An optimal control approach to the computation of g-g diagrams

Abstract

The so-called g-g diagram is widely employed to assess the performance of road vehicles since it provides the maximum longitudinal and lateral accelerations that can be extracted from the selected vehicle. The different points of the g-g diagram are usually computed independently from one another, e.g. the maximum longitudinal accelerations corresponding to given lateral accelerations are computed sequentially. In this work, the problem of computing the points of the g-g diagram is transformed into an optimal control problem, which allows to avoid one of the most annoying practical problems often encountered when deriving such diagrams, namely the ‘jumps’ between different solutions (i.e. large slip vs. small slip solutions at similar lateral acceleration) in adjacent points along the g-g envelope. In the proposed method, the objective is to maximise the area enclosed within the g-g diagram, which has a polar representation. The rate of change of the radial coordinate is the control input. Additional constraints are included to enforce the continuity between the states of the vehicle model in adjacent points along the envelope. These conditions can hardly be enforced using standard methods based on sequential and independent computation of the g-g points. An example of the application of the method is demonstrated on the classic double-track car model with nonlinear tyres.