Singular Perturbations for Control Systems Safety

Engineering notes

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Chinese explanation / 中文解读

中文解读待补充：本站会优先为 VLA、具身智能、人形机器人控制、机器人操作等高价值论文补充中文说明。

Original abstract

Control Barrier Functions (CBFs) offer a powerful theory for enforcing safety in dynamical systems. Yet, applying this framework to complex systems is challenging when subsystems are feedback-interconnected and operate at different timescales. Such structures arise naturally in multiphysics systems and in control architectures where physical plants interact with optimization, estimation, and control algorithms. In many of these settings, safety involves only part of the system, motivating the design of reduced-order certificates. Inspired by singular perturbation theory, we establish sufficient conditions, involving separation between slow and fast dynamics, under which a reduced-order safety certificate can be lifted to the full interconnected system. Specifically, we construct a composite CBF ensuring forward invariance of a lifted subset of the original safe set. We also show that the certified safe set expands monotonically as the tuning parameter accelerating the fast dynamics is reduced. Numerical results validate the approach on two robotic systems: a planar 2-DoF manipulator with motor dynamics and a 6-DoF UR10e manipulator controlled by a suboptimal optimization algorithm.

Links and sources

• Official / arXiv page
• PDF from original source

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