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Working DDP for linear systems

Carlos Mastalli requested to merge CM-devel into master

This PR contains major core improvement of the DDP, I briefly describe them:

  • Common abstraction for terminal and running cost functions.
  • Data creation for a stack of terminal and running cost functions.
  • Function for computing all quantities in the cost and dynamics abstract classes.
  • Coding a Tassa's regularization and line search.
  • Creating a spring-mass system for DDP unit-testing.
  • Adding asserts for critical components.
  • Numerical differentiation abstraction.
  • Data structure and numerical differentiation for classical and diffeomorphic systems.
  • Unit-test for DDP with linear system (i.e. spring mass).
  • Unit-test for quadratic cost functions and its derivatives.
  • Unit-test for numerical differentiation.
  • Extended, but no finished, documentation of core classes.

@nmansard, @jcarpent and @rbudhira please take time for reviewing these core changes. There is still a lot of to be done but it's time to have some loop closure. Just to quickly mention, this is a short TODO:

  • Using the integrator class for integrating the derivatives of dynamics and cost functions.
  • Adding the manipulation problem, and potentially a sort of unit-test.
  • Adding the improved version of the regularization and line search.
  • Adding the locomotion problem?

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