Learning Expert-Level Racing Strategies via Scheduled Cost Functions in Model Predictive Control

In racing sports, driving strategies necessitate meticulous control and optimal utilization of vehicle dynamics. Model predictive control (MPC) has emerged as an effective approach for imitating expert driving strategies. Traditional MPC methods typically rely on constant cost functions, which are not optimal in dynamic environments that require track-dependent strategies. This paper introduces a novel framework that enhances the imitation of expert strategies by incorporating a scheduled cost function into the MPC. We present an inverse model predictive control (iMPC) framework, equipped with a custom MPC formulation that adeptly integrates scheduled cost functions. By employing Gaussian process (GP) regression, our framework effectively maps the connection between trajectories and their respective scheduling costs, enabling dynamic adaptation of cost functions within MPC planning. Furthermore, we present a probabilistic modeling method that combines Bayesian optimization (BO) with GP. This method is designed to create datasets that closely mimic expert-level driving behaviors, enriching the data available for training and validating our iMPC approach. We evaluate our framework by emphasizing the goodness of fit and interpretability of the reconstructed cost functions and the resulting trajectories. Compared to standard imitation learning methods, our approach stands out in its ability to accurately restore trajectories. We validate our framework using human-in-the-loop expert data and demonstrate the superiority of our methodology by comparing it with a tracking MPC.