发表机构
King Abdullah University of Science and Technology (KAUST); Dartmouth College（阿卜杜拉国王科技大学; 达特茅斯学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于二次规划的安全遍历控制器，联合处理遍历性与安全约束，利用可微高斯核度量及控制障碍函数，保证可行性与指数衰减，仿真与三机实验验证性能。
AI 中文摘要
遍历控制驱动机器人在每个区域停留的时间与该区域的空间分布成比例，使其非常适合高密度的时空环境监测。现有的安全遍历控制器依赖于离线轨迹优化或分层架构，这限制了实时适用性，并将遍历性目标与安全约束分离开来。本文提出了一种基于二次规划（QP）的控制器，将遍历性和安全性联合处理。我们首先引入一种基于高斯核的遍历度量，与经典的基于指示器的度量不同，该度量在时间上是可微的。这使得度量值的指数衰减可以作为一个时变控制障碍函数（CBF）约束，并通过松弛变量放宽，同时结合硬CBF约束用于区域包含和机器人间碰撞避免。我们证明了所得到的QP从任何安全初始配置出发都是可行的，并且，在松弛项范围内，遍历度量呈指数衰减。仿真结果表明，该方法优于基线方法，并通过三架飞行器的实验在真实硬件上验证了该工作。
英文摘要
Ergodic control drives robots to spend time in each region in proportion to a spatial distribution of interest, making it well suited for dense spatiotemporal environmental monitoring. Existing safe ergodic controllers rely on offline trajectory optimization or hierarchical architectures, which limit real-time applicability and decouple the ergodicity objective from the safety constraint. This paper presents a quadratic programming (QP)-based controller that treats ergodicity and safety jointly. We first introduce a Gaussian-kernel ergodic metric that, unlike the classical indicator-based metric, is time differentiable. This allows the exponential decay of the metric to be imposed as a time-varying control barrier function (CBF) constraint, relaxed by a slack variable, alongside hard CBF constraints for region containment and inter-robot collision avoidance. We establish that the resulting QP remains feasible from any safe initial configuration and that, up to the slack term, the ergodic metric decays exponentially. Simulations show improved performance over baseline methods, and experiments with three aerial vehicles validate the work on real hardware.
