Derivation of an error model for tractor-trailer path tracking

Developing a specific model for a tractor-trailer system subject to slips in real working environment is essential for understanding its system behavior and designing controllers. This paper presents a comprehensive analysis of the kinematics of the tractor-trailer under the influence of disturbances caused by the ground onto the implements and wheels. An error model is then derived, based on the open-loop kinematic model and the desired reference path. By applying basic theory of engineering mechanics for rigid body with slips, in the form of extra velocities and angles, exerting on rear axles and steered wheel as well as the trailer's implements, the open-loop kinematic model is primarily established. Provided the current state of the vehicle and random disturbances of the environment are known with bounds, the next states of the system can be estimated, the vehicle running path is predicted, along with setting a basis for further controller design. The development is verified by simulation for both kinematic and error models with disturbances obeying the normal distribution.