mean Gaussian assumption that is typically used). (b) Same data plotted as error with respect to relative elevation showing that the measurement error's mean and variance change significantly with relative elevation. The dotted blue line represents a learned 6-degree polynomial fit of measurement bias. (c) Simple example demonstrating dilution of precision (DOP) in a 2D ranging scenario. (d) Demonstrates how three (or more) ranging antennas within a single plane produce a pair of ambiguous solutions (i.e., if all antennas are in the base's plane $z=0$, while the target's $x$ and $y$ coordinates are fully observable, the target's altitude has an ambiguity between $\pm z$).
• Figure 3: (a) Annotated diagram of three UGV agents used in Section \ref{['sec:ugv-experiments']}. UGV agents are designed with the same baseline as the UAV in Figure \ref{['fig:system-diagram']}, making them comparable surrogates to the UAV and its experiments in Section \ref{['sec:uav-experiments']}. (b) Diagram demonstrating agent $B$locally detecting violations in its a priori constraints, triggering an event-based communication. Other agents will exclude $B$ from their relative pose estimation until $B$ notifies the swarm of restored constraint status or provides a new constraint envelop.
• Figure 4: Plots from the UAV flight experiments.
• Figure 5: Error vs Time plots for Trial 2 in Table \ref{['tab:pos-err']} and \ref{['tab:yaw-err']} respectively. The line color corresponds with the algorithm's color column in the associated tables. Each colored dashed line represent that algorithm's overall mean in that trial.