Optimal path-tracking of virtual race-cars using gain-scheduled preview control

Abstract

In the search for a more capable minimum-lap-time-prediction program, the presence of an alternative solution has been introduced, which requires the development of a high-quality path-tracking controller. Preview Discrete Linear Quadratic Regulator (DLQR) theory has been used to generate optimal tracking control gains for a given car model. The calculation of such gains are performed off-line, reducing the computational burden during simulated tracking trials. A simple car model was used to develop limit-tracking control strategies, first for an understeering and then for an oversteering car, travelling at a constant forward speed. Adaptation in the controller, with respect to front-/rear-lateral-slip ratio, facilitated superior tracking performance over the non-adaptive counterpart in a number of challenging tracking manoeuvres. Once complete, development work was focused on the control of a complex car model. Such a model required an extension to the preview DLQR theory, to allow variable speed, two-channel (x,y) optimal path tracking. Significant benefits were observed when using an adaptive control strategy, firstly scheduling with respect to forward ground speed and then including adaptation with respect to mean front-lateral-slip ratio. A variable weighting strategy was used to suppress oscillations in the tracking controller when operating near the limit of the car. Such a strategy places a higher cost on control effort expenditure, relative to tracking error, as the car approaches the limit of the front axle. Further oscillatory behaviour, due to the presence of lightly-damped eigenmodes, was suppressed by increasing the car’s suspension stiffness and damping parameters. The tracking controller, that has resulted from the work documented by this thesis, has demonstrated high-quality tracking when operating in a number of different scenarios, including lateral limit tracking. Variable speed limit tracking is suggested as the next development step, which will then allow the controller to be implemented in initial learning trials. Successful development of the speed and path optimisers in such trials will complete the development of a novel solution to the minimum lap-time problem.