Least Restrictive Hyperplane Control Barrier Functions

2025-10-21

AI Summary

Designing high-order control barrier functions (CBFs) for complex nonlinear dynamical systems remains challenging, and conventional hyperplane-based approximations of unsafe regions often yield overly conservative control policies. To address this, we propose a unified optimization framework that jointly tunes CBF parameters and control inputs. Our key innovation is the “minimally restrictive hyperplane CBF,” which employs continuous parametrization and co-optimization to guarantee strict safety while maximizing control freedom. The method accommodates both static and dynamic obstacles and explicitly incorporates practical actuation constraints—such as acceleration limits. Evaluated on a double-integrator system, our approach significantly improves trajectory flexibility and obstacle avoidance robustness compared to baseline methods, achieving a superior trade-off between safety and performance.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Control Barrier Functions (CBFs) can provide provable safety guarantees for dynamic systems. However, finding a valid CBF for a system of interest is often non-trivial, especially if the shape of the unsafe region is complex and the CBFs are of higher order. A common solution to this problem is to make a conservative approximation of the unsafe region in the form of a line/hyperplane, and use the corresponding conservative Hyperplane-CBF when deciding on safe control actions. In this letter, we note that conservative constraints are only a problem if they prevent us from doing what we want. Thus, instead of first choosing a CBF and then choosing a safe control with respect to the CBF, we optimize over a combination of CBFs and safe controls to get as close as possible to our desired control, while still having the safety guarantee provided by the CBF. We call the corresponding CBF the least restrictive Hyperplane-CBF. Finally, we also provide a way of creating a smooth parameterization of the CBF-family for the optimization, and illustrate the approach on a double integrator dynamical system with acceleration constraints, moving through a group of arbitrarily shaped static and moving obstacles.

Problem

• Finding valid Control Barrier Functions for complex unsafe regions
• Optimizing CBFs and controls to maximize desired control performance
• Ensuring safety guarantees while navigating shaped static and moving obstacles

Innovation

• Optimizes combination of CBFs and safe controls
• Creates least restrictive Hyperplane-CBF for safety
• Provides smooth parameterization of CBF-family for optimization