Modelling Vehicle Systems

This chapter presents the background and a brief introduction to the need to develop mathematical models that will eventually be used in designing the controllers. First, it introduces the kinematic model of a wheeled vehicle which is front-wheel-steered and rear-wheel driven. Subsequently, this kinematic model of the wheeled vehicle is extended to incorporate a trailer attached to the vehicle at an off axle hitch point. For example, such a trailer may represent an agricultural implement attached to an agricultural vehicle. The model is developed to reflect real-life scenarios by incorporating wheel slip, both in the longitudinal and the lateral directions. The trailers are steerable and driven and therefore represent the most general scenario. The model can be easily converted to represent a passive trailer by setting the steering and propulsion of the active trailer to zero. The chapter then goes on to derive the kinematic model of a tracked vehicle which is also subsequently extended to incorporate an active trailer coupled to the tracked vehicle at an off axle hitch point. Finally, the kinematic model of a four wheel driven and four wheel steered vehicle is presented. The rest of the chapter consists of the derivation of the dynamic models of all the scenarios mentioned above. A unique part of this chapter is the presentation of partial dynamic models which describe the leading part of an articulated vehicle system using its kinematic model and the trailing part of the articulated vehicle system using its dynamic model.