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Learning Model Predictive Control with Error Dynamics Regression for Autonomous Racing

Haoru Xue, Edward L. Zhu, John M. Dolan, Francesco Borrelli

TL;DR

This work addresses safe, data-efficient control for autonomous racing near the handling limit by combining LMPC with error-dynamics regression. A nominal physics-based model is augmented with a local affine error model learned from runtime data, producing an affine-time-varying (ATV) representation that facilitates convex, online optimization. Local convex target sets and local terminal cost-to-go functions are built from past laps to enable safe, iterative improvements without requiring perfect models, and the method is demonstrated in simulation, 1/10-scale hardware, and a full-size Indy Autonomous Challenge race car. Results show enhanced robustness to data scarcity and tuning parameters, enabling reliable safety-aware exploration toward the limit of handling and effective vehicle dynamics learning in high-speed domains.

Abstract

This work presents a novel Learning Model Predictive Control (LMPC) strategy for autonomous racing at the handling limit that can iteratively explore and learn unknown dynamics in high-speed operational domains. We start from existing LMPC formulations and modify the system dynamics learning method. In particular, our approach uses a nominal, global, nonlinear, physics-based model with a local, linear, data-driven learning of the error dynamics. We conducted experiments in simulation and on 1/10th scale hardware, and deployed the proposed LMPC on a full-scale autonomous race car used in the Indy Autonomous Challenge (IAC) with closed loop experiments at the Putnam Park Road Course in Indiana, USA. The results show that the proposed control policy exhibits improved robustness to parameter tuning and data scarcity. Incremental and safety-aware exploration toward the limit of handling and iterative learning of the vehicle dynamics in high-speed domains is observed both in simulations and experiments.

Learning Model Predictive Control with Error Dynamics Regression for Autonomous Racing

TL;DR

This work addresses safe, data-efficient control for autonomous racing near the handling limit by combining LMPC with error-dynamics regression. A nominal physics-based model is augmented with a local affine error model learned from runtime data, producing an affine-time-varying (ATV) representation that facilitates convex, online optimization. Local convex target sets and local terminal cost-to-go functions are built from past laps to enable safe, iterative improvements without requiring perfect models, and the method is demonstrated in simulation, 1/10-scale hardware, and a full-size Indy Autonomous Challenge race car. Results show enhanced robustness to data scarcity and tuning parameters, enabling reliable safety-aware exploration toward the limit of handling and effective vehicle dynamics learning in high-speed domains.

Abstract

This work presents a novel Learning Model Predictive Control (LMPC) strategy for autonomous racing at the handling limit that can iteratively explore and learn unknown dynamics in high-speed operational domains. We start from existing LMPC formulations and modify the system dynamics learning method. In particular, our approach uses a nominal, global, nonlinear, physics-based model with a local, linear, data-driven learning of the error dynamics. We conducted experiments in simulation and on 1/10th scale hardware, and deployed the proposed LMPC on a full-scale autonomous race car used in the Indy Autonomous Challenge (IAC) with closed loop experiments at the Putnam Park Road Course in Indiana, USA. The results show that the proposed control policy exhibits improved robustness to parameter tuning and data scarcity. Incremental and safety-aware exploration toward the limit of handling and iterative learning of the vehicle dynamics in high-speed domains is observed both in simulations and experiments.
Paper Structure (12 sections, 13 equations, 5 figures, 2 tables)

This paper contains 12 sections, 13 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Local Learning Model Predictive Control
  4. Local Convex Target Set
  5. Local Terminal Cost-to-go Function
  6. Local LMPC
  7. Learned Vehicle Dynamics Model
  8. Experiments & Results
  9. Robustness Study on Learning Parameters
  10. Hardware Experiment Comparing Learning Performance
  11. Hardware Demonstration on a Full-Size Race Car
  12. Conclusion

Figures (5)

  • Figure 1: Overlay of the IAC car's trajectory running LMPC with error dynamics regression. The data are collected at the Putnam Park Road Course in Indiana, USA. The zoomed-in image of the hairpin turn shows iterative improvement towards optimal cornering in the 1st, 5th, and 20th lap.
  • Figure 2: Average error of the learned model (Top) and lap times (bottom) over iterations for various settings of the bandwidth $h$. Red and blue lines correspond to the error regression and full regression cases, respectively. A cross is placed where failure occurs due to the vehicle leaving the track.
  • Figure 3: Results from the CRC robustness study. The left and right plots show the iteration lap times over different CRC tunings for rosolia_learning_2020 and our error regression LMPC respectively. A red cross is placed where failure occurs due to the vehicle leaving the track.
  • Figure 4: Per-iteration results of the BARC hardware experiment. The four smaller plots on the left show the lap-time reduction of the 10 trials. The combined plot on the right compares the average lap times achieved. A red cross is placed where failure occurs due to the vehicle leaving the track.
  • Figure 5: Visualization of the 1st, 5th and 20th iteration's trajectory of LMPC with error dynamics regression on the BARC platform.