Multi-robot systems require scalable and federated methods to model complex environments under computational and communication constraints. Gaussian Processes (GPs) offer robust probabilistic modeling, but suffer from cubic computational complexity, limiting their applicability in large-scale deployments. To address this challenge, we introduce the pxpGP, a novel distributed GP framework tailored for both centralized and decentralized large-scale multi-robot networks. Our approach leverages sparse variational inference to generate a local compact pseudo-representation. We introduce a sparse variational optimization scheme that bounds local pseudo-datasets and formulate a global scaled proximal-inexact consensus alternating direction method of multipliers (ADMM) with adaptive parameter updates and warm-start initialization. Experiments on synthetic and real-world datasets demonstrate that pxpGP and its decentralized variant, dec-pxpGP, outperform existing distributed GP methods in hyperparameter estimation and prediction accuracy, particularly in large-scale networks.

翻译：多机器人系统需要在计算与通信受限条件下，通过可扩展的联邦式方法对复杂环境进行建模。高斯过程（GPs）提供了鲁棒的概率建模能力，但其立方级计算复杂度限制了其在大规模部署中的应用。为应对这一挑战，本文提出pxpGP——一种专为集中式与去中心化大规模多机器人网络设计的新型分布式高斯过程框架。该方法利用稀疏变分推断生成局部紧凑的伪表示，提出一种限制局部伪数据集规模的稀疏变分优化方案，并构建了具有自适应参数更新与热启动初始化的全局缩放近端-非精确共识交替方向乘子法（ADMM）。在合成数据集与真实数据集上的实验表明，pxpGP及其去中心化变体dec-pxpGP在超参数估计与预测精度方面优于现有分布式高斯过程方法，尤其在大规模网络中表现突出。