Deep Dynamics is a physics-constrained neural network (PCNN) designed to model the complex dynamics observed in a high-speed, competitive racing environment. Using a historical horizon of the vehicle's state and control inputs, Deep Dynamics learns to produce accurate coefficient estimates for a dynamic single-track model that best describes the vehicle's motion. Specifically, this includes Pacejka Magic Formula coefficients for the front and rear wheels, coefficients for a linear drivetrain model, and the vehicle's moment of inertia. The Physics Guard layer ensures that estimated coefficients always lie within their physically-meaningful range, determined by the meaning behind each coefficient.

It is recommended to create a new conda environment:

conda create --name deep_dynamics python=3.10
conda activate deep_dynamics

To install Deep Dynamics:

git clone [email protected]:linklab-uva/deep-dynamics.git
cd deep-dynamics/
pip install -e .

Data collected from the Bayesrace vehicle dynamics simulator and the AV-21 full-scale autonomous racecar competing in the Indy Autonomous Challenge run by the Cavalier Autonomous Racing Team is provided for training and testing.

Bayesrace:

1. deep_dynamics/data/DYN-PP-ETHZ.npz
2. deep_dynamics/data/DYN-PP-ETHZMobil.npz

Indy Autonomous Challenge (IAC):

1. deep_dynamics/data/LVMS_23_01_04_A.csv
2. deep_dynamics/data/LVMS_23_01_04_B.csv
3. deep_dynamics/data/Putnam_park2023_run2_1.csv
4. deep_dynamics/data/Putnam_park2023_run4_1.csv
5. deep_dynamics/data/Putnam_park2023_run4_2.csv

To convert data from Bayesrace to the format needed for training:

cd tools/
./bayesrace_parser.py {path to dataset} {historical horizon size}

Historical horizon size refers to the number of historical state and control input pairs used as features during training. The process is similar for IAC data:

cd tools/
./csv_parser.py {path to dataset} {historical horizon size}

The resulting file will be stored under {path to dataset}_{historical_horizon_size}.npz.

Configurations for Deep Dynamics and the closely related Deep Pacejka Model are provided under deep_dynamics/cfgs/. The items listed under PARAMETERS are the variables estimated by each model. The ground-truth coefficient values used for the Bayesrace simulator are displayed next to each coefficient (i.e. Bf: 5.579 indicates the coefficient Bf was set to 5.579). The ground-truth values are only used for evaluation purposes, they are not accessible to the models during training. The Physics Guard layer requires ranges for the coefficients estimated by Deep Dynamics and can be specified with the Min and Max arguments.

Certain properties for the vehicle are required for training. Provided under VEHICLE_SPECS, this includes the vehicle's mass and the distance from the vehicle's center of gravity (COG) to the front and rear axles (lf and lr). The Deep Pacejka Model also requires the vehicle's moment of inertia (Iz) is specified.

Under MODEL, the layers for each model can be specified. The HORIZON refers to the historical horizon of state and control inputs used as features. Under LAYERS, the input and hidden layers of the model can be specified. Lastly, the optimization parameters are provided under OPTIMIZATION.

To run an individual training experiment, use:

cd deep_dynamics/model/
python3 train.py {path to cfg} {path to dataset} {name of experiment}

The optional flag --log_wandb can also be added to track results using the Weights & Biases Platform. Model weights will be stored under ../output/{name of experiment} whenever the validation loss decreases below the previous minima.

To run multiple trials in parallel for hyperparameter tuning, use:

cd deep_dynamics/model/
python3 tune_hyperparameters.py {path to cfg}

The desired dataset must be manually specified within tune_hyperparameters.py as well as the ranges for the hyperparameter tuning experiment. Trials are run using the RayTune scheduler.

To evaluate an individual model, use:

cd deep_dynamics/model/
python3 evaluate.py {path to cfg} {path to dataset} {path to model weights}

This will evaluate the model's RMSE and maximum error for the predicted state variables across the specified dataset. Additionally, the optional flag --eval_coeffs can be used to compare the mean and standard deviation of the model's internally estimated coefficients.

To evaluate multiple trials from hyperparameter tuning, use:

cd deep_dynamics/model/
python3 test_hyperparameters.py {path to cfg}

You can cite this work using:

@ARTICLE{10499707,
  author={Chrosniak, John and Ning, Jingyun and Behl, Madhur},
  journal={IEEE Robotics and Automation Letters}, 
  title={Deep Dynamics: Vehicle Dynamics Modeling With a Physics-Constrained Neural Network for Autonomous Racing}, 
  year={2024},
  volume={9},
  number={6},
  pages={5292-5297},
  keywords={Vehicle dynamics;Mathematical models;Tires;Solid modeling;Predictive models;Physics;Autonomous vehicles;Deep learning methods;model learning for control;dynamics},
  doi={10.1109/LRA.2024.3388847}}

You can also read my Master's thesis on this work here :)