This paper proposes a framework for multi-robot systems to perform simultaneous learning and coverage of a domain of interest characterized by an unknown and potentially time-varying density function. To overcome the limitations of Gaussian Process (GP) regression, we employ Random Feature GP (RFGP) and its online variant (O-RFGP) which enables online and incremental inference. By integrating these with Voronoi-based coverage control and Upper Confidence Bound (UCB) sampling strategy, a team of robots can adaptively focus on important regions while refining the learned spatial field for efficient coverage. The incremental update mechanism of O-RFGP naturally supports time-varying environments, allowing efficient adaptation without retaining historical data. Furthermore, to the best of our knowledge, we provide the first theoretical analysis of online learning and coverage through a regret-based formulation, establishing asymptotic no-regret guarantees in the time-invariant setting. The effectiveness of the proposed framework is demonstrated through simulations with both time-invariant and time-varying density functions, along with a physical experiment with a time-varying density function.

翻译：本文提出了一种多机器人系统框架，用于对以未知且可能时变的密度函数为特征的感兴趣区域进行同步学习与覆盖。为克服高斯过程回归的局限性，我们采用随机特征高斯过程及其在线变体，实现在线增量式推断。通过将其与基于Voronoi图的覆盖控制和上置信界采样策略相结合，机器人团队能够自适应地聚焦于重要区域，同时优化学习到的空间场以实现高效覆盖。O-RFGP的增量更新机制天然支持时变环境，无需保留历史数据即可实现高效适应。此外，据我们所知，我们首次通过基于遗憾的理论分析框架对在线学习与覆盖问题进行理论分析，在时不变场景下建立了渐近无遗憾保证。通过时不变与时变密度函数的仿真实验，以及时变密度函数的物理实验，验证了所提框架的有效性。