A study into the modelling of the divergent loss of stability of a tractor-semitrailer subject to an external lateral force and a strategy for the stabilisation of its motion

In this paper, a two-link approach is used to model the tractor-semitrailer when subject to a disturbing external lateral force. The analysis is conducted in the ground plane considering only forward, lateral and yaw motion. As such, it is an extension of the well-known bicycle model typically used to model a vehicle represented by a single body. Using this simplified model the divergent loss of stability is analysed when the vehicle is undergoing steady state motion. The analysis of the divergent loss of stability for the complete tractor-semitrailer model is then reduced to the analysis of the divergent loss of stability for a model of the tractor only. Generalisations of the graphical method for determining the set of stationary states of the reduced tractor model are also considered. The conditions for a divergent loss of stability, when a tractor-semitrailer unit is cornering with a constant Ackermann angle steering input, are developed in an analytical form. The accuracy of the results obtained using this simplified approach is then evaluated through a comparison with the results obtained using a numerical method considering continuation by two parameters for a full model.