用各向异性扩散改进多机器人搜索，让覆盖更精准高效。
Anisotropic Diffusion-Driven Ergodic Coverage in Multi-Robot Systems
- 基于Perona-Malik扩散生成非均匀梯度场指导机器人移动
- 相比各向同性扩散，误差传播更适应目标分布变化
- 适用于复杂环境下的自适应全覆盖任务，适合机器人团队
我们研究多机器人系统中结合势场与遍历性搜索的问题。传统遍历性算法使用多尺度的遍历性度量来匹配目标分布。近期提出的一种热方程驱动的遍历性方法虽提升了平滑灵活性，但其各向同性扩散会均匀传播误差，无法适应分布变化。本文提出一类通用的各向异性扩散遍历性公式，生成用于遍历搜索的势场。该方法统一了此前基于径向基函数和热方程解的差异表示方式。在本方案中，机器人运动由Perona-Malik扩散解的梯度引导，且热方程为特例。我们在多种场景下通过仿真验证了该方法的有效性。
原文摘要 · Abstract (English)
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.
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