Normalizing Flow-Enhanced Message Passing for Multirobot Collaborative Localization
2026-06-29 • Robotics
Robotics
AI summaryⓘ
The authors developed a new method to help multiple robots figure out their exact positions together in a reliable way. They combined two math techniques—Gaussian belief propagation and mean-field approximation—to better estimate robot locations and noise in the measurements. Their approach uses advanced tools like gradient estimators and normalizing flows to handle complex, nonlinear data and improve accuracy through training. They also adapted their method to work with robotic movements involving rotations. Tests on surface robots using different location data showed their method is more precise and adaptable.
Collaborative localizationGaussian belief propagationMean-field approximationNonlinear measurement modelsGradient estimatorsNormalizing flowsLie groupsOdometryUltra wideband rangingGlobal Navigation Satellite System (GNSS)
Authors
Han Shen, Guanghui Wen, Liangming Chen, Ming Cao
Abstract
Accurate, robust, and adaptive localization is essential for various robotic operations. This paper proposes a new message passing (MP) algorithm for realizing collaborative localization in a distributed manner. The algorithm unifies Gaussian belief propagation (GBP) and mean-field (MF) approximation, where GBP preserves dependencies among robot states, and MF enables estimation of noise statistics. To effectively handle non-conjugate terms from nonlinear measurement models, the algorithm adopts a parametric formulation in which these terms are treated by gradient estimators. Beyond linearization and sampling, we further design a normalizing flow (NF)-based gradient estimator, enabling learnable sampling. End-to-end training tunes NF parameters according to the behavior of MP, improving the overall estimation performance. To support estimation of practical robotic states that involve rotations, the method is then extended to Lie group state spaces. Finally, the method is applied to multirobot localization task fusing odometry, global navigation satellite system (GNSS) measurements, and inter-robot ultra wideband (UWB) ranging. Simulations and experiments on autonomous surface vehicles (ASVs) demonstrate its improved accuracy, robustness, and adaptability.