用核方法实现长期覆盖任务的稳定控制，突破了传统算法时间限制。
Infinite-Horizon Ergodic Control via Kernel Mean Embeddings
- 引入扩展核均值嵌入误差状态，递归记录访问历史
- 理论证明控制器渐近收敛，保持2D/3D覆盖保证
- 适用于长时间、无限时域的覆盖任务，如巡检机器人
本文基于核均值嵌入，提出一种用于一般区域长期覆盖任务的无限时域遍历控制器。现有基于核的方法虽在一般覆盖域上提供强覆盖保障，但因计算复杂度难以处理而仅限于次遍历、有限时域，无法应用于长期覆盖。本文通过推导包含扩展核均值嵌入误差访问状态的无限时域控制器，使历史访问与未来控制解耦，将遍历控制推广至无限时间场景。此外，还提出一种基于滚动时域控制框架的变体，使用该扩展误差状态。理论证明了所提控制器的渐近收敛性，并在一类二维和三维覆盖问题中验证了遍历覆盖保障的保持。
原文摘要 · Abstract (English)
This paper derives an infinite-horizon ergodic controller based on kernel mean embeddings for long-duration coverage tasks on general domains. While existing kernel-based ergodic control methods provide strong coverage guarantees on general coverage domains, their practical use has been limited to sub-ergodic, finite-time horizons due to intractable computational scaling, prohibiting its use for long-duration coverage. We resolve this scaling by deriving an infinite-horizon ergodic controller equipped with an extended kernel mean embedding error visitation state that recursively records state visitation. This extended state decouples past visitation from future control synthesis and expands ergodic control to infinite-time settings. In addition, we present a variation of the controller that operates on a receding-horizon control formulation with the extended error state. We demonstrate theoretical proof of asymptotic convergence of the derived controller and show preservation of ergodic coverage guarantees for a class of 2D and 3D coverage problems.
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