An optimal control approach to the generation of yaw-moment diagrams

The purpose of this paper is to present an algorithm that computes yaw-moment diagrams using optimal control. Braking and acceleration scenarios based on d'Alembert's principle are included. These computations are extended to include vehicles operating on three-dimensional road surfaces that support steady-state cornering, road camber and elevation changes. Such surfaces include the oblique helicoid as well as special cases thereof. Road surface models of this type are well suited to the study of vehicle performance on track sections used in closed-circuit racing such as highly-banked NASCAR ovals. The computational procedure is motivated by the properties of the Moore-Penrose inverse used in the solution of indeterminate or over-constrained sets of linear equations. For illustrative purposes, these ideas are developed using a simple single-track vehicle model. This new procedure is then used to study the handling properties of a Gen-7 NASCAR car on representative road surfaces.