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

Thai Duong

Nikolay Atanasov

Department of Electrical and Computer Engineering
University of California, San Diego
Robotics: Science and Systems, 2021.

[Paper]

[Code]

Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This motivates the use of machine learning techniques to approximate the robot dynamics over a training set of state-control trajectories. The dynamics of many robots, including ground, aerial, and underwater vehicles, are described in terms of their SE(3) pose and generalized velocity, and satisfy conservation of energy principles. This paper proposes a Hamiltonian formulation over the SE(3) manifold of the structure of a neural ordinary differential equation (ODE) network to approximate the dynamics of a rigid body. In contrast to a black-box ODE network, our formulation guarantees total energy conservation by construction. We develop energy shaping and damping injection control for the learned, potentially underactuated SE(3) Hamiltonian dynamics to enable a unified approach for stabiliziation and trajectory tracking with various platforms, including pendulum, rigid-body, and quadrotor systems.

Paper

Thai Duong, Nikolay Atanasov

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

Robotics: Science and Systems, 2020.

[pdf]

Overview and Results

Additional Details

Settings

Given a training dataset from the true dynamics, we want to find an approximated dynamics with parameter theta that minimizes the loss function.

The dynamics of many robots, including ground, aerial, and underwater vehicles, are described in terms of their SE(3) pose and generalized velocity, which evolves on the SE(3) manifold, and satisfy conservation of energy principles

To enforce these constraints by construction, we embed these constraints in the architecture of the parametric function approximated dynamics

We place the approximated dynamics function in a neural ODE framework (Chen et. al., NeurIPS'18) which predicts the state at a future time using an ODE solver and back-propagates the loss gradients efficiently using adjoint method.

For pendulum, we collect data by applying random control on a pendulum gym simulator. After learning the dynamics from data, we design an energy-based controller to drive the pendulum toward the upright position using the learned dynamics function.

For quadrotors, we use a crazyflie drone simulator in Pybullet and collect training data from 18 flights.

After learning the dynamics from data, we design an energy-based controller for trajectory tracking. We verify our controller design with a diamond-shaped trajectory. The Crazyflie simulated drone is able to track the trajectory using the learned Halmiltonian-based dynamics.

Code

[github]

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. Robotics: Science and Systems (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}
                                  

                                }

Acknowledgements

We gratefully acknowledge support from NSF RI IIS-2007141 and ARL DCIST CRA W911NF-17-2-0181.
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