# RobustEquilibriumLib
Utility classes to check the (robust) equilibrium of a system in contact with the environment.
The main class that collects all the equilibrium-related algorithms is ```StaticEquilibrium```.
All the algorithms take as input:
* A list of contact points
* A list of contact normals
* The contact friction coefficient
* The number of generators used for the linear approximations of the friction cones
* The mass of the system

Once these input parameters have been specified the user has access to four main algorithms:
* computeEquilibriumRobustness: compute the robustness of the equilibrium of a given a CoM (center of mass) position (negative values mean the system can not be in equilibrium).
* checkRobustEquilibrium: checks whether the system can be in equilibrium in a specified CoM position and with a specified robustness level.
* findExtremumOverLine: Find the extremum com position that is in robust equilibrium along the specified line.
* findExtremumInDirection: Find the extremum com position that is in robust equilibrium in the specified direction.

All these problems boil down to solving Linear Programs.
Different formulations are implemented and tested in ```test_static_equilibrium```.
More details can be found in the code documentation.
In the end, we found the dual LP formulation (DLP) to be the fastest.

The test ```test_LP_solvers``` tries to solve some LP problems using qpOases and checks that the results are correct.

## Dependencies
* [Eigen (version >= 3.2.2)](http://eigen.tuxfamily.org/index.php?title=Main_Page)
* [cdd lib](https://www.inf.ethz.ch/personal/fukudak/cdd_home/)
* [qpOases (version >= 3.0beta)](https://projects.coin-or.org/qpOASES)

You can install cdd lib under Ubuntu 12.04 with the following command:
```
sudo apt-get install libcdd-dev
```
For Eigen and qpOases follow the instructions at the relative webpage (links in the list above).

### Optional
As an alternative to qpOases you can use [CLP](https://projects.coin-or.org/Clp) to solve linear programs.
However, we found qpOases to be faster and more reliable, so we suggest you to stick with qpOases.