3 years ago

Control Barrier Function based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria. (arXiv:2003.07819v2 [eess.SY] UPDATED)

Matheus F. Reis, A. Pedro Aguiar, Paulo Tabuada
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.

Publisher URL: http://arxiv.org/abs/2003.07819

DOI: arXiv:2003.07819v2

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.