Integrating Gradient-Based MPC and Control Barrier Functions for Safe and Performant Control

Aditya Singh, Aastha Mishra, Manan Tayal, Shishir Kolathaya

Keywords: Safety-Performance Co-Optimization, Safety-Critical Controls, Gradient-based Optimization

TL;DR: We propose a two-stage framework combining gradient-based MPC with CBF filtering to ensure safety and performance. By relaxing constraints during planning and enforcing them via CBF-QP, it reduces conservatism and outperforms sampling-based methods.

Abstract: Ensuring both safety and performance is essential for autonomous systems operating in real-world environments. While Control Barrier Function (CBF)-based safety filters enforce safety by modifying nominal controllers, they can become overly conservative when the nominal policy is not safety-aware. On the other hand, solving state-constrained optimal control problems is computationally challenging in high-dimensional settings. In this work, we propose a two-stage framework that combines gradient-based Model Predictive Control (MPC) with CBF-based safety filtering to jointly optimize safety and performance. First, safety constraints are relaxed as penalty terms in the cost function, enabling efficient gradient-based optimization and improved scalability. Second, a CBF-based Quadratic Program (CBF-QP) minimally modifies the resulting controller to enforce hard safety constraints. We validate the proposed framework on two case studies, demonstrating safe, high-performing, and computationally efficient control in complex high-dimensional systems.

Submission Number: 34