Three step plan:

Introduction

1. Middle Path Algorithm
2. Cross Entropy Method + Maximizing radii
3. Deterministic line calculation + Environment Mapping

Legend

Base Case - Middle Path

• Middle path calculation based on egde points
• maximal speed is defined by slowest curve
• base algorithm to test against

Cross Entropy & Maximizing Radii

Approach 1:

• To create optimal paths to they need to be a cycloid [1]
• Usage of Cross Entropy Method to place discriptive points on to the track (on-line) based on theoretical maximal speed of curves
• Draw splines between these points and try to maximize the radii to create a path until the limitations of the track / car are approached e.g
  • Border
  • Turning circle of the car
• These cycloids have a maximal speed which can be derived by the centrifugal force based on friction, curvature and mass of the car [2]
• Linear interpolation of the acceleration between different splines bounded by car stats

[1] Brachistochrone Problem - https://en.wikipedia.org/wiki/Brachistochrone_curve

[2] Tires & Downforce - https://www.youtube.com/watch?v=fjrOsp6S8rA

Cross Entropy & Maximizing Radii

Advantages:

• maximization of radii is deterministic
• fitness is only based only on max speed of path which can be calculated without a simulation
• Adaptation of rules to maximize radii may be used for object avoidance

Disadvantages:

• Might still be to expensive to calculate
• Connecting splines is non-trivial

Deterministic Line Calculation & Cross Entropy Method

Approach 2:

• A path consisting of cycloids with automatic connection between weighted vectors can be calculated recursivly via the friction, speed and mass of the car [3]
• This will also give the approximated ac-/deceleraion for a given subpath
• With this optimal path regarding the defined calculation time we can focus to learn the mapping of the simulation to the real world
  • a risk factor for the stochastic environment
  • online environment =>  possible limitations on the assumptions made in the cycloid calculations

[3] http://vamos.sourceforge.net/computer-controlled-cars/node2.html

Deterministic Line Calculation & Environment Mapping

Advantages:

• The calculation of the path is get better the more time it gets
• Focusing on the environment may lead to better abstraction online
• Path calculation is done without a simulation
• Reproducable path generation

Disadvantages:

• Foreign object detection might be a bigger issue
• The optimal speed will probably never be driven, need to test if the calculation accounts automatically for it, else acceleration is another issue
• From the looks of it it's way to easy and there might be hidden restrictions on the real world mapping