Control Barrier Function-Based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria
Control Barrier Function-Based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria
复制标题
基于控制势垒函数的二次规划引入了不良的渐近稳定平衡
作者：
Matheus F. Reis;Antonio Pedro Aguiar;P. Tabuada
控制李雅普诺夫函数 (CLF) 和控制屏障函数 (CBF) 已被用来通过二次规划 (QP) 开发可证明安全的控制器，以相对于给定集合的轨迹不变性的形式保证安全。在这封信中，我们表明该框架可以将除李亚普诺夫函数最小值之外的平衡点（特别是在安全集的边界处）引入闭环系统。我们得出了明确的条件，在这些条件下，这些不需要的平衡（甚至可以出现在只有一个凸不安全集的线性系统的简单情况中）是渐近稳定的。为了解决这个问题，我们提出了基于 QP 的控制器的扩展，统一了 CLF 和 CBF，这样所得到的系统轨迹就可以避免安全集边界上出现不良的平衡问题。该解决方案通过无碰撞控制器的设计进行了说明。
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 letter, we show that this framework can introduce equilibrium points (particularly at the boundary of the safe 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 such that the resulting system trajectories avoid the undesirable equilibria problem on the boundary of the safe set. The solution is illustrated in the design of a collision-free controller.