# Improved ADRC-Based Autonomous Vehicle Path-Tracking Control Study Considering Lateral Stability

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- An IADRC method is proposed in which a new continuous nonlinear function is proposed to replace the classic piecewise function.
- (2)
- An autonomous vehicle path-tracking control scheme is proposed based on the IADRC; the control system can estimate the real-time action value of the parameter uncertainty and disturbance, and then compensation in the feedback realizes the antidisturbance capability of the controller and improves the robustness of the control system against parameter uncertainty and external disturbance.
- (3)
- Using the CA concept, a control distributor is designed to optimize and coordinate of each wheel in real-time; the external yaw moment used to improve the lateral stability of the vehicle is realized in the form of differential braking.

## 2. Vehicle Model

#### 2.1. Vehicle Dynamics Model

_{1}, L

_{2}, R

_{1}, and R

_{2}of the wheels correspond to the front-left, the rear-left, the front-right, and the rear-right, respectively.

#### 2.2. Vehicle Path-Tracking Model

## 3. Improved ADRC

#### 3.1. Classic ESO Analysis and Improvement

#### 3.2. Stability Analysis of IESO

**Lemma 1 [25].**If there exists a matrix $H=\left(\begin{array}{ccc}{h}_{11}& {h}_{12}& {h}_{13}\\ -{h}_{12}& {h}_{22}& {h}_{23}\\ -{h}_{13}& -{h}_{23}& {h}_{33}\end{array}\right)$, and the principal diagonal elements of $H$ are positive such that the matrix $HG(e)$ is positive definite symmetric, then the zero solution of the system (17) is Lyapunov asymptotically stable.

## 4. The Path-Tracking Controller Design

#### 4.1. IESO for Vehicle Path Following

#### 4.2. State Error Compensator

#### 4.3. Braking Force Distributor Design

## 5. Results and Discussion

#### 5.1. Validation of Controller Effectiveness without Disturbance

#### 5.1.1. IADRC Controller Validation

#### 5.1.2. DYC Controller Validation

#### 5.2. Robustness Verification of Resistance to Disturbance

#### 5.2.1. Continuous Sinusoidal Disturbance

#### 5.2.2. Time-Changing Disturbance

#### 5.2.3. Step Disturbance

## 6. Conclusions

- (1)
- The proposed IADRC-based autonomous vehicle path-tracking control scheme has better control effect and higher antidisturbance robustness.
- (2)
- The proposed nonlinear continuous function instead of the classical piecewise function can effectively solve the jittering phenomenon of control input, and the IESO designed based on this can accurately estimate the value of disturbance and realize the disturbance compensation in the feedback.
- (3)
- The application of yaw stability control not only improves the yaw stability of the vehicle, but also further improves the path-tracking accuracy. Therefore, simultaneous yaw stability control during the path-tracking process can improve the path-tracking accuracy of the vehicle.
- (4)
- The CA-based braking force distributor can fully coordinate the four wheels to achieve external yaw moment by differential braking, improving the yaw stability of the vehicle.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Symbol | Parameters | Value and Units |
---|---|---|

$m$ | Vehicle total mass | 1610 kg |

${I}_{z}$ | Moment of inertia | 2410 kg·m^{2} |

${C}_{f}$ | Cornering stiffness of front wheel | 66,900 N/rad |

${C}_{r}$ | Cornering stiffness of rear wheel | 62,700 N/rad |

${h}_{cg}$ | Height of the vehicle center of mass | 0.65 m |

${l}_{f}$ | Front wheel base | 1.05 m |

${l}_{r}$ | Rear wheel base | 1.51 m |

${t}_{w1}$ | Track width of the front wheels | 1.565 m |

${t}_{w2}$ | Track width of the rear wheels | 1.565 m |

Lateral Deviation | Heading Error | |||
---|---|---|---|---|

Max | RMS | Max | RMS | |

LQR | 0.2052 | 0.0602 | 3.2727 | 0.9201 |

ADRC | 0.2027 | 0.0598 | 2.5001 | 0.7144 |

IADRC | 0.1840 | 0.0593 | 3.2043 | 0.8360 |

Lateral Deviation | Heading Error | |||
---|---|---|---|---|

Max | RMS | Max | RMS | |

IADRC (with DYC) | 0.1425 | 0.0456 | 2.6322 | 0.6601 |

IADRC(without DYC) | 0.1840 | 0.0539 | 3.2043 | 0.8360 |

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**MDPI and ACS Style**

Kang, N.; Han, Y.; Guan, T.; Wang, S.
Improved ADRC-Based Autonomous Vehicle Path-Tracking Control Study Considering Lateral Stability. *Appl. Sci.* **2022**, *12*, 4660.
https://doi.org/10.3390/app12094660

**AMA Style**

Kang N, Han Y, Guan T, Wang S.
Improved ADRC-Based Autonomous Vehicle Path-Tracking Control Study Considering Lateral Stability. *Applied Sciences*. 2022; 12(9):4660.
https://doi.org/10.3390/app12094660

**Chicago/Turabian Style**

Kang, Nan, Yi Han, Tian Guan, and Siyu Wang.
2022. "Improved ADRC-Based Autonomous Vehicle Path-Tracking Control Study Considering Lateral Stability" *Applied Sciences* 12, no. 9: 4660.
https://doi.org/10.3390/app12094660