Pareto Control Barrier Function for Inner Safe Set Maximization Under Input Constraints

Control Barrier Functions (CBFs) enforce safety in dynamical systems by ensuring trajectories stay within prescribed safe sets. However, traditional CBFs often overlook realistic input constraints, potentially limiting their practical effectiveness. To address this research gap, we introduce the Pareto Control Barrier Function (PCBF) algorithm, which employs a Pareto multi-task learning framework to simultaneously balance the competing objectives of maintaining safety and maximizing the volume of the safe set under input limitations. The PCBF algorithm is computationally efficient and scalable to high-dimensional systems. We demonstrate its effectiveness through comparisons with Hamilton-Jacobi reachability on an inverted pendulum and extensive simulations on a 12-dimensional quadrotor system, where PCBF consistently outperforms existing methods by yielding larger safe sets while ensuring robust safety under input constraints. Codes are available at https://github.com/XiaoyangCao1113/Pareto_CBF.