MPC application

Learning-based model predictive control for autonomous racing §

Juraj Kabzan et al., IEEE RAL 2019

• progress: 20%, link
• Main idea: Having a nominal model from physics, then use Gaussian Process to estimate the model error and niose. Handcraft cost function for the MPC
• Apply gaussian progress (GP) regression to collected data to approach the deviation between the nominal model and the real one. A GP is , is the real, unknow function. is Gaussian noise with diagonal variance , model error Use sparse GP regression to reduce the computational complexity.
• Using a dynamic bicycle model to estimate a racing car, assuming that there is a deviation between the simple model and the real model
  • , where additional learned part of the dynamics, estimating the model error , only affect part of the model, determined by
  • is determined by hand (assuming the model error only affects the dynamic part of the system)
  • real_model = nominal_model + model_error + gaussian_noise
• The model can be learned by:
• The cost function for MPC contains three parts:
  1. contouring cost
  2. (regularization) quadratic cost on the steering angle
  3. (regularization) aggressiveness
• Track, tire and input constraints

TO READ: §

• UCB, MPC team
• Ugo Rosolia and Francesco Borrelli. “Learning Model Predictive Control for Iterative Tasks. A Data-Driven Control Framework.” In IEEE Transactions on Automatic Control (2017). PDF
• Ugo Rosolia and Francesco Borrelli. “Learning how to autonomously race a car: a predictive control approach.” IEEE Transactions on Control Systems Technology (2019) PDF.
• Ugo Rosolia and Francesco Borrelli. “Learning Model Predictive Control for Iterative Tasks: A Computationally Efficient Approach for Linear System.” IFAC-PapersOnLine 50.1 (2017). PDF
• RacingLMPC