Reduced-order models (ROMs) provide lower dimensional representations of complex systems, capturing their salient features while simplifying control design. Building on previous work, this paper presents an overarching framework for the integration of ROMs and control barrier functions, enabling the use of simplified models to construct safety-critical controllers while providing safety guarantees for complex full-order models. To achieve this, we formalize the connection between full and ROMs by defining projection mappings that relate the states and inputs of these models and leverage simulation functions to establish conditions under which safety guarantees may be transferred from a ROM to its corresponding full-order model. The efficacy of our framework is illustrated through simulation results on a drone and hardware demonstrations on ARCHER, a 3D hopping robot.

翻译：降阶模型为复杂系统提供了低维表示，在简化控制设计的同时捕捉其显著特征。本文在先前研究基础上，提出一个将降阶模型与控制屏障函数相集成的总体框架，使得能够利用简化模型构建安全关键控制器，同时为复杂全阶模型提供安全保障。为实现这一目标，我们通过定义关联模型状态与输入的投影映射来形式化全阶模型与降阶模型之间的联系，并利用仿真函数建立安全保证可从降阶模型传递至相应全阶模型的条件。通过无人机仿真实验和在三维跳跃机器人ARCHER上的硬件演示，验证了本框架的有效性。