Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function

TL;DR

This paper introduces a safety-critical model predictive control approach using discrete-time control barrier functions to ensure safety and optimality in robotic systems, validated through obstacle avoidance and racing scenarios.

Contribution

It presents a novel MPC strategy that guarantees safety via control barrier functions while maintaining optimal performance, with proven stability and feasibility.

Findings

Guarantees safety within invariant sets.

Successfully applied to obstacle avoidance.

Demonstrates effectiveness in racing scenario.

Abstract

The optimal performance of robotic systems is usually achieved near the limit of state and input bounds. Model predictive control (MPC) is a prevalent strategy to handle these operational constraints, however, safety still remains an open challenge for MPC as it needs to guarantee that the system stays within an invariant set. In order to obtain safe optimal performance in the context of set invariance, we present a safety-critical model predictive control strategy utilizing discrete-time control barrier functions (CBFs), which guarantees system safety and accomplishes optimal performance via model predictive control. We analyze the stability and the feasibility properties of our control design. We verify the properties of our method on a 2D double integrator model for obstacle avoidance. We also validate the algorithm numerically using a competitive car racing example, where the ego car is able to overtake other racing cars.