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Very simplified models prevail in literature on modeling of the autonomous vehicles. More expanded models regarding this issue appear rarely. Definitively, the model with three degrees of freedom (3 DoF model) is used more often. This is due to its high numerical effectiveness, which is very important in course of planning of motion of the autonomous vehicle. Anyhow, such model features significant limitations; it is not suitable for simulation of vehicle motion in difficult weather conditions, or during maneuvers with high values of lateral acceleration due to lacking possibility to use extensive models describing impact of the roadway on the road wheels (models of tires). This model does not work well in case of a trucks, where possibility to consider distribution of the weight is very important because it affects stability and trajectory of the motion. An extended model with ten degrees of freedom (10 DoF model) was proposed in this study; this model was formulated using formalism based on the Newton–Euler equations. Analytical derivation of formulas for the matrix M and for the vector of right-hand sides h has allowed for considerable reduction of time needed for the calculations. This model was compared with another 10 DoF model, formulated with use of transformation method of homogenous and joint coordinates, which have their origins in robotics. The objective of the comparison was to determine an impact of applied formalism on computation time and mapping accuracy of real traffic conditions. The both models were compared to 3 DoF model in task of execution of overtaking maneuver in different weather conditions. In the paper is also presented execution of the real route. Results of computer simulations indicate that proposed models can find their implementation in planning of motion of the autonomous vehicle.