Safety-critical control for autonomous systems: Control barrier functions via reduced-order models

Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by highdimensional 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.