initial commit

.gitignore

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+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+
+# C extensions
+*.so
+
+# Distribution / packaging
+.Python
+env/
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.coverage
+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*,cover
+.hypothesis/
+
+# Translations
+*.mo
+*.pot
+
+# Django stuff:
+*.log
+local_settings.py
+
+# Flask stuff:
+instance/
+.webassets-cache
+
+# Scrapy stuff:
+.scrapy
+
+# Sphinx documentation
+docs/_build/
+
+# PyBuilder
+target/
+
+# Jupyter Notebook
+.ipynb_checkpoints
+
+# pyenv
+.python-version
+
+# celery beat schedule file
+celerybeat-schedule
+
+# dotenv
+.env
+
+# virtualenv
+.venv/
+venv/
+ENV/
+
+# Spyder project settings
+.spyderproject
+
+# Rope project settings
+.ropeproject
+
+# Mac os files
+.DS_store
+
+# Pycharm project files:
+.idea/
+/.project

LICENSE

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+MIT License
+
+Copyright (c) 2020 Michael Lutter
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

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+# Deep Lagrangian Networks
+The open-source implementation of Deep Lagrangian Networks presented in 
+- [Lutter et. al., (2019). Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning, \
+International Conference on Learning Representations (ICLR)](https://arxiv.org/abs/1907.04490).
+
+- [Lutter et. al., (2019). Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems,\
+ International Conference on Intelligent Robots & Systems (IROS)](https://arxiv.org/abs/1907.04489).
+
+**Abstract:** \
+Models describing the dynamics of the robot and its environment are essential to achieve precise control as well as 
+sample-efficient reinforcement learning.  Currently, engineers prefer manually engineered models due to the physical
+plausibility and robust generalization despite their labor intensive development.  To learn models that are physically
+plausible and achieve better generalization, we proposed Deep Lagrangian Networks (DeLaN). DeLaN uses the Euler-Lagrange
+differential equation from Lagrangian mechanics to derive an optimization objective that guarantees physical plausible models.
+Let $`V(\mathbf{q};\: \psi)`$ and $`T(\mathbf{q}, \dot{\mathbf{q}}; \: \psi)`$
+be deep networks representing potential and kinetic energy, then the motor torques can be computed using the Euler-Lagrange 
+differential equation and the network parameters can be learned by minimizing the residual between the predicted and 
+measured torques. Therefore, the structured objective regularizes the learning to achieve noise robustness and enables 
+the unsupervised learning of the system energies as well as gravitational, inertial and Coriolis forces. The retrieval 
+of the interpretable energies and forces is especially remarkable as these quantities cannot be recovered with other 
+grey- or black-box model learning approaches.
+
+<img src="figures/DeLaN_Networks.png" alt="drawing" width="400" align="middle"/>  
+
+Figure 1: The network structure and loss of Deep Lagrangian Networks
+
+**Example:** \
+In this example, we apply Deep Lagrangian Networks to a simulated two degree of freedom robot. For training the robots
+executes different trajectories resembling characters and records the trajectory as well as motor torques. The recorded 
+trajectory data is then used to train Deep Lagrangian Netorks using Adam. Thereby, DeLaN learns the force decomposition 
+into inertial, Coriolis & centrifugal and gravitatonal forces unsupervised from the super-imposed torques. The force 
+decomposition for testing characters not part of the training set is shown in Figure 2. DeLaN learns the true underlying
+decomposition and achieves low mean squared error on the test data (Table 1). DeLaN is computationally efficient and 
+achieves one-step prediciton with an average frequency of 1500Hz. Therefore, DeLaN can be used in real-time control applications. 
+```
+                Torque MSE = 4.327e-04
+              Inertial MSE = 7.338e-04
+Coriolis & Centrifugal MSE = 2.227e-04
+         Gravitational MSE = 7.338e-04
+    Power Conservation MSE = 4.456e-05
+      Comp Time per Sample = 6.590e-04s / 1517.4Hz
+```
+Table 1: The mean squared error of the learned force decomposition compared to the ground truth decomposition as well as 
+the average computation time per sample on a AMD 3950 CPU.   
+
+<img src="figures/DeLaN_Performance.png" alt="drawing" width="1000" align="middle"/>  
+
+Figure 2: (a) The torque $`\bm{\tau}`$ required to generate the characters 'a', 'd' and 'e' in black. Using these samples \acronym was trained offline and learns the red trajectory. DeLaN can not only learn the desired torques but also disambiguate the individual torque components even though DeLaN was trained on the super-imposed torques. Using the Euler-Lagrange equation, the inertial force $`\mathbf{H}(\mathbf{q})\ddot{\mathbf{q}}`$ (b), the Coriolis and Centrifugal forces $`\mathbf{c}(\mathbf{q}, \dot{\mathbf{q}})`$ (c) and the gravitational force $`\mathbf{g}(\mathbf{q})`$ can be computed.
+
+**Installation:** \
+For installation this python package can be cloned and installed via pip
+```
+git clone https://github.com/milutter/deep_lagrangian_networks.git deep_lagrangian_networks
+pip install deep_lagrangian_networks
+
+python deep_lagrangian_networks/example_DeLaN.py -r 1
+```
+
+**Citation:** \
+If you use this implementation within your paper, please cite:
+
+```
+@inproceedings{lutter2019deep,
+  author =      "Lutter, M. and  Ritter, C. and  Peters, J.",
+  year =        "2019",
+  title =       "Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning",
+  booktitle =   "International Conference on Learning Representations (ICLR)",
+}
+
+@inproceedings{lutter2019energy,
+  author =      "Lutter, M. and  Listmann, K. and  Peters, J.",
+  year =        "2019",
+  title =       "Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems",
+  booktitle =   "International Conference on Intelligent Robots & Systems (IROS)",
+}
+```
+
+**Contact:** \
+If you have any further questions or suggestions, feel free to reach out to me via
+```michael AT robot-learning DOT de```
+