Dynamic Constraint Tightening for Nonlinear MPC for Autonomous Racing via Contraction Analysis

TL;DR

This paper introduces a robust nonlinear MPC framework for autonomous vehicle path tracking at handling limits, utilizing a Control Contraction Metric to efficiently tighten constraints under uncertainties.

Contribution

It develops a novel robust nonlinear MPC scheme with a homothetic tube based on CCM, improving computational efficiency and handling uncertainties effectively.

Findings

The proposed method effectively tightens constraints in uncertain scenarios.

Simulation results show improved safety margins at vehicle handling limits.

The approach reduces conservatism compared to existing methods.

Abstract

This work develops a robust nonlinear Model Predictive Control (MPC) framework for path tracking in autonomous vehicles operating at the limits of handling utilizing a Control Contraction Metric (CCM) derived from a perturbed dynamic single track model. We first present a nonlinear MPC scheme for autonomous vehicles. Building on this nominal scheme, we assume limited uncertainty in tire parameters as well as bounded force disturbances in both lateral and longitudinal directions. By simplifying the perturbed model, we optimize a CCM for the uncertain model, which is validated through simulations at the dynamic limits of vehicle performance. This CCM is subsequently employed to parameterize a homothetic tube used for constraint tightening within the MPC formulation. The resulting robust nonlinear MPC is computationally more efficient than competing methods, as it introduces only a single additional state variable into the prediction model compared to the nominal scheme. Simulation results demonstrate that the homothetic tube expands most significantly in regions where the nominal scheme would otherwise violate constraints, illustrating its ability to capture all uncertain trajectories while avoiding unnecessary conservatism.