Invariance Guarantees using Continuously Parametrized Control Barrier Functions

TL;DR

This paper proposes a novel control framework using continuously parametrized control barrier functions (PCBFs) to dynamically select invariant sets within safety bounds, simplifying the design process for safety-critical control systems.

Contribution

Introducing PCBF, a flexible approach that avoids complex synthesis by dynamically choosing invariant sets, and developing a lightweight QP-based controller for safety guarantees.

Findings

Effective in maintaining safety within complex environments

Enables easier adaptation to diverse scenarios

Validated through simulation experiments

Abstract

Constructing a control invariant set with an appropriate shape that fits within a given state constraint is a fundamental problem in safety-critical control but is known to be difficult, especially for large or complex spaces. This paper introduces a safe control framework of utilizing PCBF: continuously parametrized control barrier functions (CBFs). In PCBF, each choice of parameter corresponds to a control invariant set of relatively simple shape. Invariance-preserving control is done by dynamically selecting a parameter whose corresponding invariant set lies within the safety bound. This eliminates the need for synthesizing a single complex CBF that matches the entire free space. It also enables easier adaptation to diverse environments. By assigning a differentiable dynamics on the parameter space, we derive a lightweight feedback controller based on quadratic programming (QP), namely PCBF-QP. We also discuss on how to build a valid PCBF for a class of systems and how to constrain the parameter so that the invariant set does not exceed the safety bound. The concept is also extended to cover continuously parametrized high-order CBFs, which is called high-order PCBF. Finally, simulation experiments are conducted to validate the proposed approach.