https://github.com/netgusto/car-model-prototype

Car model prototype repo (temporary)
https://github.com/netgusto/car-model-prototype

Last synced: 10 months ago
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Car model prototype repo (temporary)

• Host: GitHub
• URL: https://github.com/netgusto/car-model-prototype
• Owner: netgusto
• Created: 2017-06-26T06:47:30.000Z (over 8 years ago)
• Default Branch: master
• Last Pushed: 2017-07-04T21:31:35.000Z (over 8 years ago)
• Last Synced: 2025-01-29T02:45:23.832Z (12 months ago)
• Language: Go
• Size: 1.64 MB
• Stars: 1
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          

Car model: 1 box, 4 wheels, 2 directional in the front, 2 fixed in the rear

https://user-images.githubusercontent.com/4974818/27407504-d3114bda-56d8-11e7-811b-713aee5f4412.png

                            |--------------------|

                            | __           __    |

                            | \ \          \ \   |

                            |  \ \     x    \ \  |

                            |   \_\    |     \_\ |

                            |          |         |

                            |          |         |

                            |          |         |

                            |          |L        |

                            |          |         |

                            |   _      |     _   |

                            |  | |     |    | |  |

                            |  | |     X    | |  |

                            |  |_|          |_|  |

                            |                    |

                            |--------------------|

Simplified by approximation : consider that the left and right directional wheels are parallel when turning (they are not in real life; see "ackerman drive")

This simplification is the bycicle model.

https://user-images.githubusercontent.com/4974818/27407537-f78ee828-56d8-11e7-8210-84575f5f3034.png

                                |-------|

                                | __    |

                                | \ \   |

                                |  \ \  |  -|

                                |   \_\ |   |

                                |       |   |

                                |       |   |

                                |       |   |

                                |       |   | length L

                                |       |   |

                                |   _   |   |

                                |  | |  |   |

                                |  |x|  |  -|

                                |  |_|  |

                                |       |

                                |-------|

Given:

x & y       : Position point of center of the rear axle

L			: Length between front wheel and rear wheel axles

d           : Distance of movement of the vehicle

α (alpha)   : Angle of front wheel **relative** to center line of the vehicle

θ (theta)   : Angle of center line of the vehicle, **absolute**

We find:

β (beta)	: Turning angle

R           : Radius of turning circle

Cx & Cy     : Center point of turning circle

x' & y'     : New position point of center of the rear axle

θ'          : New angle of center line of the vehicle, **absolute**

β = (d / L) * tan(α)

R = d / β

If β < 0.001 : linear movement approximation

    x' = x + d * cos(θ)

    y' = y + d * sin(θ)

    θ' = (θ + β) mod 2π

Else :

    Cx = x - sin(θ) * R

    Cy = y + cos(θ) * R

    x' = Cx + sin(θ + β) * R

    y' = Cy - cos(θ + β) * R

    θ' = (θ + β) mod 2π