Gaussian Processes for Modelling Spatial Fields with Robot Swarms

This paper presents a framework for mapping unknown scalar fields using a sensor-equipped autonomous robot operating in unsafe environments. The unsafe regions are defined as regions of high-intensity, where the field value exceeds a predefined safety threshold. For safe and efficient mapping of the scalar field, the sensor-equipped robot must avoid high-intensity regions during the measurement process. In this paper, the scalar field is modeled as a sample from a Gaussian process (GP), which enables Bayesian inference and provides closed-form expressions for both the predictive mean and the uncertainty. Concurrently, the spatial structure of the high-intensity regions is estimated in real-time using the Hough transform (HT), leveraging the evolving GP posterior. A safe sampling strategy is then employed to guide the robot towards safe measurement locations, using probabilistic safety guarantees on the evolving GP posterior. The estimated high-intensity regions also facilitate the design of safe motion plans for the robot. The effectiveness of the approach is verified through two numerical simulation studies and an indoor experiment for mapping a light-intensity field using a wheeled mobile robot.

State estimation is a fundamental requirement in robotics, where the accurate determination of a robot's state is essential for stable operation despite inherent process disturbances and sensor noise. Traditionally, this is achieved through Kalman filtering, providing a statistically optimal estimate by balancing predictive models with noisy measurements. In the context of robotic swarms, the challenge shifts from individual accuracy to collective coordination, where the integration of global dynamics can significantly enhance the precision of the entire group. Existing estimation techniques rely on centralized processing or heavy communication protocols to reach a global consensus, which are frequently impractical in real-world deployments. Here we show that a localized, "greedy" approach to distributed state estimation (termed "Greedy Kalman-Swarm") allows individual robots to leverage relative inter-robot sensing for improved accuracy without requiring full data availability or global communication. Simulations in communication-constrained environments show robots can effectively integrate all currently available neighbor data at each iteration to refine their internal states, yet remain robust and functional even when data is missing. This results in a performance profile that strikes a balance between the low overhead of independent estimation and the high accuracy of centralized systems, specifically under harsh or dynamic environmental conditions. Our results demonstrate that global state awareness can be emergent rather than enforced, providing a scalable framework for maintaining swarm cohesion in unpredictable terrains. We anticipate that this decentralized methodology will serve as a foundation for more resilient autonomous systems, particularly in search-and-rescue or space exploration missions where reliable, high-bandwidth communication cannot be guaranteed.

Maintaining situational awareness in high-stakes multi-robot applications requires balancing exploration of unobserved regions with sustained monitoring of changing Regions of Interest (ROIs), often under unknown and time-varying distributions, partial observability, and limited communication. We propose a decentralized multi-agent coverage framework that serves as a high-level planning strategy, in which each agent computes an adaptive ergodic policy, implemented via a Markov-chain, that tracks an updated belief over the underlying importance map. Beliefs are maintained online via Gaussian Process (GP) regression from local noisy observations exchanged with neighbors. The resulting policy drives agents to spend time in ROIs in proportion to their estimated importance, while preserving sufficient exploration to detect and adapt to time-varying environmental changes. Unlike existing approaches that assume known importance maps, centralized coordination, or a static environment, our framework addresses the combined challenges of unknown, time-varying distributions under a decentralized, partially observable setting. We further show that our framework is robust to communication and memory degradation, robot loss, and can scale up to hundreds of robots.