Safe and Performant Controller Synthesis using Gradient-based Model Predictive Control and Control Barrier Functions

TL;DR

This paper introduces a two-stage control synthesis framework combining gradient-based MPC and Control Barrier Functions to achieve scalable, safe, and high-performance control for complex autonomous systems.

Contribution

It proposes a novel approach that relaxes safety constraints for scalability and refines safety enforcement with CBFs, improving safety and performance in high-dimensional systems.

Findings

Scalable controller synthesis for high-dimensional systems.

Controllers that are both safe and high-performing.

Validated on complex autonomous system case studies.

Abstract

Ensuring both performance and safety is critical for autonomous systems operating in real-world environments. While safety filters such as Control Barrier Functions (CBFs) enforce constraints by modifying nominal controllers in real time, they can become overly conservative when the nominal policy lacks safety awareness. Conversely, solving State-Constrained Optimal Control Problems (SC-OCPs) via dynamic programming offers formal guarantees but is intractable in high-dimensional systems. In this work, we propose a novel two-stage framework that combines gradient-based Model Predictive Control (MPC) with CBF-based safety filtering for co-optimizing safety and performance. In the first stage, we relax safety constraints as penalties in the cost function, enabling fast optimization via gradient-based methods. This step improves scalability and avoids feasibility issues associated with hard constraints. In the second stage, we modify the resulting controller using a CBF-based Quadratic Program (CBF-QP), which enforces hard safety constraints with minimal deviation from the reference. Our approach yields controllers that are both performant and provably safe. We validate the proposed framework on two case studies, showcasing its ability to synthesize scalable, safe, and high-performance controllers for complex, high-dimensional autonomous systems.