Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of reduced-order models in robotics, this paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). To this end, we provide a unified formulation of techniques in the literature that share a common foundation of constructing CBFs for complex systems from CBFs for much simpler systems. Such ideas are illustrated through formal results, simple numerical examples, and case studies of real-world systems to which these techniques have been experimentally applied.

翻译：现代自主系统（如飞行机器人、足式机器人和轮式机器人）通常具有高维非线性动力学特性，这给基于模型的安全关键控制设计带来了挑战。受机器人领域降阶模型成功应用的启发，本文提供了一篇关于通过降阶模型与控制障碍函数（CBFs）实现构造性安全关键控制的教程。为此，我们统一阐述了文献中基于从简单系统CBF构建复杂系统CBF这一共同基础的相关技术方法。这些思想通过形式化结论、简单数值算例以及已通过实验验证的真实系统案例研究加以说明。