:orphan:

========
Examples
========



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Beginner
========



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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_path_constraints_thumb.png
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  :ref:`sphx_glr_examples_beginner_plot_path_constraints.py`

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      <div class="sphx-glr-thumbnail-title">Path Constraints</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_betts_10_7_thumb.png
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  :ref:`sphx_glr_examples_beginner_plot_betts_10_7.py`

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      <div class="sphx-glr-thumbnail-title">Hypersensitive Control</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_betts_10_50_thumb.png
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  :ref:`sphx_glr_examples_beginner_plot_betts_10_50.py`

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      <div class="sphx-glr-thumbnail-title">Delay Equation (Göllmann, Kern, and Maurer)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objective ---------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_pendulum_swing_up_fixed_duration_thumb.gif
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  :ref:`sphx_glr_examples_beginner_plot_pendulum_swing_up_fixed_duration.py`

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      <div class="sphx-glr-thumbnail-title">Fixed Duration Pendulum Swing Up</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_pendulum_swing_up_variable_duration_thumb.gif
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  :ref:`sphx_glr_examples_beginner_plot_pendulum_swing_up_variable_duration.py`

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      <div class="sphx-glr-thumbnail-title">Variable Duration Pendulum Swing Up</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This is the single parameter identification problem presented in section 7 of [Betts2003]_.">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_betts2003_thumb.png
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  :ref:`sphx_glr_examples_beginner_plot_betts2003.py`

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      <div class="sphx-glr-thumbnail-title">Parameter Identification: Betts & Huffman 2003</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example is taken from [Vyasarayani2011]_. In Section 3.1 there is a simple example of a single pendulum parameter identification that has many local minima.">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_vyasarayani_thumb.png
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  :ref:`sphx_glr_examples_beginner_plot_vyasarayani.py`

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      <div class="sphx-glr-thumbnail-title">Multi-minimum Parameter Identification</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objective ---------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_betts_10_103_104_thumb.png
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  :ref:`sphx_glr_examples_beginner_plot_betts_10_103_104.py`

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      <div class="sphx-glr-thumbnail-title">Compare DAE vs. ODE Formulation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Simulation of a particle subject to the force of gravity and air drag as it traverses an elevation profile with a specified numerical shape to reach the course finish line in minimal time.">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_hilly_race_thumb.gif
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  :ref:`sphx_glr_examples_beginner_plot_hilly_race.py`

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      <div class="sphx-glr-thumbnail-title">Hilly Race</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objective ---------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_brachistochrone_thumb.gif
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  :ref:`sphx_glr_examples_beginner_plot_brachistochrone.py`

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      <div class="sphx-glr-thumbnail-title">Brachistochrone</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_light_diffraction_thumb.gif
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  :ref:`sphx_glr_examples_beginner_plot_light_diffraction.py`

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      <div class="sphx-glr-thumbnail-title">Light Diffraction</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objective ---------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_sliding_block_thumb.gif
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  :ref:`sphx_glr_examples_beginner_plot_sliding_block.py`

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      <div class="sphx-glr-thumbnail-title">Block Sliding Over a Hill</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/beginner/images/thumb/sphx_glr_plot_wheel_on_bumpy_road_thumb.gif
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  :ref:`sphx_glr_examples_beginner_plot_wheel_on_bumpy_road.py`

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      <div class="sphx-glr-thumbnail-title">Quarter Car Model on a Bumpy Road</div>
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Intermediate
============



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    <div class="sphx-glr-thumbcontainer" tooltip="In parameter estimation it is common to collect measurements of a system&#x27;s trajectories from distinct experiments. For example, if you are identifying the parameters of a mass-spring-damper system, you may excite the system with different initial conditions multiple times and measure the position of the mass. The data cannot simply be stacked end-to-end in time and the identification run because the measurement data would be discontinuous between each measurement trial.">

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  .. image:: /examples/intermediate/images/thumb/sphx_glr_plot_non_contiguous_parameter_identification_thumb.png
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  :ref:`sphx_glr_examples_intermediate_plot_non_contiguous_parameter_identification.py`

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      <div class="sphx-glr-thumbnail-title">Parameter Identification from Noncontiguous Measurements</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Given the nonholonomic bicycle model of the car find a solution for parallel parking it.">

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  .. image:: /examples/intermediate/images/thumb/sphx_glr_plot_parallel_park_thumb.gif
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  :ref:`sphx_glr_examples_intermediate_plot_parallel_park.py`

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      <div class="sphx-glr-thumbnail-title">Parallel Park a Car</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/intermediate/images/thumb/sphx_glr_plot_countersteer_thumb.gif
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  :ref:`sphx_glr_examples_intermediate_plot_countersteer.py`

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      <div class="sphx-glr-thumbnail-title">Bicycle Countersteering</div>
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  .. image:: /examples/intermediate/images/thumb/sphx_glr_plot_crane_moving_a_load_thumb.png
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  :ref:`sphx_glr_examples_intermediate_plot_crane_moving_a_load.py`

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      <div class="sphx-glr-thumbnail-title">Crane Moving a Load</div>
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  .. image:: /examples/intermediate/images/thumb/sphx_glr_plot_two_link_pendulum_on_a_cart_thumb.gif
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  :ref:`sphx_glr_examples_intermediate_plot_two_link_pendulum_on_a_cart.py`

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      <div class="sphx-glr-thumbnail-title">Upright a Double Pendulum</div>
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  .. image:: /examples/intermediate/images/thumb/sphx_glr_plot_drone_thumb.gif
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  :ref:`sphx_glr_examples_intermediate_plot_drone.py`

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      <div class="sphx-glr-thumbnail-title">Drone Flight</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objective ---------">

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  .. image:: /examples/intermediate/images/thumb/sphx_glr_plot_betts_10_47_thumb.png
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  :ref:`sphx_glr_examples_intermediate_plot_betts_10_47.py`

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      <div class="sphx-glr-thumbnail-title">Singular Arc Problem</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/intermediate/images/thumb/sphx_glr_plot_mississippi_steamboat_thumb.gif
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  :ref:`sphx_glr_examples_intermediate_plot_mississippi_steamboat.py`

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      <div class="sphx-glr-thumbnail-title">Mississippi Steamboat</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objective --------- - Show various way to use inequalities for equations of motion. - unknown input trajectories can vary discontinuously. If, for whatever   physical reason, this is not desiriable, a way is shown how to make is   smooth.">

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  .. image:: /examples/intermediate/images/thumb/sphx_glr_plot_car_on_racecourse_smooth_thumb.png
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  :ref:`sphx_glr_examples_intermediate_plot_car_on_racecourse_smooth.py`

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      <div class="sphx-glr-thumbnail-title">Car on a Race Course</div>
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Advanced
========



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    <div class="sphx-glr-thumbcontainer" tooltip="   This example requires SciPy_, symmeplot_, yeadon_, and PyDy_ in addition to    opty and its required dependencies.">

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  .. image:: /examples/advanced/images/thumb/sphx_glr_plot_park2004_thumb.gif
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  :ref:`sphx_glr_examples_advanced_plot_park2004.py`

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      <div class="sphx-glr-thumbnail-title">Standing Balance Control Identification</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="The optimal control goal is to find the joint torques (hip, knee, ankle) that generate a minimal mean-torque for a person to stand from a seated position. gait2d provides a joint torque driven 2D bipedal human dynamical model with seven body segments (trunk, thighs, shanks, feet) and foot-ground contact forces based on the description in [Ackermann2010]_ suitable for this simulation.">

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  .. image:: /examples/advanced/images/thumb/sphx_glr_plot_sit_to_stand_thumb.gif
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  :ref:`sphx_glr_examples_advanced_plot_sit_to_stand.py`

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      <div class="sphx-glr-thumbnail-title">Sit to Stand</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="    pygait2d and symmeplot and their dependencies must be installed first to     run this example. Note that pygait2d has not been released to PyPi or Conda     Forge::">

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  .. image:: /examples/advanced/images/thumb/sphx_glr_plot_human_gait_thumb.gif
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  :ref:`sphx_glr_examples_advanced_plot_human_gait.py`

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      <div class="sphx-glr-thumbnail-title">Human Gait</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ---------- - Show how to use inequality constrains for equations of motion - Show how to come close to intermediate points on a solution path at times   specified by opty.">

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  .. image:: /examples/advanced/images/thumb/sphx_glr_plot_car_around_pylons_thumb.gif
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  :ref:`sphx_glr_examples_advanced_plot_car_around_pylons.py`

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      <div class="sphx-glr-thumbnail-title">Car around Pylons</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/advanced/images/thumb/sphx_glr_plot_car_in_garage_thumb.gif
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  :ref:`sphx_glr_examples_advanced_plot_car_in_garage.py`

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      <div class="sphx-glr-thumbnail-title">Park a Car in a Garage</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Objectives ----------">

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  .. image:: /examples/advanced/images/thumb/sphx_glr_plot_ball_rolling_on_spinning_disc_thumb.gif
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  :ref:`sphx_glr_examples_advanced_plot_ball_rolling_on_spinning_disc.py`

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      <div class="sphx-glr-thumbnail-title">Ball Rolling on Spinning Disc</div>
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  .. image:: /examples/advanced/images/thumb/sphx_glr_plot_particle_in_tube_thumb.gif
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  :ref:`sphx_glr_examples_advanced_plot_particle_in_tube.py`

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      <div class="sphx-glr-thumbnail-title">Particle Flight in Tube</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This is the model used in plot_park2004.py.">

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  .. image:: /examples/advanced/images/thumb/sphx_glr_model_park2004_thumb.png
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  :ref:`sphx_glr_examples_advanced_model_park2004.py`

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      <div class="sphx-glr-thumbnail-title">Planar 2D Human Standing Model</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Given a single human leg with four driving lumped muscles powering a fixed gear bicycle and the crank inertia and resistance mimic the torque felt if accelerating the whole bicycle with rider on flat ground, the objective is to travel a specific distance in the shortest amount of time given that the leg muscles have to coordinate.">

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  .. image:: /examples/advanced/images/thumb/sphx_glr_plot_one_legged_time_trial_thumb.gif
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  :ref:`sphx_glr_examples_advanced_plot_one_legged_time_trial.py`

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      <div class="sphx-glr-thumbnail-title">One-Legged Cycling Time Trial</div>
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.. toctree::
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   :includehidden:


   /examples/beginner/index.rst
   /examples/intermediate/index.rst
   /examples/advanced/index.rst


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

      :download:`Download all examples in Python source code: examples_python.zip </examples/examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: examples_jupyter.zip </examples/examples_jupyter.zip>`


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

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