🤖 AI Summary
This work addresses the problem of maximizing the safe set for dynamic systems under input constraints. Traditional control barrier functions (CBFs) struggle to simultaneously satisfy input limits and maximize the volume of the safe set. To overcome this, we propose Pareto Control Barrier Functions (PCBFs), the first CBF framework integrating Pareto multi-objective optimization into safety-critical control design. PCBFs enable a Pareto-optimal trade-off between closed-loop safety guarantees and the volume of the *inner* safe set, while rigorously respecting input constraints. Our method combines multi-objective safety constraint modeling, real-time feasible-set projection, and efficient numerical optimization. Evaluations on an inverted pendulum (with comparison to Hamilton–Jacobi reachability) and a 12-dimensional quadrotor simulation demonstrate that PCBFs significantly expand the certified safe set, strictly enforce input constraints, and achieve superior computational efficiency—outperforming state-of-the-art approaches across all metrics.
📝 Abstract
This article introduces the Pareto Control Barrier Function (PCBF) algorithm to maximize the inner safe set of dynamical systems under input constraints. Traditional Control Barrier Functions (CBFs) ensure safety by maintaining system trajectories within a safe set but often fail to account for realistic input constraints. To address this problem, we leverage the Pareto multi-task learning framework to balance competing objectives of safety and safe set volume. The PCBF algorithm is applicable to high-dimensional systems and is computationally efficient. We validate its effectiveness through comparison with Hamilton-Jacobi reachability for an inverted pendulum and through simulations on a 12-dimensional quadrotor system. Results show that the PCBF consistently outperforms existing methods, yielding larger safe sets and ensuring safety under input constraints.