Learning-Based MPC Leveraging SINDy for Vehicle Dynamics Estimation

Self-driving technology aims to minimize human error and improve safety, efficiency, and mobility through advanced autonomous driving algorithms. Among these, Model Predictive Control (MPC) is highly valued for its optimization capabilities and ability to manage constraints. However, its effectiveness depends on an accurate system model, as modeling errors and disturbances can degrade performance, making uncertainty management crucial. Learning-based MPC addresses this challenge by adapting the predictive model to changing and unmodeled conditions. However, existing approaches often involve trade-offs: robust methods tend to be overly conservative, stochastic methods struggle with real-time feasibility, and deep learning lacks interpretability. Sparse regression techniques provide an alternative by identifying compact models that retain essential dynamics while eliminating unnecessary complexity. In this context, the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm is particularly appealing, as it derives governing equations directly from data, balancing accuracy and computational efficiency. This work investigates the use of SINDy for learning and adapting vehicle dynamics models within an MPC framework. The methodology consists of three key phases. First, in offline identification, SINDy estimates the parameters of a three-degree-of-freedom single-track model using simulation data, capturing tire nonlinearities to create a fully tunable vehicle model. This is then validated in a high-fidelity CarMaker simulation to assess its accuracy in complex scenarios. Finally, in the online phase, MPC starts with an incorrect predictive model, which SINDy continuously updates in real time, improving performance by reducing lap time and ensuring a smoother trajectory. Additionally, a constrained version of SINDy is implemented to avoid obtaining physically meaningless parameters while aiming for an accurate approximation of the effects of unmodeled states. Simulation results demonstrate that the proposed framework enables an adaptive and efficient representation of vehicle dynamics, with potential applications to other control strategies and dynamical systems.