The field of trajectory tracking control for ground vehicles has problems such as unknown control object manipulation characteristics, missing dynamic digital models, and susceptibility to distortion of upper-layer tracking control algorithms. This paper first proposes a method for identifying the chassis forward/inverse dynamics model based on vehicle-level state variables and control variable methods to solve these issues. Secondly, the control object manipulation characteristics and dynamic fitting digital model are obtained based on a specific electric drive-tracked chassis. Thirdly, a linear quadratic regulator is used as the core path tracking algorithm, and a dual closed-loop trajectory tracking control algorithm based on the inverse dynamics fitting model is established for both lateral and longitudinal position feedforward + velocity feedback correction. Finally, systematic verification is conducted using the Simulink simulation environment and real vehicles. The verification results show that the proposed model identification method supports vehicle-level state fitting accuracy maintained within 3%, and the trajectory tracking control algorithm maintains tracking accuracy within 0.1m under extreme U-turn conditions. The dual closed-loop control structure enhances control accuracy and robustness.