Maximal Controlled Invariant-MPC: Enhancing Feasibility and Reducing Conservatism through Terminal CBF Constraint in Safety-Critical Control

TL;DR

This paper introduces a Model Predictive Control approach using Control Barrier Functions as terminal constraints to enhance safety feasibility and reduce conservatism, validated through simulations on a nonholonomic system.

Contribution

It proposes a novel MPC formulation with CBF terminal constraints that improves feasibility and reduces conservatism, with proofs enabling warm-starting for computational efficiency.

Findings

Infeasible points decreased by a factor of 1.7 to 2.7.

Reachable state space increased, allowing trajectory tracking inside unsafe regions.

Simulation results validate improved feasibility and reduced conservatism.

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.