I think autonomous performance cars are using different but related techniques. I am not close enough to what the autonomous performance cars are doing to say where things are in terms of the state of the art but I think there is opportunity.

For Micromouse, there are several methods people use. One is to create a trapezoidal angular velocity profile while holding the forward speed constant. The trapezoidal profile parameters are determined through iterative simulation.

Another approach - the one I use - uses cubic spirals which is described in: Smooth Local Path Planning for Autonomous Vehicles by Yutaka Kanayama and Bruce I. Hartman. What is amazing about this technique is that it is closed form, is like four or five multiply and adds and executes in trivial time on (even) an 8-bit processor. For my latest entry, I have a more sophisticated scheme where I try to maximize the load on the tires and the lateral and longitudinal loads are asymmetric.

In this article: http://www.dtweed.com/circuitcellar/xottenda.htm#183 - David Otten describes a scheme where he controls the rotational velocity such that the load on the tires is maximised.

I think you can get very far with simulations and then trying it on a RC car and then on a real car.

A few years back, there was some amazing work that was done at Stanford where they developed tire models and a controller that could handle sliding modes.

I encourage you to explore because if nothing else, you will learn.