对比三种安全过滤器，揭示其内在联系与保守性来源。
Backup-Based Safety Filters: A Comparative Review of Backup CBF, Model Predictive Shielding, and gatekeeper
- 统一框架下分析三类备份式安全过滤机制。
- 发现MPS是gatekeeper的特例，且与Backup CBF有几何关联。
- 适合控制理论研究者理解安全策略设计差异。
本文通过统一的比较框架重新审视三种基于备份的安全过滤器——备份控制屏障函数（Backup CBF）、模型预测屏蔽（MPS）和gatekeeper。采用共同的安全过滤抽象和共享符号体系，明确揭示了它们共有的备份策略结构及关键算法差异。通过分析滤波器不激活集（即名义策略保持不变的状态集合），我们证明MPS是gatekeeper的特例，并进一步将gatekeeper与隐式安全集内Backup CBF不激活集的内部区域相联系。这一统一看法也指出了备份式安全过滤器的一个核心保守性来源：安全性的评估往往依赖于备份动作的可行性，而非名义策略持续安全执行的能力。本文旨在作为简洁教程与综述，澄清这些方法间的理论关联与区别。
原文摘要 · Abstract (English)
This paper revisits three backup-based safety filters -- Backup Control Barrier Functions (Backup CBF), Model Predictive Shielding (MPS), and gatekeeper -- through a unified comparative framework. Using a common safety-filter abstraction and shared notation, we make explicit both their common backup-policy structure and their key algorithmic differences. We compare the three methods through their filter-inactive sets, i.e., the states where the nominal policy is left unchanged. In particular, we show that MPS is a special case of gatekeeper, and we further relate gatekeeper to the interior of the Backup CBF inactive set within the implicit safe set. This unified view also highlights a key source of conservatism in backup-based safety filters: safety is often evaluated through the feasibility of a backup maneuver, rather than through the nominal policy's continued safe execution. The paper is intended as a compact tutorial and review that clarifies the theoretical connections and differences among these methods.
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