Development and Research of the Mathematical Model of Planar Motion of a Vehicle with a Semitrailer

Abstract

On horizontal nondeformable ground, we consider the movement of a road train consisting of a biaxial tractor car and triaxial semitrailer treated as solid bodies. Based on the Lagrange’s equations of the second kind, we develop a nonlinear mathematical model of its plane motion, using the position of the fifth-wheel coupling and rotating angles of the tractor and semitrailer body as generalized coordinates. We analyze and linearize the constructed system of equations and obtain a linear mathematical model describing the small lateral displacements and rotations of the elements of a road train when it is moving at a high longitudinal speed, small jackknifing angle, and small rotation angle of the steering wheels. Using the equivalent transformations of the obtained system of equations, we construct a state-space linear model of the lateral motion of the road train. A comparative analysis of the use of linear and nonlinear models to describe the road train’s motion, carrying out standard maneuvers, is performed. It is shown that, if the restrictions are satisfied, then the results of nonlinear and linear model usage are quite close to each other and sufficiently well agree with the results of the field tests. The developed model, unlike the already known ones, is fairly simple (linear). Further, it could be used for an analytical synthesis of the control laws for the lateral component of the motion of road trains.