The focus of my PhD research is enabling autonomous driving capabilities in challenging conditions. This involves effectively capturing complex underlying dynamics and developing feedback controllers to achieve precise path tracking. 

Traditionally, modeling of UGV has relied on first-principles based white-box models to represent complex dynamics and wheel-terrain interactions. However, due to inherent nonlinearities, prediction and control synthesis are often difficult. On the other hand, black-box learning-based methods create an implicit system representation, generating policies that achieve desired objectives but often sacrifice explainability and interpretability.

This is where Koopman Operator Theory (KOT) becomes pivotal. By lifting nonlinear systems into a higher-dimensional space where their dynamics can be approximated linearly, this approach enables us to model and control complex systems through the lens of linear systems theory.

However, applying the KOT in data-driven context requires a finite-dimensional approximation of the Koopman operator. A crucial component of which is choosing the right set of lifting function. My research addresses this by constructing observables suited to the kinematic constraints of UGVs to effectively capture dynamics, forming the basis for robust, real-world solutions.

With initial success showcased on 1/10th scale vehicles, I expanded my research to develop an end-to-end framework that retains the explainability of linear models while tackling challenges like data bias, generalizability through pose-independent modeling, and bridging Sim2Real gaps using dynamic planners. This led to the development of the Multi-Model Parameterized Koopman (MMPK) framework, which is the foundation of Project Varuna.

Over time, MMPK has evolved, enabling seamless, data-driven autonomy across a wide range of platforms from regular operation to extreme off-road environment ensuring adaptability, robustness, and high-performance autonomy in any terrain.