opty 0.1.1

Tools for optimizing dynamic systems using direct collocation.

Introduction

opty utilizes symbolic descriptions of ordinary differential 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. In general, if one can express the continuous first order ordinary differential 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 Jabcobian of the constraints, manually is a time consuming and error prone process. opty eliminates both of those issues.

Features

• Both implicit and explicit forms of the first order ordinary differential equations are supported, i.e. there is no need to solve for x’.

• Backward Euler or Midpoint integration methods.

• Supports both trajectory optimization and parameter identification.

• Easy specification of bounds on free variables.

• Easily specify additional “instance” constraints.

• Built with support of sympy.physics.mechanics in mind.

Installation

The core dependencies are as follows:

• python 2.7 or 3.5+

• sympy >= 0.7.6

• ipopt >= 3.11

• numpy >= 1.8.1

• scipy >= 0.14.1

• cython >= 0.20.1

• cyipopt >= 0.1.7

To run all of the examples the following additional dependencies are required:

• matplotlib >= 1.3.1

• pydy >= 0.2.1

• pytables

• pandas

• yeadon

If you are installing on Linux or Mac, the easiest way to get started is to install Anaconda (or Miniconda) and use conda to install all of the dependencies from the Conda Forge channel:

$ conda config --add channels conda-forge
$ conda install sympy numpy scipy cython ipopt cyipopt matplotlib pytables pydy pandas

Next download the opty source files and install with:

$ conda develop /path/to/opty

or:

$ cd /path/to/opty
$ python setup.py install

If you are using Windows or want a custom installation of 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 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 pip numpy scipy cython matplotlib pytables sympy pydy pandas
$ source activate opty
(opty)$ pip install https://github.com/matthias-k/cyipopt/archive/master.zip
(opty)$ conda develop /path/to/opty

Usage

There are several examples available in the examples directory. For example, the optimal torque to swing up a pendulum with minimal energy can be found with:

$ python examples/pendulum_swing_up.py