.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/plot_forward_sim.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_plot_forward_sim.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_plot_forward_sim.py:


Forward Simulation
==================

This example simulates and visualizes the uncontrolled motion of the model such
that the model falls down on the treadmill. It also compares the evaluation
speed of PyDy's and Autolev's models.

.. GENERATED FROM PYTHON SOURCE LINES 9-21

.. code-block:: Python

    import timeit

    from algait2de.gait2de import evaluate_autolev_rhs
    from pydy.codegen.ode_function_generators import generate_ode_function
    from pygait2d import derive, simulate
    from pygait2d import utils
    from scipy.integrate import odeint
    import matplotlib.pyplot as plt
    import numpy as np
    import sympy as sm
    import yaml








.. GENERATED FROM PYTHON SOURCE LINES 22-24

Derive the equations of motion, including a constant treadmill motion and
passive joint torques.

.. GENERATED FROM PYTHON SOURCE LINES 24-29

.. code-block:: Python

    symbolics = derive.derive_equations_of_motion(treadmill=True,
                                                  passive_torques=True,
                                                  stiffness_exp=3,
                                                  )
                                              







.. GENERATED FROM PYTHON SOURCE LINES 30-32

Load a parameter mapping from pygait2d symbol to numerical value, as well as
a mapping of the symbol string to numerical value.

.. GENERATED FROM PYTHON SOURCE LINES 32-43

.. code-block:: Python

    try:
        par_map = simulate.load_constants(symbolics.constants,
                                          'example_constants.yml')
        with open('example_constants.yml', 'r') as f:
            constants_dict = yaml.load(f, Loader=yaml.SafeLoader)
    except FileNotFoundError:
        par_map = simulate.load_constants(symbolics.constants,
                                          'examples/example_constants.yml')
        with open('examples/example_constants.yml', 'r') as f:
            constants_dict = yaml.load(f, Loader=yaml.SafeLoader)








.. GENERATED FROM PYTHON SOURCE LINES 44-48

Use PyDy to generate a function that can evaluate the right hand side of the
ordinary differential equations of the multibody system. This uses PyDy's
code generation settings that result in the fastest numerical evaluation
times at the cost of a slower code generation and compilation time.

.. GENERATED FROM PYTHON SOURCE LINES 48-62

.. code-block:: Python

    rhs = generate_ode_function(
        symbolics.kanes_method.forcing,
        symbolics.coordinates,
        symbolics.speeds,
        constants=list(par_map.keys()),
        mass_matrix=symbolics.kanes_method.mass_matrix,
        coordinate_derivatives=sm.Matrix(symbolics.speeds),
        specifieds=symbolics.specifieds,
        generator='cython',
        linear_sys_solver='sympy',
        constants_arg_type='array',
        specifieds_arg_type='array',
    )








.. GENERATED FROM PYTHON SOURCE LINES 63-64

Prepare numerical arrays to be passed to the ODE functions.

.. GENERATED FROM PYTHON SOURCE LINES 64-74

.. code-block:: Python

    specifieds_vals = np.zeros(len(symbolics.specifieds))  # zero torques
    specifieds_vals[-1] = 1.0  # treadmill speed

    args = (specifieds_vals, np.array(list(par_map.values())))

    initial_conditions = np.zeros(len(symbolics.states))
    initial_conditions[1] = 1.0  # set hip above ground
    initial_conditions[3] = np.deg2rad(5.0)  # right hip angle
    initial_conditions[6] = -np.deg2rad(5.0)  # left hip angle








.. GENERATED FROM PYTHON SOURCE LINES 75-76

Time the average execution of PyDy's ODE function evaluation.

.. GENERATED FROM PYTHON SOURCE LINES 76-79

.. code-block:: Python

    print('PyDy evaluation time:',
          timeit.timeit(lambda: rhs(initial_conditions, 0.0, *args), number=1000))





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    PyDy evaluation time: 0.003741227999853436




.. GENERATED FROM PYTHON SOURCE LINES 80-81

Time the average execution of Autolev s ODE function evaluation.

.. GENERATED FROM PYTHON SOURCE LINES 81-89

.. code-block:: Python

    autolev_constants_dict = simulate.map_values_to_autolev_symbols(constants_dict)
    print('Autolev evaluation time:',
          timeit.timeit(lambda: evaluate_autolev_rhs(initial_conditions[:9],
                                                     initial_conditions[9:],
                                                     specifieds_vals,
                                                     autolev_constants_dict),
                        number=1000))





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Autolev evaluation time: 0.005319942999904015




.. GENERATED FROM PYTHON SOURCE LINES 90-92

Simulate the model for two seconds using the LSODA integrator (switches
between stiff and non-stiff modes).

.. GENERATED FROM PYTHON SOURCE LINES 92-95

.. code-block:: Python

    time_vector = np.linspace(0.0, 2.0, num=61)
    trajectories = odeint(rhs, initial_conditions, time_vector, args=args)








.. GENERATED FROM PYTHON SOURCE LINES 96-97

Visualization of the resulting motion from the forward simulation.

.. GENERATED FROM PYTHON SOURCE LINES 97-106

.. code-block:: Python

    scene, fig, ax = utils.plot(symbolics, time_vector, initial_conditions,
                                args[0], args[1])
    ax.set_xlim((-0.8, 0.8))
    ax.set_ylim((-0.2, 1.4))
    ani = utils.animate(scene, fig, time_vector, trajectories,
                        np.zeros((len(time_vector), len(symbolics.specifieds))),
                        args[1])

    plt.show()



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     "


         /* set a timeout to make sure all the above elements are created before
            the object is initialized. */
         setTimeout(function() {
             anim76668fcd6d6346c49e9d0821953e3769 = new Animation(frames, img_id, slider_id, 33.0,
                                      loop_select_id);
         }, 0);
       })()
     </script>







.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 12.901 seconds)


.. _sphx_glr_download_examples_plot_forward_sim.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_forward_sim.ipynb <plot_forward_sim.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_forward_sim.py <plot_forward_sim.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_forward_sim.zip <plot_forward_sim.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_