Inverse dynamics
================

Computation of the system inverse dynamics. It computes the required forces and 
torques in the actuated joints to follow a given motion. For more information, 
see `Robotran theoretical framework <http://robotran-doc.git-page.immc.ucl.ac.be/RobotranBasic/Robotran_basics.pdf>`_.

Code sample
-----------

For running the inverse dynamics, in the current configuration, insert the following 
code in your main script and adapt it to your need:

.. code-block:: python

    mbs_data.process = 6
    mbs_invdyn = MBsysPy.MbsInvdyn(mbs_data)
    mbs_invdyn.set_options(motion = "oneshot")
    mbs_invdyn.run()


You can compute the inverse dynamics for a time-define trajectory by providing the 
trajectory files as follow:

.. code-block:: python

    # Set all driven joint as independent
    mbs_data.set_qu(mbs_data.qc[1:].tolist())

    mbs_data.process = 6
    mbs_invdyn = MBsysPy.MbsInvdyn(mbs_data)

    # Set the motion to be solved as a trajectory
    mbs_invdyn.set_options(motion = "trajectory")

    # Provide the trajectory files to use
    mbs_invdyn.set_options(trajectoryqname = "../resultsR/inverse_kinematics_q.res",
                           trajectoryqdname = "../resultsR/inverse_kinematics_qd.res",
                           trajectoryqddname = "../resultsR/inverse_kinematics_qdd.res")

    # Provide the time interval and time step to solve the inverse dynamics.
    mbs_invdyn.set_options(t0 = 0.0, tf = 6.0, dt = 1e-3)
    # The final time "tf' must be less than the last time of the trajectory files.

    mbs_invdyn.run()

In all cases the analysis requires actuated joint, see next section to set them.

Use
---

.. py:currentmodule:: MBsysPy.mbsyspy.mbs_invdyn

The inverse dynamics computation is requires an instance of :py:class:`MbsInvdyn`. 
Then the analysis is performed by calling the function :py:func:`MbsInvdyn.run`.

The options of the module are set with the function :py:func:`MbsInvdyn.set_options`.

.. py:currentmodule:: MBsysPy.mbsyspy.mbs_data

The force and torques are computed on the actuated joints (see `Robotran 
theoretical framework <http://robotran-doc.git-page.immc.ucl.ac.be/RobotranBasic/Robotran_basics.pdf>`_). 
A joint is (de)selected as actuated with the function :py:func:`MbsData.set_qa` (resp. :py:func:`MbsData.unset_qa`).

Requirements on the system
--------------------------

The system either:

* contains independent joints:

  * The driven joints cannot be actuated;
  
  * The independent and dependent joint can be actuated;
  
  * The number of actuated joint must be equal or greather (over-actuated) than the number of independent joints.

* does not contain any independent joints:
  
  * The driven joints must be actuated;
  
  * The dependent joints cannot be actuated