Risk-Averse Model Predictive Control for Racing in Adverse Conditions

Abstract

Model predictive control (MPC) algorithms can be sensitive to model mismatch when used in challenging nonlinear control tasks. In particular, the performance of MPC for vehicle control at the limits of handling suffers when the underlying model overestimates the vehicle's capabilities. In this work, we propose a risk-averse MPC framework that explicitly accounts for uncertainty over friction limits and tire parameters. Our approach leverages a sample-based approximation of an optimal control problem with a conditional value at risk (CVaR) constraint. This sample-based formulation enables planning with a set of expressive vehicle dynamics models using different tire parameters. Moreover, this formulation enables efficient numerical resolution via sequential quadratic programming and GPU parallelization. Experiments on a Lexus LC 500 show that risk-averse MPC unlocks reliable performance, while a deterministic baseline that plans using a single dynamics model may lose control of the vehicle in adverse road conditions.

Figures (7)

• Figure 1: Racing results through a wet area. The proposed risk-averse MPC reliably handles the vehicle throughout the turn. In contrast, a deterministic MPC controller consistently spins out the vehicle as it over-predicts the attainable tire forces.
• Figure 2: Vehicle on the reference path.
• Figure 3: Tire forces $F_{yf}$ as a function of the slip angle $\alpha$.
• Figure 4: Top: Nominal vs risk-averse solutions. Bottom: Closed-loop trajectories for different parameters $\theta$ corresponding to solutions to OCP (dashed lines) and RA-OCP (solid lines).
• Figure 5: Closed-loop trajectories for different parameters $\theta$ corresponding to solutions to OCP with low friction values $\mu_f=\mu_r=0.7$ (dashed lines), and RA-OCP (solid lines).

Theorems & Definitions (2)

• Remark 1: On closed-loop uncertainty propagation
• Remark 2: Alternatives and lessons learned