Resource-Efficient Cooperative Online Scalar Field Mapping via Distributed Sparse Gaussian Process Regression

TL;DR

The paper tackles the computational and communication bottlenecks of online Gaussian process regression for cooperative multi-robot field mapping, where standard GPR scales as $O(N^3)$ and centralized solutions are impractical. It introduces a distributed sparse Gaussian process framework built on dynamic average consensus, with a recursive online GP update and a novel distributed online evaluation method that uses global information to select informative observations. Core contributions include provable error bounds comparing distributed fusion to centralized PoE, a Bhattacharyya-Riemannian-based sparse selection metric, and an Algorithm 1 that achieves resource-efficient online mapping with favorable time, memory, and communication complexity. The approach is validated experimentally on light-field mapping with multiple TurtleBot3 robots, demonstrating convergence to a centralized reference and improved sparse-prediction accuracy, indicating strong practical impact for scalable, real-time multi-robot mapping with uncertainty quantification.

Abstract

Cooperative online scalar field mapping is an important task for multi-robot systems. Gaussian process regression is widely used to construct a map that represents spatial information with confidence intervals. However, it is difficult to handle cooperative online mapping tasks because of its high computation and communication costs. This letter proposes a resource-efficient cooperative online field mapping method via distributed sparse Gaussian process regression. A novel distributed online Gaussian process evaluation method is developed such that robots can cooperatively evaluate and find observations of sufficient global utility to reduce computation. The bounded errors of distributed aggregation results are guaranteed theoretically, and the performances of the proposed algorithms are validated by real online light field mapping experiments.

Figures (7)

• Figure 1: Light field mapping experiments in a $7.5~\mathrm{m} \times 5~\mathrm{m}$ workspace (top) and distributed light field mapping results (bottom). The value is the light intensity (lx).
• Figure 2: A 1-D toy example with different compression methods. There are 2 robots sampling and predicting the objective function, respectively, where Robot 1 samples points ($N=300$) from $x_{1,0}=3$ to $x_{1,300}=0$ and Robot 2 samples from $x_{2,0}=1$ to $x_{2,300}=4$. The shaded area represents $95\%$ of the distributed GP confidence intervals. The diamond and star represent the sparse training data ($M=10$) after the online compression. The toy objective function is $f(x) = \sin(2x)+\cos(6x)+0.5$. (a) The centralized compression requires all real-time sample data. (b) Each robot compresses sample data locally, causing information repeated and globally inefficient. (c) Each robot compresses sample data based on distributed predictions with better performance.
• Figure 3: Pipeline of the proposed Algorithm 1.
• Figure 4: The averaged distributed predictions and centralized PoE results for all test points.
• Figure 5: A team of 5 robots cooperatively construct the online map of the light fields. (a) Experiment snapshots and the robot number. (b) Distributed online GP variance predictions for Robot $3$ and the exploration trajectories of all robots. The black points denote the sparse subsets for GP predictions. (c) Distributed online GP mean predictions for Robot $3$, which gradually converges to the real light field in (a).

Theorems & Definitions (1)

• proof