Research on Trajectory Tracking Control of Driverless Electric Formula Racing Car Based on Game Theory
Abstract
:1. Introduction
2. Game Theory Based on Trajectory Tracking Control Strategy
3. Design of the Controller
3.1. The Whole Vehicle Parameters of Driverless Electric Formula Racing Car
3.2. Vehicle Dynamics Modeling
3.3. Tire Force Analysis
3.4. Design of Model Predictive Controller
3.5. The Design Requirements of the Objective Function
- 1.
- The tracking process maintains a small tracking error, and the error can converge to zero quickly and steadily, and remain balanced.
- 2.
- The front wheel angle control input in the tracking process is as small as possible, and the change should be smooth.
3.6. Evolutionary Game Model Predictive Controller Design
3.6.1. Determining the Players of the Evolutionary Game
3.6.2. Establishing the Game Gain Matrix
3.6.3. Determining the Payment Function
3.6.4. Constructing the Dynamic Replication System
3.6.5. Analyzing the Stability of the Evolutionary Game
3.6.6. Verifying the Stability of the Evolutionary Game
4. Verifying the Stability of the Evolutionary Game
4.1. Low-Speed Road Simulation Verification
4.2. Medium-Speed Pavement Simulation Verification
4.3. High-Speed Pavement Simulation Validation
5. Conclusions
- Our proposed trajectory tracking control strategy based on game theory effectively coordinates the weight coefficients of trajectory tracking accuracy and driving stability, solves the dual-objective optimization problem, and improves the trajectory tracking accuracy and driving stability.
- Combining the model predictive control with game theory, the model predictive controller based on the evolutionary game of both players is designed, the lateral error is controlled within 0.1 m, and the transverse swing angle error is controlled within 0.5 rad under the high-speed tracing condition, which has a smaller change of control increment and better control effect compared with the single model predictive controller.
- The model prediction controller based on the evolutionary game of both sides has good trajectory tracking with strong robustness at high, medium, and low speeds.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Symbol | Parameters | Value | Units |
---|---|---|---|
m | Vehicle mass | 260 | kg |
a | Distance from the center of mass to the front axis | 706.5 | mm |
b | Distance from the center of mass to the rear axis | 863.5 | mm |
L | Wheelbase of vehicle | 1570 | mm |
radius of wheel | 228.6 | mm | |
Height of the center of mass | 270 | mm | |
Gauge of the front axle | 1200 | mm | |
Gauge of the rear axle | 1180 | mm |
Player | Q | R |
---|---|---|
Strategy space | = (High accuracy, Low accuracy) | = (Low stability, High stability) |
Tracing Process and the Loss of Control Energy R | |||
---|---|---|---|
R1 Low stability (1 − x) | R2 High stability (x) | ||
Cumulative path deviation value Q | Q1 Low accuracy (y) | (A,E) | (B,F) |
Q2 High accuracy (1 − y) | (C,G) | (D,H) |
Equilibrium Point | ||
---|---|---|
0 |
Number | Equilibrium Point | Conditions | Stability | ||
---|---|---|---|---|---|
1 | + | - | ESS | ||
2 | - | Uncertain | Unstable | ||
3 | - | Uncertain | Unstable | ||
4 | + | - | ESS | ||
5 | Saddle point under any condition | Uncertain | 0 | Saddle point |
MPC Controller | MPC Controller Based on Game Theory | |
---|---|---|
Predicted time domain | 17 | 17 |
Control time domain | 9 | 9 |
Sampling period (s) | 0.01 | 0.01 |
Weight matrix coefficients |
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Share and Cite
Tian, T.; Li, G.; Li, N.; Bai, H. Research on Trajectory Tracking Control of Driverless Electric Formula Racing Car Based on Game Theory. World Electr. Veh. J. 2023, 14, 84. https://doi.org/10.3390/wevj14040084
Tian T, Li G, Li N, Bai H. Research on Trajectory Tracking Control of Driverless Electric Formula Racing Car Based on Game Theory. World Electric Vehicle Journal. 2023; 14(4):84. https://doi.org/10.3390/wevj14040084
Chicago/Turabian StyleTian, Tian, Gang Li, Ning Li, and Hongfei Bai. 2023. "Research on Trajectory Tracking Control of Driverless Electric Formula Racing Car Based on Game Theory" World Electric Vehicle Journal 14, no. 4: 84. https://doi.org/10.3390/wevj14040084