Anisotropic Diffusion-Driven Ergodic Coverage in Multi-Robot Systems

2026-05-22

AI Summary

This work addresses the limitations of existing multi-robot ergodic coverage approaches under non-uniform target distributions—specifically, their unidirectional error propagation and insufficient adaptability—by proposing a novel anisotropic diffusion–based method. The approach uniquely integrates the Perona–Malik diffusion equation into the ergodic control framework, leveraging the gradient of its solution to construct a potential field that guides robot motion and enables adaptive tracking of spatially varying target densities. Unlike conventional isotropic diffusion schemes or methods based on radial basis functions or the heat equation, the proposed technique dynamically adjusts the direction of error propagation in response to local variations in the target distribution. Simulation results demonstrate that this method significantly enhances both coverage accuracy and efficiency across diverse scenarios.

Abstract

We consider the problem of combining potential field and ergodic search on multi-robot systems. Traditional ergodic search algorithms use metrics for ergodicity that account for the desired distribution at different scales. Recently, a heat equation-driven ergodic approach was proposed, which adds flexibility to the smoothing of the ergodic metric. However, such an approach, as it is an isotropic diffusion, propagates the error uniformly in all directions, regardless of changes in the desired distribution. We introduce a general class of anisotropic diffusion formulation of the ergodicity problem, which generates a potential field for the ergodic search. We demonstrate that this approach generalizes previous results, which consider radial basis functions and the solution of the heat equation to represent the difference between the goal density distribution and the covered trajectories. In our solution, the agent movement is directed using the gradient of the solution of the Perona-Malik diffusion, and our formulation includes the heat equation as a special case. We demonstrate the methodology with a series of simulations in different scenarios.

Problem

• anisotropic diffusion
• ergodic coverage
• multi-robot systems
• potential field
• heat equation

Innovation

• anisotropic diffusion
• ergodic coverage
• multi-robot systems
• Perona-Malik diffusion
• potential field