  The pervasive integration of Unmanned Aerial Vehicles (UAVs) across
multifarious domains necessitates a nuanced understanding of control
methodologies to ensure their optimal functionality. This exhaustive review
meticulously examines two pivotal control paradigms in the UAV landscape,
Geometric Control and Feedback Linearization. Delving into the intricate
theoretical underpinnings, practical applications, strengths, and challenges of
these methodologies, the paper endeavors to provide a comprehensive overview.
Geometric Control, grounded in the principles of differential geometry, offers
an elegant and intuitive approach to trajectory tracking and mission execution.
In contrast, Feedback Linearization employs nonlinear control techniques to
linearize UAV dynamics, paving the way for enhanced controllability. This
review not only dissects the theoretical foundations but also scrutinizes
real-world applications, integration challenges, and the ongoing research
trajectory of Geometric Control and Feedback Linearization in the realm of
UAVs.
