{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "![McLaren Maze Race Banner](media/banner.png)\n", "\n", "# Welcome to Pro Driver - level 4 of the McLaren Maze Race!\n", "\n", "This level is all about grip, as we introduce tyres, aerodynamics, and rain. From an AI point-of-view we will look at time series forecasting and *latent variable modelling* - dealing with variables you can't measure.\n", "\n", "Grip is the most important parameter in Formula 1 (although our reliability engineers might dispute that, afterall a broken car wins no races). You can have the most powerful engine on the grid but grip is what allows that power to be turned into acceleration and your driver to keep the power on in the corners. In our Maze Race grip is applied as a multiplier to both the speed deltas obtained when you apply a throttle or braking action and the maximum speed you can corner at. Hence, a high grip level will allow you to accelerate faster, brake later, and corner faster than a low grip level. \n", "\n", "The figure below shows the effect of grip on a straight of length 15. At each point along the straight we compute the maximum speed that the car can achieve given it starts from stationary and needs to safely make it round the corner.\n", "\n", "![A sweep of grip values on a straight](media/grip_sweep.png)\n", "\n", "We can see how the car is able to reach maximum speed for much of the straight when the grip level is high and how this drops away as the grip lowers. The plot on the right shows the effect on the race time for this straight relative to a grip of 1.0. Initially the driver doesn't lose too much time but as the grip gets towards its lowest levels the amount of time lost becomes much more serious.\n", "\n", "In this level we will carry forward the AI we designed in the previous level and extend it to cope with the varying levels of grip that it comes across. Recall that the heart of our AI driver was the dynamics model it learnt, which predicted what the next car speed would be given the current speed and a particular action to be taken. Previously, the change in car speed was only affected by these two parameters but now we have to take the grip level into account. As a first step towards this we are going to switch from modelling the next speed directly to modelling the change in speed, as we are told above the grip is applied as a multiplier to the speed delta. Our model is now,\n", "\n", "