论文标题
基于控制屏障函数的二次程序引入了不良的渐近稳定平衡
Control Barrier Function based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria
论文作者
论文摘要
控制Lyapunov功能（CLF）和控制屏障功能（CBF）已被用于通过二次程序（QPS）来开发可证明的安全控制器，从而以相对于给定集的轨迹不变性来确保安全性。在本手稿中，我们表明该框架可以将平衡点（尤其是在不安全集的边界）引入闭环系统中的最小值外，除了Lyapunov函数的最小值外。我们得出了这些不希望的平衡（甚至可以在仅一个凸线不安全集的线性系统的简单情况下出现）的明确条件，在渐近稳定。为了解决此问题，我们建议将基于QP的控制器扩展到统一CLF和CBF，该控制器明确避免了安全集合边界上不良的平衡。在无碰撞控制器的设计中说明了解决方案。
Control Lyapunov functions (CLFs) and control barrier functions (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs), guaranteeing safety in the form of trajectory invariance with respect to a given set. In this manuscript, we show that this framework can introduce equilibrium points (particularly at the boundary of the unsafe set) other than the minimum of the Lyapunov function into the closed-loop system. We derive explicit conditions under which these undesired equilibria (which can even appear in the simple case of linear systems with just one convex unsafe set) are asymptotically stable. To address this issue, we propose an extension to the QP-based controller unifying CLFs and CBFs that explicitly avoids undesirable equilibria on the boundary of the safe set. The solution is illustrated in the design of a collision-free controller.
