Title: Control Barrier Function Synthesis for Nonlinear Systems with Dual Relative Degree Show Chinese title

Title: 具有双相对阶的非线性系统的控制障碍函数综合

Abstract: Control barrier functions (CBFs) are a powerful tool for synthesizing safe control actions; however, constructing CBFs remains difficult for general nonlinear systems. In this work, we provide a constructive framework for synthesizing CBFs for systems with dual relative degree -- where different inputs influence the outputs at two different orders of differentiation; this is common in systems with orientation-based actuation, such as unicycles and quadrotors. In particular, we propose dual relative degree CBFs (DRD-CBFs) and show that these DRD-CBFs can be constructively synthesized and used to guarantee system safety. Our method constructs DRD-CBFs by leveraging the dual relative degree property -- combining a CBF for an integrator chain with a Lyapunov function certifying the tracking of safe inputs generated for this linear system. We apply these results to dual relative degree systems, both in simulation and experimentally on hardware using quadruped and quadrotor robotic platforms. Show Chinese abstract

Abstract: 控制屏障函数（CBFs）是合成安全控制动作的强大工具；然而，对于一般的非线性系统，构造CBFs仍然具有挑战性。 在本工作中，我们提供了一个构造框架，用于为具有双相对阶的系统合成CBFs——其中不同的输入以两种不同的微分阶数影响输出；这在基于方向的执行机构系统中很常见，例如独轮车和四旋翼飞行器。 特别是，我们提出了双相对阶控制屏障函数（DRD-CBFs），并证明这些DRD-CBFs可以被构造性地合成，并用于保证系统安全。 我们的方法通过利用双相对阶特性来构造DRD-CBFs——将一个积分器链的CBF与一个Lyapunov函数结合，该Lyapunov函数验证为此线性系统生成的安全输入的跟踪性能。 我们将这些结果应用于双相对阶系统，在仿真中以及使用四足和四旋翼机器人平台的硬件实验中进行了验证。