Normalizing Flow-Enhanced Message Passing for Multirobot Collaborative Localization

2026-06-29

AI Summary

This work addresses the challenges of nonlinear observations and unknown noise in multi-robot cooperative localization within complex environments by proposing a distributed message-passing algorithm that integrates Gaussian belief propagation with mean-field approximation. The method innovatively incorporates a learnable normalizing flow gradient estimator to enable end-to-end optimization and, for the first time, embeds normalizing flows into the message-passing framework to jointly handle state-dependent dynamics and noise statistics estimation. Furthermore, the algorithm is extended to Lie group state spaces to support practical pose estimation involving rotational components. Evaluated on both simulated and real-world autonomous surface vehicles, the approach demonstrates substantial improvements in localization accuracy, robustness, and adaptability to dynamic environmental conditions.

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.

Problem

• collaborative localization
• multirobot systems
• nonlinear measurement models
• noise statistics estimation
• Lie group state spaces

Innovation

• Normalizing Flow
• Message Passing
• Collaborative Localization
• Lie Group
• Gradient Estimator