Self-Optimizing Path Tracking Controller for Intelligent Vehicles Based on Reinforcement Learning
Abstract
:1. Introduction
- In this paper, we propose a self-optimized PID controller with a new adaptive updating rule, based on a reinforcement learning framework for autonomous vehicle path tracking control systems, in order to track a predefined path with high accuracy and, simultaneously, provide a comfortable riding experience.
- According to the pre-defined path geometry and the real-time status of the vehicle, the environment interactive learning mechanism, based on RL framework, can realize the online self-tuning of PID control parameters.
- In order to verify the stability and generalizability of the controller under complex paths and variable speed conditions, the proposed self-optimizing controller was tested in different path tracking scenarios. Finally, a realistic vehicle platform test was carried out to validate the practicability.
2. Vehicle Dynamic Constraints and Reference Trajectory Generation
- By ignoring the movement in the Z-axis direction, only the movement in the XY horizontal plane is considered; this is referred to as the planar bicycle model.
- By assuming that the rotation angles of the tires on the left and right sides of the vehicle body are identical, the tires on both sides can be combined into one tire.
- The rear wheels are not considered as steering wheels; only the front wheels are.
- The aerodynamic forces are ignored.
- (a)
- State space variable description
- (b)
- Action space variable description
- (c)
- Reward function description
3. Self-Optimizing Path Tracking Controller Based on a Reinforcement Learning (RL) Framework
- (1)
- Initialize the state of the controlled object, including the initial position and heading angle of the vehicle.
- (2)
- Pre-set the parameters for the optimizing controller, including the weight of the actor–critic network, the learning rate, the discount factor, and the selection of the activation function.
- (3)
- Adopt the DDPG algorithm to train the model, where the actor network outputs the PID gain, and the critic network maximizes the total reward value.
- (4)
- According to the calculation formula for the self-optimizing PID controller, calculate the control commands.
- (5)
- Use the time series control commands to act on the controlled object, while simultaneously observing the state of the environment at the next moment and calculating the reward function value.
- (6)
- The actor network uses the DDPG algorithm to update its own weights. The critic network updates its weight, based on the mean squared error (MSE) loss function.
- (7)
- If the system performance indicators meet the given requirements, or the maximum number of run episodes is reached, the training is terminated, the execution process is exited, and the experiment state is reset.
- a.
- Actor–critic network architecture design
- b.
- RL deep deterministic policy gradient (DDPG) algorithm
Algorithm 1. Pseudo-code programming process of the deterministic policy gradient (DDPG) algorithm |
Actor uses a gradient algorithm to update the network parameters; Critic uses the mean squared error (MSE) loss function to update the network parameters. Algorithm input: Episode number, T; state dimension, n; action set, A; learning rate, α,β; discount, γ; exploration rate, ; actor–critic network structure; randomly initialize the weighting parameter. |
Algorithm output: Actor network parameters, , critic network parameters, . |
1: for Episode from 1 to (Max Episode -1) do |
2: Receive initial observation state, obtain environment state vector . |
3: Initialize buffer replay data-buff. |
3: for t from 1 to T do |
4: Select action . |
5: Execute action and observe new state . Calculate instant reward feedback. |
6: Store transition in data-buff. |
7: Random mini-batch of N transitions from data-buff. |
8: Set . 9: Update critic by minimizing MSE loss function: 10: . |
11: Update the actor policy using the policy gradient function: 12: . 13: Update the target networks: 14: , 15: . 16: End for time step 17: End for Episode |
4. Experiment and Analysis of Results
4.1. Experimental Setting
- a.
- Simulation experiment platform
- b.
- Realistic autobus experiment platform
- c.
- Software version and hardware computing platform
4.2. Performance Verification and Results Analysis
- a.
- Simulation experiment setup and performance during training process
- b.
- Evaluating the performance of self-optimizing proportional–integral–derivative (PID) controller, based on RL framework
- The smoothness indicator represents the comfort resulting from the path-following control. In this paper, the vibration amplitude of the steering wheel was used to represent the smoothness indicator.
- The lateral track error, , and heading angle error, Δφ, evaluate the effects of the path tracking.
- The maximum speed and average speed indicators characterize the driving efficiency.
- c.
- Generalization of self-optimizing PID controller based on the RL framework
- d.
- Steering of a realistic autobus platform, based on the self-optimizing PID controller
5. Conclusions
6. Discussion of Limitations and Future Work
Author Contributions
Funding
Conflicts of Interest
References
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Symbol | Parameter | Units |
---|---|---|
Front and rear tires longitudinal force | N | |
Front and rear tires lateral force | N | |
Front and rear tires force in the x direction | N | |
Front and rear tires force in the y direction | N | |
a | Front axle to center of gravity (CG) | m |
b | Rear axle to CG | m |
Steer angle input | Rad | |
Front tire slip | rad | |
Yaw rate | rad/s | |
e | Lateral path deviation | m |
Vehicle heading deviation | rad | |
Longitudinal velocity | m/s |
Hyper-Parameter | Pre-Set Value |
---|---|
Actor network learning rate | 0.001 |
Critic network learning rate | 0.01 |
State space dimension | 4 |
Action space dimension | 4 |
Discount factor | 0.95 |
Run max episode | 200,000 |
Sensors | Position | Function Description | Precision |
---|---|---|---|
GPS+IMU *1 | Top | Precise location of the vehicle. | Positioning accuracy: 5 cm |
IBEO Lidar *6 | Front, Rear | 1. Vehicle, pedestrian detection. 2. Relative distance, speed, angle | Detection accuracy: 90% Effective distance: 80 m |
ESR Radar *6 | Front, Rear | 1. Long-distance obstacle detection. 2. Road edge detection. | Detection accuracy: 90% Effective distance: 120 m |
Vision Camera *12 | Front, Rear Top sides | 1. Traffic light status detection. 2. Lane line detection. | Detection accuracy: 95% Effective angle: 178° |
Ultrasonic radar *8 | Front, Rear, Both sides | 1. Short-distance obstacle detection. 2. Blind field detection. | Detection accuracy: 90% 360° coverage |
Vehicle Information Parameters | |||
---|---|---|---|
Length (mm) | 8010 | Maximum Total Mass (kg) | 13000 |
Width (mm) | 2390 | Front Suspension/Rear Suspension (mm) | 1820/1690 |
Height (mm) | 3090 | Approach Angle/Departure Angle (°) | 8/12 |
Wheelbase (mm) | 4500 | Maximum Speed (km/h) | 69 |
Turning Radius (mm) | 9000 | Tire Size × Number | 245/70R19.5 × 4 |
Software and Hardware Technical Parameters of the On-Board Computing Unit | ||
---|---|---|
| GPU | 512-core Volta GPU with Tensor Core |
CPU | 8-core ARM 64-bit CPU | |
RAM | 32 GB | |
Compute DL-TOPs | 30 TOPs | |
Operating system | Ubuntu 18.04 | |
RL framework | Tensorflow-1.14 |
Number Episode | Iteration Step | Drive Distance | Training Time | |
---|---|---|---|---|
Map-A | 180 | 8858 | 2387.64 | 0.75 h |
Map-B | 210 | 16,139 | 3242.83 | 1.2 h |
Map-C | 410 | 38,926 | 2935.72 | 2.3 h |
Map-D | 600 | 61,538 | 6470.38 | 3.6 h |
Number Episode | Iteration Step | Drive Distance | Training Time | |
---|---|---|---|---|
Map-A | 2 | 3858 | 2987.4 | 9.8 min |
Map-B | 2 | 5139 | 3642.3 | 11.2 min |
Map-C | 3 | 6926 | 4732.8 | 13.1 min |
Map-D | 3 | 8738 | 6870.2 | 18.3 min |
Standard Deviation | Minimum | Maximum | |
---|---|---|---|
PID−Steer | 0.11785 | −0.5 | 0.17068 |
RL−Steer | 0.13907 | −0.96124 | 0.18131 |
PID−RL−Steer |
Standard Deviation | Minimum | Maximum | |
---|---|---|---|
PID−cross−track error (CTE) | 0.1616 | −0.12305 | 0.33338 |
RL−CTE | 0.1220 | −0.17023 | 0.34481 |
PID−RL−CTE |
Standard Deviation | Minimum | Maximum | |
---|---|---|---|
PID-Head | 0.0343 | −0.0247 | 0.0625 |
RL-Head | 0.0349 | −0.0353 | 0.0534 |
PID–RL-Head |
Mean | Standard Deviation | Sum | Minimum | Median | Maximum | |
---|---|---|---|---|---|---|
0.84623 | 0.21836 | 206.48024 | 0.15364 | 0.86328 | 1.49518 | |
0.59826 | 0.10214 | 145.97583 | 0.33797 | 0.59185 | 0.87246 | |
0.90078 | 0.05179 | 219.78983 | 0.75222 | 0.90156 | 1.0384 | |
0.30479 | 0.05151 | 74.36867 | 0.16412 | 0.30233 | 0.42815 |
50 km/h Driving Condition on the Road of Map-E | ||||
Mean | Standard Deviation | Minimum | Maximum | |
PID–RL Controller | 0.09325 | −0.32759 | ||
ADRC-Controller | −0.06622 | 0.10941 | −0.37658 | 0.18714 |
60 km/h Driving Condition on Road of Map-E | ||||
Mean | Standard Deviation | Minimum | Maximum | |
PID–RL Controller | 0.10994 | −0.35013 | ||
ADRC-Controller | −0.04492 | 0.10508 | −0.37490 | 0.27655 |
Indicators | Mean | Standard Deviation | Minimum | Maximum | |
---|---|---|---|---|---|
PID Controller | Speed | 41.0455 | 8.4158 | 0 | 55 |
Lateral error | −0.1030 | 0.3573 | −1.1125 | 0.9966 | |
PID–RL Controller | Speed | 84.6887 | 16.9462 | 0 | 101 |
Lateral error | −0.0137 | 0.1089 | −0.3844 | 0.6640 | |
Human Driver | Speed | 51.5378 | 11.8857 | 0 | 71 |
Lateral error | −0.0014 | 0.1135 | −0.6068 | 0.5521 |
Mean | Standard Deviation | Minimum | Maximum | |
---|---|---|---|---|
Human−steer | −22.15445 | 69.05777 | −386 | 325 |
PID−Steer | −42.81777 | 88.80323 | −447 | 536 |
PID−RL−Steer | −22.06958 ↓ | 80.69866 ↓ | −390.8 ↓ | 403.2 ↓ |
Mean | Standard Deviation | Minimum | Median | Maximum | |
---|---|---|---|---|---|
53.84405 | 10.34426 | 16.2258 | 56.0301 | 79.3932 | |
92.10457 | 2.05332 | 85.6766 | 92.0764 | 98.2066 | |
39.07703 | 0.49852 | 37.5222 | 39.0849 | 40.747 | |
6.46417 | 0.24382 | 5.6081 | 6.46435 | 7.1453 |
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Ma, J.; Xie, H.; Song, K.; Liu, H. Self-Optimizing Path Tracking Controller for Intelligent Vehicles Based on Reinforcement Learning. Symmetry 2022, 14, 31. https://doi.org/10.3390/sym14010031
Ma J, Xie H, Song K, Liu H. Self-Optimizing Path Tracking Controller for Intelligent Vehicles Based on Reinforcement Learning. Symmetry. 2022; 14(1):31. https://doi.org/10.3390/sym14010031
Chicago/Turabian StyleMa, Jichang, Hui Xie, Kang Song, and Hao Liu. 2022. "Self-Optimizing Path Tracking Controller for Intelligent Vehicles Based on Reinforcement Learning" Symmetry 14, no. 1: 31. https://doi.org/10.3390/sym14010031