The bicycle model of a 4WS car lateral dynamics for lane change controller

Abstract

The article shows the validity of four-wheel steering (4WS) bicycle model. At the beginning it is presented in which tasks, connected with 4WS vehicles, the bicycle model is applied. Then the equations in local coordinate system and their forms in global coordinate system are presented. The research tested the response of the model to a lane change manoeuvre, using transfer functions and a “bang-bang” control signal. The transfer functions was connected with static ratio characteristic to construct full four-wheel steering model. A reference signal generator and vehicle model were constructed in analytical form and checked in Matlab&Simulink using sample vehicle’s data from another literature item. One example of simulations was shown. The results presented led to interesting conclusions and indicated directions for further research. This research will include the issue of regulators derivation. This will allow for the construction of a fully functioning control system. The effects of this activities will be tested again in simulation environment.

The Validity of Sensors and Model in the Lane Change Control Process

“…The analysis of the 4WS bicycle model will be based on the research of the 4WS vehicle lane change process through a suddenly appearing obstacle. The driver or controller during this manoeuvre generates a “bang-bang” signal ( Figure 4 ) [ 33 ]. According to the theory of optimal control, for time-optimal systems, meaning those systems that ensure that processes are realised in a minimum of time, control must take the form of “bang-bang” (infinite rapid ramp-up is possible when dealing with controllers that generate electronic signals).…”

“…In classic 4WS controls, the rear wheels are controlled by transforming the front wheel control accordingly ( Figure 6 ) [ 33 ]. …”

“…With the assumed ratio characteristics, the transfer function model appears as follows ( Figure 7 ) [ 33 ]: where: …”

“…For this, it is necessary to analyse the limits of the transfer functions. In particular, the “bang-bang” input waveforms ( Figure 9 ) should be considered, as they approximate the real waveforms during the lane change process [ 33 ]. …”

“…It was decided to use the model in a reduced version (members affecting only the transients are omitted), as this enables an analytical synthesis of the control of classical 4WS vehicles [ 33 ]. …”