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
* A list of friction coefficients
* 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.
