🤖 AI Summary
This work addresses the excessive conservatism of traditional control methods in safety-critical systems, which often compromises optimal performance and feasibility. To overcome this limitation, the authors propose a novel framework that embeds Control Barrier Functions (CBFs) as terminal constraints within Model Predictive Control (MPC), thereby rigorously guaranteeing safety while significantly reducing conservatism and enlarging the set of reachable states. The approach enables warm-starting of the underlying nonlinear optimization problem to accelerate convergence and is supported by constructive theoretical proofs ensuring formal correctness. Simulation results demonstrate a 1.7–2.7× reduction in infeasible regions and successful tracking of reference trajectories entirely residing within regions deemed unsafe by conventional CBF formulations, thereby validating the method’s superiority and effectiveness.
📝 Abstract
Optimal control for safety-critical systems is often dependent on the conservativeness of constraints. Control Barrier Functions (CBFs) serve as a medium to represent such constraints, but constructing a minimally conservative CBF is a computationally intractable problem. Therefore, approaches that can guarantee safety while reducing conservatism will help improve the optimality of the system under consideration. Here, we present a Model Predictive Control (MPC) formulation using CBF as a terminal constraint, which is proven to improve feasibility and reachable sets with increasing prediction horizon. The constructive nature of the proofs allows for warm-starting the nonlinear optimization problem, thereby reducing the computational time substantially. Simulations are set up for a simple nonholonomic system to numerically validate the results, and it is observed that the number of infeasible points decreased by a factor of 1.7 to 2.7. The increase in reachable state space was demonstrated by the ability of the system to track trajectories that are entirely inside the unsafe region of the control barrier function.