A Distributed Gaussian Process Model for Multi-Robot Mapping

TL;DR

It is shown that such distributed, asynchronous training can reach the same performance as a centralised, batch-trained model, albeit with slower convergence, and compares to DiNNO, a distributed neural network optimiser, and finds DistGP achieves superior accuracy, is more robust to sparse communication and is better able to learn continually.

Abstract

We propose DistGP: a multi-robot learning method for collaborative learning of a global function using only local experience and computation. We utilise a sparse Gaussian process (GP) model with a factorisation that mirrors the multi-robot structure of the task, and admits distributed training via Gaussian belief propagation (GBP). Our loopy model outperforms Tree-Structured GPs \cite{bui2014tree} and can be trained online and in settings with dynamic connectivity. We show that such distributed, asynchronous training can reach the same performance as a centralised, batch-trained model, albeit with slower convergence. Last, we compare to DiNNO \cite{yu2022dinno}, a distributed neural network (NN) optimiser, and find DistGP achieves superior accuracy, is more robust to sparse communication and is better able to learn continually.

Figures (6)

• Figure 1: In DistGP, each robot maintains a block of inducing points which parameterise their local GP (far-left) and into which observations can be fused. Communicating robots harmonise models by connecting inducing points via GP consistency factors and exchanging GBP messages (far-right). Here, the map at each point is predicted by the closest robot. Before communication (centre-left) the map is discontinuous and inaccurate, but this is resolved using only local inter-robot exchanges (centre-right).
• Figure 2: Limitations of TSGP. Some robots remain unconnected to ensure tree connectivity (as in \ref{['subfig:tspgp_analysis:tsgp_preds']}). This leads to discontinuities in the prediction at the boundary between unconnected robots (\ref{['subfig:tspgp_analysis:tsgp_error']}), which can be reduced significantly by adding loop-forming edges (\ref{['subfig:tspgp_analysis:tsgp_extra_error']}) (see white rectangles).
• Figure 3: Benefit of additional edges. The prediction error (vertical axis) reduces as more edges are added to the TSGP model (horizontal axis, $x=0$ is TSGP), but plateaus after $\sim9$ extra edges, where accuracy is equal to a dense GP prior on all inducing points (green). Results averaged over $10$ seeds, errorbars cover $\pm1$ standard error (SE) around mean.
• Figure 4: Asynchronous + distributed vs batch + centralised model. We compare i) online learning, ad-hoc inter-robot connections, ad-hoc GBP (blue) against ii) a centralised implementation with synchronous GBP sweeps on batch data (red, orange, green). The former converges to the same performance as the centralised, dense prior (green). Averages over $10$ seeds, error bars cover $\pm1$ SE around the mean.
• Figure 5: Distributed occupancy mapping. Our method converges to an accurate map in a single pass through the robots' trajectories, as observations are fully fused into the model. In contrast, DiNNO trains NNs iteratively and therefore requires many passes to overcome catastrophic forgetting. We note that our map at convergence is also more accurate than DiNNO's.