Extent-compatible control barrier functions

• Published in: Systems & control letters 2021-04, Vol.150, p.104895, Article 104895
• Main Authors: Srinivasan, Mohit, Abate, Matthew, Nilsson, Gustav, Coogan, Samuel
• Format: Article
• Language: English
• Subjects: Control barrier functions; Quadratic programs; Set invariance
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2021.104895

Safety requirements in dynamical systems are commonly enforced with set invariance constraints over a safe region of the state space. Control barrier functions, which are Lyapunov-like functions for guaranteeing set invariance, are an effective tool to enforce such constraints and guarantee safety when the system is represented as a point in the state space. In this paper, we introduce extent-compatible control barrier functions as a tool to enforce safety for the system explicitly accounting for its volume (extent) within an ambient workspace. In order to implement the extent-compatible control barrier functions framework, we first propose a sum-of-squares optimization program that is solved pointwise in time to ensure safety. Since sum-of-squares programs can be computationally prohibitive, we next propose an approach that instead considers a finite number of points sampled on the extent boundary. The result is a quadratic program for guaranteed safety that retains the computational advantage of traditional barrier functions. While this alternative is generally more conservative than the sum-of-squares approach, we show that conservatism is reduced by increasing the number of sampled points. Simulation and robotic implementation results are provided.