基于高阶平均场控制屏障函数的领导者-跟随者密度安全控制

中文摘要 AI 辅助

大规模多智能体系统的安全过滤器可以通过平均场控制屏障函数（MF-CBF）在群体层面进行构建。现有的大多数公式是一阶的，要求控制输入显式出现在安全泛函的一阶时间导数中；高阶扩展仅最近才针对单个直接驱动的群体提出。我们考虑的情况是，需要保持安全的群体并非直接驱动，而是由第二个受控群体产生的场来传输。针对这一设置，我们为密度动力学开发了一个高阶MF-CBF框架，其安全约束的相对阶数大于一。我们的主要结果是，这种间接驱动不会破坏安全条件的控制仿射结构：安全泛函的二阶时间导数中与控制相关的部分以闭式形式获得，并且关于控制速度场是线性的，其核由驱动密度乘以一阶变分的空间梯度给出。因此，相对阶数为二的安全约束仍然可以通过凸二次规划来强制执行。然后，我们将该框架专门应用于存在危险区域的领导者-跟随者密度控制问题，其中通过将每个群体与这些区域的重叠保持在规定阈值以下来确保安全。我们表明，跟随者安全泛函相对于领导者控制场具有相对阶数二，而领导者安全泛函具有相对阶数一。我们进一步精确刻画了两个同时约束何时不可行，引入了一种自适应增益机制以缓解潜在冲突，并限定了由安全校正引起的跟踪误差。在杂乱环境中的数值模拟说明了由此产生的安全-性能权衡。

英文摘要

Safety filters for large-scale multi-agent systems can be formulated at the population level through mean-field control barrier functions (MF-CBFs). Most existing formulations are first-order, requiring the control input to appear explicitly in the first time derivative of the safety functional; higher-order extensions have only very recently been proposed for a single, directly actuated population. We consider instead the case in which the population to be kept safe is not directly actuated, but is transported by a field generated by a second, controlled population. For this setting, we develop a higher-order MF-CBF framework for density dynamics with safety constraints of relative degree larger than one. Our main result is that indirect actuation of this kind does not destroy the control-affine structure of the safety condition: the control-dependent part of the second time derivative of the safety functional is obtained in closed form and is linear in the control velocity field, with a kernel given by the actuated density times the spatial gradient of a first variation. Relative-degree-two safety constraints can therefore still be enforced through a convex quadratic program. We then specialize the framework to a leader-follower density control problem in the presence of dangerous regions, where safety is ensured by keeping the overlap of each population with those regions below a prescribed threshold. We show that the follower safety functional has relative degree two with respect to the leader control field, while the leader safety functional has relative degree one. We further characterize exactly when the two simultaneous constraints are infeasible, introduce an adaptive-gain mechanism to mitigate potential conflicts, and bound the tracking errors induced by the safety correction. Numerical simulations in cluttered environments illustrate the resulting safety-performance trade-off.

发表机构

• University of Naples Federico II（那不勒斯费德里科二世大学）

机构由 AI 辅助整理，请以论文原文为准。