Distributed Coverage Control for Time-Varying Spatial Processes

TL;DR

This paper presents a fully distributed framework for multi-robot coverage in unknown, time-varying spatial fields by coupling Gaussian Process regression with a Voronoi-based coverage strategy. The method jointly learns the spatial field online and optimizes coverage, using a UCB-inspired acquisition to balance exploration and exploitation, while incorporating exponential time decay and data filtering to handle non-stationarity and scalability. The authors validate the approach through simulations on real datasets, Webots drone simulations, and real TurtleBot3 experiments, showing robust adaptation to changing environments with bounded computational load. The work advances scalable, distributed environmental monitoring by enabling continuous online estimation and adaptive deployment in dynamic settings. Potential impact includes improved efficiency and reliability of autonomous sensing in agriculture, pollution tracking, and disaster response, especially where centralized planning is infeasible.

Abstract

Multi-robot systems are essential for environmental monitoring, particularly for tracking spatial phenomena like pollution, soil minerals, and water salinity, and more. This study addresses the challenge of deploying a multi-robot team for optimal coverage in environments where the density distribution, describing areas of interest, is unknown and changes over time. We propose a fully distributed control strategy that uses Gaussian Processes (GPs) to model the spatial field and balance the trade-off between learning the field and optimally covering it. Unlike existing approaches, we address a more realistic scenario by handling time-varying spatial fields, where the exploration-exploitation trade-off is dynamically adjusted over time. Each robot operates locally, using only its own collected data and the information shared by the neighboring robots. To address the computational limits of GPs, the algorithm efficiently manages the volume of data by selecting only the most relevant samples for the process estimation. The performance of the proposed algorithm is evaluated through several simulations and experiments, incorporating real-world data phenomena to validate its effectiveness.

Figures (13)

• Figure 1: Comparison between a time invariant and time variant approach with a 1-D signal estimation. We presume the 6 samples are tidily taken from left to right every 10 seconds. Hence, the older sample is in $x \sim 2$ and the latest is in $x \sim 10$. In figure (a) with the time invariant approach all the samples are equally processed and the uncertainty of the estimation is zero in the sample locations. In figure (b) we are using a time-varying learning approach, in which the samples are processed differently depending on the time they were taken. The older samples have greater uncertainties than the newer ones. Moreover the latest sample has a zero standard deviation since it was taken at the current time $t_6 = 60s$ and hence $\Delta t_6 = 0$. The parameters used in this example for the time-varying approach are $\epsilon = 1\mathrm{e}{-4}$ and $\tau = 1\mathrm{e}{2}$.
• Figure 2: The figure illustrates the control architecture implemented on each robot. Each robot implements the coverage control strategy by utilizing the locations of neighboring robots and information about the estimated spatial process and environmental uncertainty. The data used in GP estimation are collected from neighboring robots and sampled from the environment. This dataset undergoes a filtering process before being used in GP training, which diminishes the sample size required for effective GP estimation. Post-GP training, the dataset is cleaned of any obsolete samples that add excessive uncertainty to the process estimation.
• Figure 3: The figure presents three subfigures, each corresponding to a different time step in a simulation where a team of robots is tasked to estimate and optimally cover a constant spatial process. The first image of each subfigure illustrates the robots (represented by large black dots), the Voronoi partitioning (depicted with black lines), and the calculated centroids of each Voronoi cell (small black dots), against the backdrop of the spatial process they are estimating. The second image displays the estimation of robot 0 up to that moment. The third image visualizes the uncertainty across the domain, with white areas indicating high uncertainty and black areas indicating low uncertainty. Due to space constraints, only the process pertaining to robot 0 is depicted.
• Figure 4: The figure presents five subfigures, each corresponding to a different time step in a simulation where a team of robots is assigned to estimate and optimally cover a time-varying spatial process. Each subfigure illustrates various aspects of the simulation: the first image on the left depicts the robot team (represented by large black dots), the Voronoi partitions (black lines), and the calculated centroids for each Voronoi cell (small black dots). The spatial process, which evolves over time and is being estimated by the robots, is displayed in the background. The second image shows the estimation by robot 0 up to that moment. The third image illustrates the uncertainty across the domain, with white areas indicating high uncertainty and black areas indicating low uncertainty. Due to space constraints, only the process pertaining to robot 0 is depicted.
• Figure 5: This figure shows the RMSE of robot estimates during a simulation where robots explore an environment with a dynamic spatial process. At time step 60 (black dashed line), the process shifts, causing a temporary RMSE increase as outdated data is filtered out. Over time, each robot's estimate (colored lines) converges toward the ground truth, while the inter-robot estimate deviation (light gay plot) remains below $10\%$, demonstrating effective distributed estimation.