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opty utilizes symbolic descriptions of differential algebraic equations
expressed with SymPy to form the constraints needed to solve optimal control
and parameter identification problems using the direct collocation method and
non-linear programming (NLP). In general, if one can express the continuous
first order differential algebraic equations of the system as symbolic
expressions opty will automatically generate a function to efficiently
evaluate the dynamical constraints and a function that evaluates the sparse
Jacobian of the constraints, which have been optimized for speed and memory
consumption. The translation of the dynamical system description to the NLP
form, primarily the formation of the constraints and the Jacobian of the
constraints, manually is a time consuming and error prone process. opty
eliminates both of those issues.
- Both implicit and explicit forms of the first order ordinary differential equations and differential algebraic equations are supported, i.e. there is no need to solve for the derivatives of the dependent variables.
- Backward Euler or Midpoint integration methods.
- Supports both trajectory optimization and parameter identification, independently or simultaneously.
- Solve fixed duration or variable duration problems.
- Easy specification of bounds on free variables.
- Easily specify additional "instance" constraints.
- Efficient numerical execution of large equations of motion.
- Automatic parallel execution using openmp if installed.
- Built with support of sympy.physics.mechanics and PyDy in mind.
The required dependencies are as follows:
- cyipopt >= 1.1.0 [with ipopt >= 3.11 (Linux & OSX), >= 3.13 (Windows)]
- cython >= 0.29.19 [with a C compiler]
- numpy >= 1.19.0
- python 3.8-3.12
- scipy >= 1.5.0
- sympy >= 1.6.0
The optional dependencies are as follows:
- matplotlib >= 3.2.0
- openmp
To run all of the examples the following additional dependencies may be needed:
- pandas
- pydy >= 0.5.0
- pytables
- yeadon
The easiest way to install opty is to first install Anaconda (or Miniconda or Miniforge) and use the conda package manager to install opty and any desired optional dependencies from the Conda Forge channel, e.g. opty:
$ conda install --channel conda-forge opty
and the optional dependencies:
$ conda install --channel conda-forge matplotlib openmp pandas pydy pytables yeadon
Opty can be installed with pip, but this will require installing and compiling cyipopt if it is not already installed:
$ pip install opty
See the cyipopt documentation for information on installing that package.
If you want a custom installation of any of the dependencies, e.g. Ipopt, you must first install Ipopt along with it's headers. For example, on Debian based systems you can use the package manager:
$ sudo apt-get install coinor-libipopt1v5 coinor-libipopt-dev
or prebuilt binaries can be downloaded from https://www.coin-or.org/download/binary/Ipopt/.
For customized installation (usually desired for performance) follow the
instructions on the Ipopt documentation to compile the library. If you install
to a location other than /usr/local on Unix systems you will likely have to
set the LD_LIBRARY_PATH so that you can link to Ipopt when installing
cyipopt.
Once Ipopt is installed and accessible, install conda then create an environment:
$ conda create -n opty-custom -c conda-forge cython numpy pip scipy sympy $ source activate opty-custom (opty-custom)$ pip install cyipopt # this will compile cyipopt against the available ipopt (opty-custom)$ pip install opty
If you want to develop opty, create a conda environment with all of the dependencies installed:
$ conda config --add channels conda-forge $ conda create -n opty-dev python sympy numpy scipy cython ipopt cyipopt matplotlib pytables pydy pandas pytest sphinx sphinx-gallery numpydoc $ source activate opty-dev
Next download the opty source files and install with:
(opty-dev)$ cd /path/to/opty (opty-dev)$ python setup.py develop
There are several examples available in the examples and
examples-gallery directories. The optimal torque to swing up a pendulum
with minimal energy can be run with:
$ python examples-gallery/plot_pendulum_swing_up_fixed_duration.py
If compilation fails it may be helpful to manually compile the generated Cython
extension. To do so, provide a destination path to the tmp_dir kwarg when
you instantiate Problem(), e.g.:
p = Problem(..., tmp_dir='opty_source')You can then compile the files manually by navigating into the opty_source
directory and running:
$ cd /path/to/opty_source $ python ufuncify_matrix_X_setup.py build_ext --inplace
The highest integer value of X will be the most recently generated set of
source files.
Build the HTML documentation with:
(opty-dev)$ cd /path/to/opty/docs (opty-dev)$ make html
and open the result with your web browser, for example:
$ firefox _build/html/index.html
The work was partially funded by the State of Ohio Third Frontier Commission through the Wright Center for Sensor Systems Engineering (WCSSE), by the USA National Science Foundation under Grant No. 1344954, and by National Center of Simulation in Rehabilitation Research 2014 Visiting Scholarship at Stanford University, and the CZI grant CZIF2021-006198 and grant DOI https://doi.org/10.37921/240361looxoj from the Chan Zuckerberg Initiative Foundation (funder DOI 10.13039/100014989).
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