Robot swarms require cohesive collective behaviour to address diverse challenges, including shape formation and decision-making. Existing approaches often treat consensus in discrete and continuous decision spaces as distinct problems. We present DANCeRS, a unified, distributed algorithm leveraging Gaussian Belief Propagation (GBP) to achieve consensus in both domains. By representing a swarm as a factor graph our method ensures scalability and robustness in dynamic environments, relying on purely peer-to-peer message passing. We demonstrate the effectiveness of our general framework through two applications where agents in a swarm must achieve consensus on global behaviour whilst relying on local communication. In the first, robots must perform path planning and collision avoidance to create shape formations. In the second, we show how the same framework can be used by a group of robots to form a consensus over a set of discrete decisions. Experimental results highlight our method's scalability and efficiency compared to recent approaches to these problems making it a promising solution for multi-robot systems requiring distributed consensus. We encourage the reader to see the supplementary video demo.

Multi-agent path planning is a critical challenge in robotics, requiring agents to navigate complex environments while avoiding collisions and optimizing travel efficiency. This work addresses the limitations of existing approaches by combining Gaussian belief propagation with path integration and introducing a novel tracking factor to ensure strict adherence to global paths. The proposed method is tested with two different global path-planning approaches: rapidly exploring random trees and a structured planner, which leverages predefined lane structures to improve coordination. A simulation environment was developed to validate the proposed method across diverse scenarios, each posing unique challenges in navigation and communication. Simulation results demonstrate that the tracking factor reduces path deviation by 28% in single-agent and 16% in multi-agent scenarios, highlighting its effectiveness in improving multi-agent coordination, especially when combined with structured global planning.

Building a distributed spatial awareness within a swarm of locally sensing and communicating robots enables new swarm algorithms. We use local observations by robots of each other and Gaussian Belief Propagation message passing combined with continuous swarm movement to build a global and distributed swarm-centric frame of reference. With low bandwidth and computation requirements, this shared reference frame allows new swarm algorithms. We characterise the system in simulation and demonstrate two example algorithms.

Visual sensors are not only becoming better at capturing high-quality images but also they have steadily increased their capabilities in processing data on their own on-chip. Yet the majority of Visual Odometry (VO) pipelines rely on the transmission and processing of full images in a centralized unit (e.g. CPU or GPU), which often contain much redundant and low-quality information for the task. In this paper, we address the task of frame-to-frame rotational estimation but, instead of reasoning about relative motion between frames using the full images, distribute the estimation at pixel-level. In this paradigm, each pixel produces an estimate of the global motion by only relying on local information and local message-passing with neighbouring pixels. The resulting per-pixel estimates can be then communicated to downstream tasks, yielding higher-level, informative cues instead of the original raw pixel-readings. We evaluate the proposed approach on real public datasets, where we offer detailed insights about this novel technique and open-source our implementation for the future benefit of the community.

We present a novel scalable, fully distributed, and online method for simultaneous localisation and extrinsic calibration for multi-robot setups. Individual a priori unknown robot poses are probabilistically inferred as robots sense each other while simultaneously calibrating their sensors and markers extrinsic using Gaussian Belief Propagation. In the presented experiments, we show how our method not only yields accurate robot localisation and auto-calibration but also is able to perform under challenging circumstances such as highly noisy measurements, significant communication failures or limited communication range.

This paper presents a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose correlations between variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edgewise partial correlations. We provide a walk-sum interpretation of Gaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles. This perspective leads to a better understanding of Gaussian belief propagation and of its convergence in loopy graphs.

Precise coordinated planning over a forward time window enables safe and highly efficient motion when many robots must work together in tight spaces, but this would normally require centralised control of all devices which is difficult to scale. We demonstrate GBP Planning, a new purely distributed technique based on Gaussian Belief Propagation for multi-robot planning problems, formulated by a generic factor graph defining dynamics and collision constraints over a forward time window. In simulations, we show that our method allows high performance collaborative planning where robots are able to cross each other in busy, intricate scenarios. They maintain shorter, quicker and smoother trajectories than alternative distributed planning techniques even in cases of communication failure. We encourage the reader to view the accompanying video demonstration at https://youtu.be/8VSrEUjH610.

Precise coordinated planning enables safe and highly efficient motion when many robots must work together in tight spaces, but this would normally require centralised control of all devices which is difficult to scale. We demonstrate a new purely distributed technique based on Gaussian Belief Propagation on multi-robot planning problems formulated by a generic factor graph defining dynamics and collision constraints. We show that our method allows extremely high performance collaborative planning in a simulated road traffic scenario, where vehicles are able to cross each other at a busy multi-lane junction while maintaining much higher average speeds than alternative distributed planning techniques. We encourage the reader to view the accompanying video demonstration to this work at https://youtu.be/5d4LXbxgxaY.

Bayesian probability theory is the fundamental framework for dealing with uncertain data, and is at the core of practical systems in machine learning and robotics [23, 11]. A probabilistic model relates unknown variables of interest to observable, known or assumed quantities and most generally takes the form of a graph whose connections encode those relationships. Inference is the process of forming the posterior distribution to determine properties of the unknown variables, given the observations, such as their most probable values or their full marginal distributions. There are various possible algorithms for probabilistic inference, many of which take advantage of specific problem structure for fast performance. Efficient inference on models represented by large, dynamic and highly inter-connected graphs however remains computationally challenging and is already a limiting factor in real embodied systems.

We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same first and second moments. We also derive a memory-friendly version of the proposed algorithm by applying a perturbation treatment commonly used in the literature of approximate message passing. In addition, a damping technique, which is demonstrated to be crucial for optimal performance, is introduced without computational strain, and the relationship to the message-passing version of alternating least squares, a method reported to be optimal in certain settings, is discussed. Experiments on synthetic datasets show that while the proposed algorithm quantitatively exhibits almost the same performance under settings where the earlier algorithm is optimal, it is advantageous when the observed datasets are corrupted by non-Gaussian noise. Experiments on real-world datasets also emphasize the performance differences between the two algorithms.