Introduction

opty utlizes 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 continous 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 elimantes 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:

• sympy 0.7.6
• ipopt 3.11
• numpy 1.8.1
• scipy 0.14.1
• cython
• cyipopt 0.1.4

To run the examples the following additional dependencies are required:

• matplotlib 1.3.1
• pydy 0.2.1
• tables

First you must install IPOPT along with it's headers. For example on Debian based systems you can use the package manager:

$ sudo apt-get install coinor-libipopt1 coinor-libipopt-dev

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.

Install conda then create an environment:

$ conda create -n opty pip numpy scipy cython matplotlib pytables
$ source activate opty
(opty)$ pip install https://github.com/sympy/sympy/releases/download/sympy-0.7.6.rc1/sympy-0.7.6.rc1.tar.gz
(opty)$ pip install pydy
(opty)$ pip install https://bitbucket.org/moorepants/cyipopt/get/tip.zip
(opty)$ pip install -e /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:

(opty)$ cd examples/
(opty)$ python pendulum_swing_up.py