Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation
This work addresses safety-critical control problems in robotics and autonomous systems, offering an incremental improvement over existing CBF methods.
The paper tackles the challenge of designing Control Barrier Functions (CBFs) that balance performance and complex safety constraints in systems with high relative degree and actuation limits, introducing a self-supervised learning framework that achieves a 15% increase in control invariant set volume for a 2D double integrator and a 10% increase for a 7D fixed-wing aircraft system.
Control Barrier Functions (CBFs) provide an elegant framework for constraining nonlinear control system dynamics to remain within an invariant subset of a designated safe set. However, identifying a CBF that balances performance-by maximizing the control invariant set-and accommodates complex safety constraints, especially in systems with high relative degree and actuation limits, poses a significant challenge. In this work, we introduce a novel self-supervised learning framework to comprehensively address these challenges. Our method begins with a Boolean composition of multiple state constraints that define the safe set. We first construct a smooth function whose zero superlevel set forms an inner approximation of this safe set. This function is then combined with a smooth neural network to parameterize the CBF candidate. To train the CBF and maximize the volume of the resulting control invariant set, we design a physics-informed loss function based on a Hamilton-Jacobi Partial Differential Equation (PDE). We validate the efficacy of our approach on a 2D double integrator (DI) system and a 7D fixed-wing aircraft system (F16).