# Trajectory Tracking Coordinated Control of 4WID-4WIS Electric Vehicle Considering Energy Consumption Economy Based on Pose Sensors

^{*}

## Abstract

**:**

## 1. Introduction

- A hierarchical architecture for chassis coordinated control is designed including target planning layer, and coordinated control layer.
- The MPC path tracking controller is constructed, which takes into account stability constraints, such as yaw rate and tire slip angle.
- The MPSO algorithm is also used to create a mapping of the distribution coefficients by optimizing the torque distribution between the front and rear wheels offline, thereby reducing the computational cost.

## 2. Trajectory Tracking Coordinated Control

#### 2.1. Vehicle Model

#### 2.1.1. Vehicle Dynamic Model

#### 2.1.2. Tire Model

#### 2.1.3. Motor Model

- In-wheel motor model

- 2.
- Steering Motor Model

#### 2.2. Vehicle State Acquisition

#### 2.3. Chassis Control Architecture

#### 2.4. Target Planning

#### 2.4.1. Longitudinal Velocity Tracking

- (1)
- When $\left|e\left(k\right)\right|>{M}_{max}$, it means that the velocity error is unacceptably large. At this time, the controller should be directly output at full load, that is, $u(k)={F}_{\mathrm{xmax}}$.
- (2)
- When $e\left(k\right)\ast \Delta e\left(k\right)>0,\Delta e\left(k\right)=0$, it means that the velocity deviation is changing in the direction of increasing the absolute value of the deviation, or the deviation is a certain fixed value, then$$u(k)=u(k-1)+{k}_{1}\left\{{k}_{i}e(k)+{k}_{p}\mathsf{\Delta}e(k)+{k}_{d}\Delta \mathsf{\Delta}e(k)\right\}$$

- (3)
- When $e(k)\mathsf{\Delta}e(k)<0,\mathsf{\Delta}e(k)\mathsf{\Delta}e(k-1)0,e(k)=0$, it means that the absolute value of the velocity deviation is changing in the direction of decreasing, or has reached the equilibrium state. Then, the controller output remains unchanged, that is, $u\left(k\right)=u\left(k-1\right)$.
- (4)
- When $e(k)\mathsf{\Delta}e(k)<0,\mathsf{\Delta}e(k)\mathsf{\Delta}e(k-1)0$, it means that the velocity deviation is in the limit state, then,$$u(k)=u(k-1)+{k}_{2}{k}_{i}e(k)$$

- (5)
- When $\left|e\left(k\right)\right|<{M}_{min}$, it means that the absolute value of the velocity deviation is very small. In order to reduce the static error of the system, PI control is implemented:$$u(k)=u(k-1)+{k}_{i}e(k)+{k}_{p}\mathsf{\Delta}e(k)$$

#### 2.4.2. Lateral Path Tracking

- Predictive model design

- 2.
- Objective function design

- 3.
- Constraints design

#### 2.5. Coordinated Control

#### 2.5.1. Torque Distribution Control

- The rule-based torque distribution control does not consider the operating efficiency of motor, resulting in unnecessary power loss.
- The real-time optimization of torque distribution places a large burden on the controller. The solution speed may be slow and this problem may even be unsolvable under certain working conditions.
- The economic evaluation generally uses the size of the control variables as the index, ignoring the efficiency characteristics of the motor. This is mainly due to the nonlinearity of the motor model, which makes it impossible to optimize the system efficiency in real-time.

- Left-right distribution

- 2.
- Front-rear distribution

- (1)
- The MPSO algorithm

- (2)
- Distribution coefficient optimization

- (3)
- Torque calculation for each wheel

#### 2.5.2. Wheel Angle Distribution Control

## 3. Simulation and Results

#### 3.1. Environment and Configuration

#### 3.1.1. Average Distribution Strategy

#### 3.1.2. Wheel Load Distribution Strategy

#### 3.2. Results and Analysis

#### 3.2.1. Single-Lane Change

- Trajectory tracking effect

- 2.
- Economy optimization effect

#### 3.2.2. Slalom Test

- Trajectory tracking effect

- 2.
- Economy optimization effect

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Velocity tracking results under single-lane change: (

**a**) The results of velocity; (

**b**) The results of longitudinal tracking error.

**Figure 9.**Path tracking results under single-lane change: (

**a**) The results of lateral displacement; (

**b**) The results of heading angle; (

**c**) The results of lateral displacement tracking error; (

**d**) The results of heading angle tracking error.

**Figure 13.**Wheel angles under single-lane change: (

**a**) Front-left wheel; (

**b**) Front-right wheel; (

**c**) Rear-left wheel; (

**d**) Rear-right wheel.

**Figure 17.**Velocity tracking results under slalom test: (

**a**) The results of velocity; (

**b**) The results of longitudinal tracking error.

**Figure 18.**Path tracking results under slalom test: (

**a**) The results of lateral displacement; (

**b**) The results of heading angle; (

**c**) The results of lateral displacement tracking error; (

**d**) The results of heading angle tracking error.

**Figure 22.**Wheel angles under slalom test: (

**a**) Front-left wheel; (

**b**) Front-right wheel; (

**c**) Rear-left wheel; (

**d**) Rear-right wheel.

Performance Index | 40 km/h | 80 km/h | 120 km/h | |
---|---|---|---|---|

Lateral displacement tracking error (m) | Maximum | 0.0115 | 0.0171 | 0.0234 |

Average | 0.0024 | 0.0036 | 0.0053 | |

Standard deviations | 0.0040 | 0.0058 | 0.0075 | |

Heading angle tracking error (rad) | Maximum | 0.0012 | 0.0036 | 0.0042 |

Average | 0.0002 | 0.0009 | 0.0009 | |

Standard deviations | 0.0004 | 0.0012 | 0.0012 |

Velocity (km/h) | Strategy | Maximum | Average |
---|---|---|---|

40 | Rule 1 | 0.7356 | 0.7303 |

Rule 2 | 0.7347 | 0.7283 | |

Rule 3 | 0.8411 | 0.8375 | |

80 | Rule 1 | 0.8969 | 0.8877 |

Rule 2 | 0.8970 | 0.8882 | |

Rule 3 | 0.9276 | 0.9241 | |

120 | Rule 1 | 0.8973 | 0.8791 |

Rule 2 | 0.8972 | 0.8793 | |

Rule 3 | 0.9147 | 0.9107 |

Performance Index | 30 km/h | 60 km/h | |
---|---|---|---|

Lateral displacement tracking error (m) | Maximum | 0.0412 | 0.0603 |

Average | 0.0158 | 0.0241 | |

Standard deviations | 0.0147 | 0.0214 | |

Heading angle tracking error (rad) | Maximum | 0.0058 | 0.0129 |

Average | 0.0011 | 0.0033 | |

Standard deviations | 0.0010 | 0.0029 |

Velocity (km/h) | Strategy | Maximum | Average |
---|---|---|---|

30 | Rule 1 | 0.6404 | 0.6151 |

Rule 2 | 0.6409 | 0.6121 | |

Rule 3 | 0.7857 | 0.7484 | |

60 | Rule 1 | 0.8973 | 0.7995 |

Rule 2 | 0.8971 | 0.7987 | |

Rule 3 | 0.9345 | 0.8829 |

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**MDPI and ACS Style**

Qiao, Y.; Chen, X.; Liu, Z.
Trajectory Tracking Coordinated Control of 4WID-4WIS Electric Vehicle Considering Energy Consumption Economy Based on Pose Sensors. *Sensors* **2023**, *23*, 5496.
https://doi.org/10.3390/s23125496

**AMA Style**

Qiao Y, Chen X, Liu Z.
Trajectory Tracking Coordinated Control of 4WID-4WIS Electric Vehicle Considering Energy Consumption Economy Based on Pose Sensors. *Sensors*. 2023; 23(12):5496.
https://doi.org/10.3390/s23125496

**Chicago/Turabian Style**

Qiao, Yiran, Xinbo Chen, and Zhen Liu.
2023. "Trajectory Tracking Coordinated Control of 4WID-4WIS Electric Vehicle Considering Energy Consumption Economy Based on Pose Sensors" *Sensors* 23, no. 12: 5496.
https://doi.org/10.3390/s23125496