Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control

This repo provides code for our paper "Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control". Please check out our project website for more details: https://thaipduong.github.io/SE3HamDL/.

Dependencies

Our code is tested with Ubuntu 18.04 and Python 3.7. It depends on the following Python packages:

torchdiffeq 0.1.1

gym 0.18.0

gym-pybullet-drones: https://github.com/utiasDSL/gym-pybullet-drones

torch 1.4.0 and torch 1.9.0

numpy 1.20.1

scipy 1.5.3

matplotlib 3.3.4

Notes: For some reasons, the code does not work with torch 1.10.0. Pending investiation.

Demo with pendulum

Run python ./examples/pendulum/train_pend_SO3.py to train the model with data collected from the pendulum environment. It might take some time to train. A pretrained model is stored in ./examples/pendulum/data/pendulum-so3ham_ode-rk4-5p.tar

Run python ./examples/pendulum/analyze_pend_SO3.py to plot the generalized mass inverse M^-1(q), the potential energy V(q), and the control coefficient g(q)

Run python ./examples/pendulum/rollout_pend_SO3.py to verify that our framework respect energy conservation and SE(3) constraints by construction, and plots phase portrait of a trajectory rolled out from our dynamics.

Run python ./examples/pendulum/control_pend_SO3.py to test the energy-based controller with the learned dynamics.

Demo with quadrotor

Run python ./examples/quadrotor/train_quadrotor_SE3.py to train the model with data collected from the pybullet drone environment. It might take some time to train. A pretrained model is stored in ./examples/quadrotor/data/quadrotor-se3ham-rk4-5p.tar

Data collection

Run python ./examples/quadrotor/analyze_quadrotor_SE3.py to plot the generalized mass inverse M^-1(q), the potential energy V(q), and the control coefficient g(q)

Run python ./examples/quadrotor/rollout_quadrotor_SE3.py to verify that our framework respect energy conservation and SE(3) constraints by construction, and plots phase portrait of a trajectory rolled out from our dynamics.

Run python ./examples/quadrotor/control_quadrotor_SE3.py to test the energy-based controller with the learned dynamics.

Citation

If you find our papers/code useful for your research, please cite our work as follows.

1. T. Duong, N. Atanasov. Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control. RSS, 2021

@inproceedings{duong21hamiltonian,
author = {Thai Duong AND Nikolay Atanasov},
title = {{Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control}},
booktitle = {Proceedings of Robotics: Science and Systems},
year = {2021},
address = {Virtual},
month = {July},
DOI = {10.15607/RSS.2021.XVII.086} 
}