# Study on an Automatic Parking Method Based on the Sliding Mode Variable Structure and Fuzzy Logical Control

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Algorithm of the Sliding Mode Variable Structure Control

**Lemma**

**1.**

## 3. Fuzzy Logical Controller

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Diagram of the error between $\left({x}_{c},{y}_{c},{\theta}_{c}\right)$ and $\left({x}_{r},{y}_{r},{\theta}_{r}\right).$

Input | Output | |||||||
---|---|---|---|---|---|---|---|---|

$\text{}{\mathit{x}}_{\mathit{a}}\text{}$ | $\text{}{\mathit{y}}_{\mathit{a}}\text{}$ | $\text{}\mathit{\theta}$ | $\text{}\mathit{\phi}$ | |||||

FuzzySubset | S | Triangular | S | Triangular | N | Trapezoidal | NB | Triangular |

[−0.23,0.20,0.57] | [−0.30,0.40,1.21] | [−44.6,−27.6,−17.6,−2.30] | [−35,−32.14,−29.15] | |||||

B | Triangular | B | Triangular | Z | Triangular | NM | Triangular | |

[0.40,0.70,1.00] | [0.94,1.65,2.24] | [−4.46,0,2.03] | [−29.77,−20.43,−11.09] | |||||

P | Triangular | PM | Triangular | P | Trapezoidal | N | Triangular | |

[0.93,1.47,1.92] | [2.18,2.52,2.75] | [0.11,7.37,56.3,91] | [−20.43,−11.71,−2.87] | |||||

PB | Trapezoidal | PB | Trapezoidal | PM | Triangular | Z | Triangular | |

[1.74,2.14,2.37,2.50] | [2.75,3.23,4.40,5.40] | [88,90,93.2] | [−3.85,0,4.12] | |||||

PB | Trapezoidal | P | Triangular | |||||

[92.45,97,120,120] | [2.87,11.71,20.43] | |||||||

PM | Triangular | |||||||

[4.98,14.95,24.91] | ||||||||

PB | Trapezoidal | |||||||

[23.67,26.16,37.37,37.37] |

$\text{}{\mathit{y}}_{\mathit{a}}$ | S | B | PM | PB | |
---|---|---|---|---|---|

θ | |||||

N | – | – | – | – | |

Z | – | – | – | – | |

P | NB | NB | – | – | |

PM | Z | – | – | – | |

PB | – | – | – | – |

$\text{}{\mathit{y}}_{\mathit{a}}$ | S | B | PM | PB | |
---|---|---|---|---|---|

θ | |||||

N | – | – | – | – | |

Z | – | – | – | – | |

P | – | NB | – | – | |

PM | – | – | – | – | |

PB | – | – | – | – |

$\text{}{\mathit{y}}_{\mathit{a}}$ | S | B | PM | PB | |
---|---|---|---|---|---|

θ | |||||

N | – | – | – | – | |

Z | – | NB | – | – | |

P | – | NB | – | – | |

PM | – | – | – | – | |

PB | – | – | – | – |

$\text{}{\mathit{y}}_{\mathit{a}}$ | S | B | PM | PB | |
---|---|---|---|---|---|

θ | |||||

N | – | NB | – | – | |

Z | – | Z | – | – | |

P | – | PB | – | – | |

PM | – | – | – | – | |

PB | – | – | – | – |

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**MDPI and ACS Style**

Xu, Y.; Lu, Z.; Shan, X.; Jia, W.; Wei, B.; Wang, Y.
Study on an Automatic Parking Method Based on the Sliding Mode Variable Structure and Fuzzy Logical Control. *Symmetry* **2018**, *10*, 523.
https://doi.org/10.3390/sym10100523

**AMA Style**

Xu Y, Lu Z, Shan X, Jia W, Wei B, Wang Y.
Study on an Automatic Parking Method Based on the Sliding Mode Variable Structure and Fuzzy Logical Control. *Symmetry*. 2018; 10(10):523.
https://doi.org/10.3390/sym10100523

**Chicago/Turabian Style**

Xu, Ying, Zefeng Lu, Xin Shan, Wenhao Jia, Bo Wei, and Yingqing Wang.
2018. "Study on an Automatic Parking Method Based on the Sliding Mode Variable Structure and Fuzzy Logical Control" *Symmetry* 10, no. 10: 523.
https://doi.org/10.3390/sym10100523