Control Barrier Function-Based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Matheus F. Reis (Author) Other; António Pedro Aguiar (Author) FEUP; Paulo Tabuada (Author) Other

Journal

Title: IEEE Control Systems Letters

Vol. 5 No. 2

Pages: 731-736

Publisher: IEEE

Indexing

Scopus - 2 Citations

Other information

Authenticus ID: P-00R-YQF

DOI: 10.1109/lcsys.2020.3004797

Abstract (EN): 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. © 2017 IEEE.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 6