A Robot Web for Distributed Many-Device Localisation

TL;DR

This work addresses distributed, true multi-device localisation without a central computer by deploying Gaussian Belief Propagation on a dynamic factor graph, where each device stores a local fragment and asynchronously shares messages via a web-like interface. The Robot Web framework supports general robot and sensor models, uses robust factors to down-weight outliers, and extends GBP to Lie Groups for SE(2)/SE(3) pose handling. Key contributions include the open asynchronous inter-device communication protocol, the Lie Group GBP extension, and extensive simulations with up to 1000 agents plus nine real-robot experiments, showing localisation accuracy comparable to centralised solvers and strong robustness to communication faults. The approach advances scalable, privacy-preserving distributed Spatial AI and suggests a future where heterogeneous devices collaboratively maintain global maps through an open, interoperable protocol.

Abstract

We show that a distributed network of robots or other devices which make measurements of each other can collaborate to globally localise via efficient ad-hoc peer to peer communication. Our Robot Web solution is based on Gaussian Belief Propagation on the fundamental non-linear factor graph describing the probabilistic structure of all of the observations robots make internally or of each other, and is flexible for any type of robot, motion or sensor. We define a simple and efficient communication protocol which can be implemented by the publishing and reading of web pages or other asynchronous communication technologies. We show in simulations with up to 1000 robots interacting in arbitrary patterns that our solution convergently achieves global accuracy as accurate as a centralised non-linear factor graph solver while operating with high distributed efficiency of computation and communication. Via the use of robust factors in GBP, our method is tolerant to a high percentage of faults in sensor measurements or dropped communication packets.

Figures (11)

• Figure 1: In the Robot Web, we assume that a set of robots move through space while using their sensors to observe each other. The circles represent the variables -- where ${{\mathbf {v}}}_t^\alpha$ denotes a variable at timestamp $t$ which belongs to robot $\alpha$ --, and the squares are the factors. Robot $\gamma$ starts at timestamp 3 for clarity of visualisation. The full-factor graph for multi-robot localisation is used. Responsibility for storing and updating it is divided up between the multiple robots participating, as shown by the coloured regions separated by dotted lines. Each robot maintains its own pose variable nodes, odometry factors, and factors for the inter-robot measurements made by its sensors, and carries out continuous GBP on this graph fragment. Message passing across dotted line boundaries happens on an asynchronous and ad-hoc basis.
• Figure 2: In a simulated environment, N robots are moving around in an environment with 10 known landmarks for 100 poses each. GTSAM optimises the factor graph after every pose insertion rather than solving after all poses are inserted to keep the comparison fair. GBP uses the full factor graph to optimise, while Windowed GBP only uses only the last 5 poses. The results are the average of 10 runs with different random initialisation, and the error bar represents one standard deviation of uncertainty.
• Figure 3: Increasing the number of iterations per step decreases the overall error. Even with a small number of iterations, GBP is able to provide good localisation, which can be further refined by increasing the iterations. The red line shows the median, the box extends from the first quartile to the third quartile, the whisker extends from the box by 1.5 inter-quartile range, and the outliers are marked with a cross. In a simulated environment, 50 robots are moving in an environment with 10 known landmarks for 100 poses each. Each result is a summary of 50 runs with different random initialisation.
• Figure 4: Extreme scaling: in a simulated environment, we increase the number of robots in the arena to over 1000, with each robot communicating with only one other per iteration of Windowed GBP, and therefore having a per-robot bounded computation and communication workload. The average ATE in all robots' poses continues to decrease as we increase the number of robots. Each result is a summary of 10 runs with different random initialisation.
• Figure 5: Robust factors enable remarkable resilience to a large fraction of outlier inter-robot sensor measurements, with ATE remaining low up to 70--80% of corrupt measurements to which a large amount of uniform noise is added. In a simulated environment, 50 robots are moving in an environment with 10 known landmarks for 100 poses each. Each result is a summary of 50 runs with different random initialisation.