  Autonomous racing is a research field gaining large popularity, as it pushes
autonomous driving algorithms to their limits and serves as a catalyst for
general autonomous driving. For scaled autonomous racing platforms, the
computational constraint and complexity often limit the use of Model Predictive
Control (MPC). As a consequence, geometric controllers are the most frequently
deployed controllers. They prove to be performant while yielding implementation
and operational simplicity. Yet, they inherently lack the incorporation of
model dynamics, thus limiting the race car to a velocity domain where tire slip
can be neglected. This paper presents Model- and Acceleration-based Pursuit
(MAP) a high-performance model-based trajectory tracking algorithm that
preserves the simplicity of geometric approaches while leveraging tire
dynamics. The proposed algorithm allows accurate tracking of a trajectory at
unprecedented velocities compared to State-of-the-Art (SotA) geometric
controllers. The MAP controller is experimentally validated and outperforms the
reference geometric controller four-fold in terms of lateral tracking error,
yielding a tracking error of 0.055m at tested speeds up to 11m/s.
