Predictive Control Barrier Functions: Bridging model predictive control and control barrier functions

TL;DR

This paper introduces a novel MPC-based framework that uses Predictive Control Barrier Functions to ensure safety and invariance without strict stability assumptions, simplifying previous approaches.

Contribution

We propose a simpler MPC formulation that guarantees safety using a new type of CBF called PCBF, with weaker assumptions than existing methods.

Findings

The proposed MPC ensures safety without requiring the value function to decrease strictly.

Numerical examples demonstrate effective safety guarantees and non-conservative CBF construction.

The approach bridges the gap between MPC and control barrier functions, simplifying existing methods.

Abstract

In this paper, we establish a connection between model predictive control (MPC) techniques and Control Barrier Functions (CBFs). Recognizing the similarity between CBFs and Control Lyapunov Functions (CLFs), we propose a MPC formulation that ensures invariance and safety without relying on explicit stability conditions. The value function of our proposed MPC is a CBF, which we refer to as the Predictive Control Barrier Function (PCBF), similar to traditional MPC formulations which encode stability by having value functions as CLFs. Our formulation is simpler than previous PCBF approaches and is based on weaker assumptions while proving a similar theorem that guarantees safety recovery. Notably, our MPC formulation does not require the value function to be strictly decreasing to ensure convergence to a safe invariant set. Numerical examples demonstrate the effectiveness of our approach in guaranteeing safety and constructing non-conservative CBFs.