# Coordinated Control of Unmanned Electric Formula Car

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Introduction to UEFC’s Mechanical Structure

#### 2.2. Mathematical Model of UEFC

_{l}or the lateral force F

_{c}or the return moment M

_{z}; x is the input variable, which can be determined by the tire side slip angle α or longitudinal slip ratio s; B. C, D and E are stiffness factor, shape factor, peak factor and curvature factor, respectively.

#### 2.3. Lateral Controller Based on Fuzzy Neural Network

#### 2.3.1. Torque Control Layer

#### 2.3.2. Distribution of Torque and Control Layer of Slip Rate

- (1)
- Torque distribution and restraint

- (2)
- Motor failure

- (3)
- Slip rate control

#### 2.4. Longitudinal Controller of Racing Car Based on Incremental PID

_{c}. The fuzzy controller adjusts the changes of the three parameters of PID online according to the experience rules accumulated in the past [22]. Then, the adjusted three changes ${K}_{p}$, ${K}_{i}$ and ${K}_{D}$ are added to the previously set initial value of the PID controller to obtain the final output, as shown in Equation (19).

#### 2.5. Lateral and Longitudinal Controller of UEFC

## 3. Results

^{2}; the wheel radius of the racing car is 0.355 m and the height of the mass center is 0.565 m.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Dolara, A.; Leva, S.; Moretti, G.; Mussetta, M.; De Novaes, Y.R. Design of a Resonant Converter for a Regenerative Braking System Based on Ultracap Storage for Application in a Formula SAE Single-Seater Electric Racing Car. Electronics
**2021**, 10, 161. [Google Scholar] [CrossRef] - Li, Y.; Hong, H.; D’Apolito, L. Reliability Control of Electric Racing Car’s Accelerator and Brake Pedals. World Electr. Veh. J.
**2020**, 12, 1. [Google Scholar] [CrossRef] - Xie, Y.; Wang, C.; Hu, X.; Lin, X.; Li, W. An MPC-based control strategy for low-temperature electric vehicle battery cooling considering energy saving and battery lifespan. IEEE Trans. Veh. Technol.
**2020**, 69, 14657–14673. [Google Scholar] [CrossRef] - Henao-Muñoz, A.C.; Pereirinha, P.; Bouscayrol, A. Regenerative Braking Strategy of a Formula SAE Electric Race Car Using Energetic Macroscopic Representation. World Electr. Veh. J.
**2020**, 11, 45. [Google Scholar] [CrossRef] - Karmakar, G.; Chowdhury, A.; Das, R.; Kamruzzaman, J.; Islam, S. Assessing Trust Level of a Driverless Car Using Deep Learning. IEEE Trans. Intell. Transp. Syst.
**2021**, 22, 4457–4466. [Google Scholar] [CrossRef] - Zhang, H.; Yang, P.; Zhang, G.W.; Sun, H. Research on stability of electric vehicle based on terminal sliding mode control. Comput. Simul.
**2020**, 37, 134–138. [Google Scholar] - Li, W.; Xie, Z.; Wong, P.K.; Mei, X.; Zhao, J. Adaptive-Event-Trigger-Based Fuzzy Nonlinear Lateral Dynamic Control for Autonomous Electric Vehicles under Insecure Communication Networks. IEEE Trans. Ind. Electron.
**2020**, 68, 2447–2459. [Google Scholar] [CrossRef] - Yang, J.; Zhang, T.; Hong, J.; Zhang, H.; Zhao, Q.; Meng, Z. Research on driving control strategy and Fuzzy logic optimization of a novel mechatronics-electro-hydraulic power coupling electric vehicle. Energy
**2021**, 233, 121221. [Google Scholar] [CrossRef] - Wu, J.; Ji, Y.; Sun, X.; Xu, Y. Price regulation mechanism of travelers’ travel mode choice in the unmanned transportation network. J. Adv. Transp.
**2020**, 2020, 9191834. [Google Scholar] - Subroto, R.K.; Wang, C.Z.; Lian, K.L. Four-Wheel Independent Drive Electric Vehicle Stability Control Using Novel Adaptive Sliding Mode Control. IEEE Trans. Ind. Appl.
**2020**, 56, 5995–6006. [Google Scholar] [CrossRef] - Sungyoul, P.; Kwangseok, O.; Yonghwan, J. Model predictive control-based fault detection and reconstruction algorithm for longitudinal control of autonomous driving vehicle using multi-sliding mode observer. Microsyst. Technol.
**2020**, 26, 239–264. [Google Scholar] - Ge, L.; Zhao, Y.; Ma, F.; Guo, K. Towards longitudinal and lateral coupling control of autonomous vehicles using offset free MPC. Control Eng. Pract.
**2022**, 121, 105074. [Google Scholar] [CrossRef] - Wang, Y.; Shao, Q.; Zhou, J.; Zheng, H.; Chen, H. Longitudinal and lateral control of autonomous vehicles in multi-vehicle driving environments. IET Intell. Transp. Syst.
**2020**, 14, 924–935. [Google Scholar] [CrossRef] - Vicente, B.A.H.; James, S.S.; Anderson, S.R. Linear System Identification Versus Physical Modeling of Lateral–Longitudinal Vehicle Dynamics. IEEE Trans. Control Syst. Technol.
**2020**, 29, 1380–1387. [Google Scholar] [CrossRef] - Guo, J.H.; Li, K.Q.; Luo, Y.G. Coordinated Control of Autonomous Four Wheel Drive Electric Vehicles for Platooning and Trajectory Tracking Using a Hierarchical Architecture. J. Dyn. Syst. Meas. Control
**2015**, 137, 101001. [Google Scholar] [CrossRef] - Zhao, H.; Sun, D.; Zhao, M.; Pu, Q.; Tang, C. Combined Longitudinal and Lateral Control for Heterogeneous Nodes in Mixed Vehicle Platoon Under V2I Communication. IEEE Trans. Intell. Transp. Syst.
**2021**, 23, 6751–6765. [Google Scholar] [CrossRef] - Han, H.; Liu, H.; Liu, Z.; Qiao, J. Interactive Transfer Learning-Assisted Fuzzy Neural Network. IEEE Trans. Fuzzy Syst.
**2021**, 30, 1900–1913. [Google Scholar] [CrossRef] - Sohn, C.; Andert, J.; Manfouo, R.N.N. A Driveability Study on Automated Longitudinal Vehicle Control. IEEE Trans. Intell. Transp. Syst.
**2020**, 21, 3273–3280. [Google Scholar] [CrossRef] - Huang, Y.; Chen, Y. Vehicle Lateral Stability Control Based on Shiftable Stability Regions and Dynamic Margins. IEEE Trans. Veh. Technol.
**2020**, 69, 14727–14738. [Google Scholar] [CrossRef] - Sun, X.; Wang, G.; Fan, Y. Adaptive trajectory tracking control of vector propulsion unmanned surface vehicle with disturbances and input saturation. NonlinearDyn.
**2021**, 106, 2277–2291. [Google Scholar] [CrossRef] - Verma, B.; Padhy, P.K. Robust Fine Tuning of Optimal PID Controller with Guaranteed Robustness. IEEE Trans. Ind. Electron.
**2020**, 67, 4911–4920. [Google Scholar] [CrossRef] - Zhao, P.; Chen, J.J.; Song, Y.; Tao, X.; Xu, T.; Mei, T. Design of a Control System for an Autonomous Vehicle Based on Adaptive-PID. Int. J. Adv. Robot. Syst.
**2012**, 9, 44–46. [Google Scholar] [CrossRef] - Victor, S.; Receveur, J.-B.; Melchior, P.; Lanusse, P. Optimal Trajectory Planning and Robust Tracking Using Vehicle Model Inversion. IEEE Trans. Intell. Transp. Syst.
**2021**, 23, 4556–4569. [Google Scholar] [CrossRef] - Attia, R.; Orjuela, R.; Basset, M. Combined longitudinal and lateral control for automated vehicle guidance. Veh. Syst. Dyn.
**2014**, 52, 261–279. [Google Scholar] [CrossRef] [Green Version]

**Figure 6.**Comparison results of racing position tracking. (

**a**) Lateral position. (

**b**) Longitudinal position.

Time/s | Steering Wheel Angle/Deg |
---|---|

0 | 0 |

1 | 20 |

2 | 40 |

3 | 20 |

4 | 0 |

5 | −20 |

6 | −40 |

7 | −20 |

8 | 0 |

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**MDPI and ACS Style**

Tao, H.; Yang, B.
Coordinated Control of Unmanned Electric Formula Car. *World Electr. Veh. J.* **2023**, *14*, 58.
https://doi.org/10.3390/wevj14030058

**AMA Style**

Tao H, Yang B.
Coordinated Control of Unmanned Electric Formula Car. *World Electric Vehicle Journal*. 2023; 14(3):58.
https://doi.org/10.3390/wevj14030058

**Chicago/Turabian Style**

Tao, Hua, and Baocheng Yang.
2023. "Coordinated Control of Unmanned Electric Formula Car" *World Electric Vehicle Journal* 14, no. 3: 58.
https://doi.org/10.3390/wevj14030058