This paper describes a new general framework for the action of an automated driver (or driver model) to provide the control of longitudinal and lateral dynamics of a road vehicle. The context of the problem is assumed to be in high-speed competitive driving, as in motor racing, where the requirement is for maximum possible speed along a track, making use of a reference path (racing line) but with the capacity for obstacle avoidance and recovery from large excursions. While not necessarily representative of a human driver, the analysis provides worthwhile insight into the nature of the driving task and offers a new approach for vehicle lateral and longitudinal control; it also has applications in less demanding applications such as Advanced Cruise Control systems. As is common in the literature, the driving task is broken down into two distinct subtasks: path planning and local feedback control. In the first of these tasks, an essentially geometric approach is taken here, which makes use of a vector field analysis. At each location x the automated driver is to prescribe a vector w for the desired vehicle mass centre velocity; the spatial distribution and global properties of w( x) provide essential information for stability analysis, as well as control reference. The resulting vector field is considered in the context of limited friction and limited mass centre accelerations, leading to constraints on ∇ w. Provided such constraints are satisfied, and using suitable adaptation of w( x) when required, it is shown that feedback control can be applied to guarantee stable asymptotic tracking of a reference path, even under limit handling conditions. A specific implementation of the method is included, using dual non-linear SISO (single-input single-output) controllers.
THE BURNSIDE RING-VALUED MORSE FORMULA FOR VECTOR FIELDS ON MANIFOLDS WITH BOUNDARY