证明互补约束与控制屏障函数等价，统一机器人安全控制方法
Unifying Complementarity Constraints and Control Barrier Functions for Safe Whole-Body Robot Control
- 首次证明两类安全控制方法在采样数据系统中的数学等价性
- 适用于单约束与多约束场景，理论框架可跨方法复用
- 为机器人实时避障提供更灵活的算法设计思路，适合控制领域研究者
安全关键型全身机器人控制需要能够实时响应的碰撞规避方法。互补约束和控制屏障函数（CBF）已成为确保此类安全约束的核心工具，各自发展成熟。尽管二者解决相似问题，其内在联系仍不明确。本文通过形式化证明，在采样数据、一阶系统下，这两类方法在单约束与多约束场景中具有等价性。该统一视角为两套技术提供了理论衔接，促进了鲁棒性保障与算法改进的跨框架应用。我们讨论了由此带来的协同优势，并推动未来在更一般情形下对两种方法的比较研究。
原文摘要 · Abstract (English)
Safety-critical whole-body robot control demands reactive methods that ensure collision avoidance in real-time. Complementarity constraints and control barrier functions (CBF) have emerged as core tools for ensuring such safety constraints, and each represents a well-developed field. Despite addressing similar problems, their connection remains largely unexplored. This paper bridges this gap by formally proving the equivalence between these two methodologies for sampled-data, first-order systems, considering both single and multiple constraint scenarios. By demonstrating this equivalence, we provide a unified perspective on these techniques. This unification has theoretical and practical implications, facilitating the cross-application of robustness guarantees and algorithmic improvements between complementarity and CBF frameworks. We discuss these synergistic benefits and motivate future work in the comparison of the methods in more general cases.
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