Data-Driven Vehicle Dynamics: Leveraging SINDy for Optimization-Based Vehicular Motion Planning

Motion planning remains a crucial challenge for the widespread adoption of autonomous vehicles. This paper presents a novel approach that integrates an empirical plant model within an optimization-based motion planning architecture. The model prioritizes performance and efficiency while maintaining interpretability. We introduce a methodology that utilizes a data-driven approach to derive an interpretable description of the evolution of vehicle states over time using sparse regression. This method allows effective learning from limited datasets, eliminating the need for extensive and expensive data collection. Our approach addresses the trade-off between performance and accuracy, enabling adaptation to diverse driving scenarios. We affirm the efficacy of our methodology via an extensive analysis, evaluating the independent prediction performance across diverse metrics. Additionally, we examine the overall tracking performance when incorporated into an optimization-based framework. Finally, we present a comparative analysis and discuss the subsequent impact on overall motion planning and decision-making in relation to a state-of-the-art single-track model.