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<li class="toctree-l2"><a class="reference internal" href="../hopper/">Hopper</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../humanoid_standup/">Humanoid Standup</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../inverted_double_pendulum/">Inverted Double Pendulum</a></li>
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<li class="toctree-l2 current current-page"><a class="current reference internal" href="#">Inverted Pendulum</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../pusher/">Pusher</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../reacher/">Reacher</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../walker2d/">Walker2D</a></li>
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</ul>
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<li class="toctree-l1"><a class="reference internal" href="../../atari/">Atari</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../../third_party_environments/">External Environments</a></li>
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</ul>
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<p class="caption" role="heading"><span class="caption-text">Tutorials</span></p>
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<ul>
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<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/gymnasium_basics/load_quadruped_model/">Load custom quadruped robot environments</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/gymnasium_basics/handling_time_limits/">Handling Time Limits</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/gymnasium_basics/implementing_custom_wrappers/">Implementing Custom Wrappers</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/gymnasium_basics/environment_creation/">Make your own custom environment</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/gymnasium_basics/vector_envs_tutorial/">Training A2C with Vector Envs and Domain Randomization</a></li>
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</ul>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../../../tutorials/training_agents/">Training Agents links in the Gymnasium Documentation</a><input class="toctree-checkbox" id="toctree-checkbox-9" name="toctree-checkbox-9" role="switch" type="checkbox"/><label for="toctree-checkbox-9"><div class="visually-hidden">Toggle navigation of Training Agents links in the Gymnasium Documentation</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul>
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<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/training_agents/reinforce_invpend_gym_v26/">Training using REINFORCE for Mujoco</a></li>
|
||
<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/training_agents/blackjack_tutorial/">Solving Blackjack with Q-Learning</a></li>
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||
<li class="toctree-l2"><a class="reference internal" href="../../../tutorials/training_agents/FrozenLake_tuto/">Frozenlake benchmark</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../../../tutorials/third-party-tutorials/">Third-Party Tutorials</a></li>
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</ul>
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<p class="caption" role="heading"><span class="caption-text">Development</span></p>
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<li class="toctree-l1"><a class="reference external" href="https://github.com/Farama-Foundation/Gymnasium">Github</a></li>
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<li class="toctree-l1"><a class="reference external" href="https://arxiv.org/abs/2407.17032">Paper</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../../../gymnasium_release_notes/">Gymnasium Release Notes</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../../../gym_release_notes/">Gym Release Notes</a></li>
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<li class="toctree-l1"><a class="reference external" href="https://github.com/Farama-Foundation/Gymnasium/blob/main/docs/README.md">Contribute to the Docs</a></li>
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<article role="main">
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||
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||
<section class="tex2jax_ignore mathjax_ignore" id="inverted-pendulum">
|
||
<h1>Inverted Pendulum<a class="headerlink" href="#inverted-pendulum" title="Link to this heading">¶</a></h1>
|
||
<figure class="align-default" id="id1">
|
||
<a class="reference internal image-reference" href="../../../_images/inverted_pendulum.gif"><img alt="../../../_images/inverted_pendulum.gif" src="../../../_images/inverted_pendulum.gif" style="width: 200px;" />
|
||
</a>
|
||
</figure>
|
||
<p>This environment is part of the Mujoco environments which contains general information about the environment.</p>
|
||
<div class="table-wrapper colwidths-auto docutils container">
|
||
<table class="docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p></p></th>
|
||
<th class="head"><p></p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>Action Space</p></td>
|
||
<td><p><code class="docutils literal notranslate"><span class="pre">Box(-3.0,</span> <span class="pre">3.0,</span> <span class="pre">(1,),</span> <span class="pre">float32)</span></code></p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>Observation Space</p></td>
|
||
<td><p><code class="docutils literal notranslate"><span class="pre">Box(-inf,</span> <span class="pre">inf,</span> <span class="pre">(4,),</span> <span class="pre">float64)</span></code></p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>import</p></td>
|
||
<td><p><code class="docutils literal notranslate"><span class="pre">gymnasium.make("InvertedPendulum-v5")</span></code></p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<section id="description">
|
||
<h2>Description<a class="headerlink" href="#description" title="Link to this heading">¶</a></h2>
|
||
<p>This environment is the Cartpole environment, based on the work of Barto, Sutton, and Anderson in <a class="reference external" href="https://ieeexplore.ieee.org/document/6313077">“Neuronlike adaptive elements that can solve difficult learning control problems”</a>,
|
||
just like in the classic environments, but now powered by the Mujoco physics simulator - allowing for more complex experiments (such as varying the effects of gravity).
|
||
This environment consists of a cart that can be moved linearly, with a pole attached to one end and having another end free.
|
||
The cart can be pushed left or right, and the goal is to balance the pole on top of the cart by applying forces to the cart.</p>
|
||
</section>
|
||
<section id="action-space">
|
||
<h2>Action Space<a class="headerlink" href="#action-space" title="Link to this heading">¶</a></h2>
|
||
<p>The agent take a 1-element vector for actions.</p>
|
||
<p>The action space is a continuous <code class="docutils literal notranslate"><span class="pre">(action)</span></code> in <code class="docutils literal notranslate"><span class="pre">[-3,</span> <span class="pre">3]</span></code>, where <code class="docutils literal notranslate"><span class="pre">action</span></code> represents
|
||
the numerical force applied to the cart (with magnitude representing the amount of
|
||
force and sign representing the direction)</p>
|
||
<div class="table-wrapper colwidths-auto docutils container">
|
||
<table class="docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>Num</p></th>
|
||
<th class="head"><p>Action</p></th>
|
||
<th class="head"><p>Control Min</p></th>
|
||
<th class="head"><p>Control Max</p></th>
|
||
<th class="head"><p>Name (in corresponding XML file)</p></th>
|
||
<th class="head"><p>Joint</p></th>
|
||
<th class="head"><p>Type (Unit)</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>0</p></td>
|
||
<td><p>Force applied on the cart</p></td>
|
||
<td><p>-3</p></td>
|
||
<td><p>3</p></td>
|
||
<td><p>slider</p></td>
|
||
<td><p>slide</p></td>
|
||
<td><p>Force (N)</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
</section>
|
||
<section id="observation-space">
|
||
<h2>Observation Space<a class="headerlink" href="#observation-space" title="Link to this heading">¶</a></h2>
|
||
<p>The observation space consists of the following parts (in order):</p>
|
||
<ul class="simple">
|
||
<li><p><em>qpos (2 element):</em> Position values of the robot’s cart and pole.</p></li>
|
||
<li><p><em>qvel (2 elements):</em> The velocities of cart and pole (their derivatives).</p></li>
|
||
</ul>
|
||
<p>The observation space is a <code class="docutils literal notranslate"><span class="pre">Box(-Inf,</span> <span class="pre">Inf,</span> <span class="pre">(4,),</span> <span class="pre">float64)</span></code> where the elements are as follows:</p>
|
||
<div class="table-wrapper colwidths-auto docutils container">
|
||
<table class="docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>Num</p></th>
|
||
<th class="head"><p>Observation</p></th>
|
||
<th class="head"><p>Min</p></th>
|
||
<th class="head"><p>Max</p></th>
|
||
<th class="head"><p>Name (in corresponding XML file)</p></th>
|
||
<th class="head"><p>Joint</p></th>
|
||
<th class="head"><p>Type (Unit)</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>0</p></td>
|
||
<td><p>position of the cart along the linear surface</p></td>
|
||
<td><p>-Inf</p></td>
|
||
<td><p>Inf</p></td>
|
||
<td><p>slider</p></td>
|
||
<td><p>slide</p></td>
|
||
<td><p>position (m)</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>1</p></td>
|
||
<td><p>vertical angle of the pole on the cart</p></td>
|
||
<td><p>-Inf</p></td>
|
||
<td><p>Inf</p></td>
|
||
<td><p>hinge</p></td>
|
||
<td><p>hinge</p></td>
|
||
<td><p>angle (rad)</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>2</p></td>
|
||
<td><p>linear velocity of the cart</p></td>
|
||
<td><p>-Inf</p></td>
|
||
<td><p>Inf</p></td>
|
||
<td><p>slider</p></td>
|
||
<td><p>slide</p></td>
|
||
<td><p>velocity (m/s)</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>3</p></td>
|
||
<td><p>angular velocity of the pole on the cart</p></td>
|
||
<td><p>-Inf</p></td>
|
||
<td><p>Inf</p></td>
|
||
<td><p>hinge</p></td>
|
||
<td><p>hinge</p></td>
|
||
<td><p>angular velocity (rad/s)</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
</section>
|
||
<section id="rewards">
|
||
<h2>Rewards<a class="headerlink" href="#rewards" title="Link to this heading">¶</a></h2>
|
||
<p>The goal is to keep the inverted pendulum stand upright (within a certain angle limit) for as long as possible - as such, a reward of +1 is given for each timestep that the pole is upright.</p>
|
||
<p>The pole is considered upright if:
|
||
<span class="math notranslate nohighlight">\(|angle| < 0.2\)</span>.</p>
|
||
<p>and <code class="docutils literal notranslate"><span class="pre">info</span></code> also contains the reward.</p>
|
||
</section>
|
||
<section id="starting-state">
|
||
<h2>Starting State<a class="headerlink" href="#starting-state" title="Link to this heading">¶</a></h2>
|
||
<p>The initial position state is <span class="math notranslate nohighlight">\(\mathcal{U}_{[-reset\_noise\_scale imes I_{2}, reset\_noise\_scale imes I_{2}]}\)</span>.
|
||
The initial velocity state is <span class="math notranslate nohighlight">\(\mathcal{U}_{[-reset\_noise\_scale imes I_{2}, reset\_noise\_scale imes I_{2}]}\)</span>.</p>
|
||
<p>where <span class="math notranslate nohighlight">\(\mathcal{U}\)</span> is the multivariate uniform continuous distribution.</p>
|
||
</section>
|
||
<section id="episode-end">
|
||
<h2>Episode End<a class="headerlink" href="#episode-end" title="Link to this heading">¶</a></h2>
|
||
<section id="termination">
|
||
<h3>Termination<a class="headerlink" href="#termination" title="Link to this heading">¶</a></h3>
|
||
<p>The environment terminates when the Inverted Pendulum is unhealthy.
|
||
The Inverted Pendulum is unhealthy if any of the following happens:</p>
|
||
<ol class="arabic simple">
|
||
<li><p>Any of the state space values is no longer finite.</p></li>
|
||
<li><p>The absolute value of the vertical angle between the pole and the cart is greater than 0.2 radians.</p></li>
|
||
</ol>
|
||
</section>
|
||
<section id="truncation">
|
||
<h3>Truncation<a class="headerlink" href="#truncation" title="Link to this heading">¶</a></h3>
|
||
<p>The default duration of an episode is 1000 timesteps.</p>
|
||
</section>
|
||
</section>
|
||
<section id="arguments">
|
||
<h2>Arguments<a class="headerlink" href="#arguments" title="Link to this heading">¶</a></h2>
|
||
<p>InvertedPendulum provides a range of parameters to modify the observation space, reward function, initial state, and termination condition.
|
||
These parameters can be applied during <code class="docutils literal notranslate"><span class="pre">gymnasium.make</span></code> in the following way:</p>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">gymnasium</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">gym</span>
|
||
<span class="n">env</span> <span class="o">=</span> <span class="n">gym</span><span class="o">.</span><span class="n">make</span><span class="p">(</span><span class="s1">'InvertedPendulum-v5'</span><span class="p">,</span> <span class="n">reset_noise_scale</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
|
||
</pre></div>
|
||
</div>
|
||
<div class="table-wrapper colwidths-auto docutils container">
|
||
<table class="docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>Parameter</p></th>
|
||
<th class="head"><p>Type</p></th>
|
||
<th class="head"><p>Default</p></th>
|
||
<th class="head"><p>Description</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">xml_file</span></code></p></td>
|
||
<td><p><strong>str</strong></p></td>
|
||
<td><p><code class="docutils literal notranslate"><span class="pre">"inverted_pendulum.xml"</span></code></p></td>
|
||
<td><p>Path to a MuJoCo model</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">reset_noise_scale</span></code></p></td>
|
||
<td><p><strong>float</strong></p></td>
|
||
<td><p><code class="docutils literal notranslate"><span class="pre">0.01</span></code></p></td>
|
||
<td><p>Scale of random perturbations of initial position and velocity (see <code class="docutils literal notranslate"><span class="pre">Starting</span> <span class="pre">State</span></code> section)</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
</section>
|
||
<section id="version-history">
|
||
<h2>Version History<a class="headerlink" href="#version-history" title="Link to this heading">¶</a></h2>
|
||
<ul class="simple">
|
||
<li><p>v5:</p>
|
||
<ul>
|
||
<li><p>Minimum <code class="docutils literal notranslate"><span class="pre">mujoco</span></code> version is now 2.3.3.</p></li>
|
||
<li><p>Added support for fully custom/third party <code class="docutils literal notranslate"><span class="pre">mujoco</span></code> models using the <code class="docutils literal notranslate"><span class="pre">xml_file</span></code> argument (previously only a few changes could be made to the existing models).</p></li>
|
||
<li><p>Added <code class="docutils literal notranslate"><span class="pre">default_camera_config</span></code> argument, a dictionary for setting the <code class="docutils literal notranslate"><span class="pre">mj_camera</span></code> properties, mainly useful for custom environments.</p></li>
|
||
<li><p>Added <code class="docutils literal notranslate"><span class="pre">env.observation_structure</span></code>, a dictionary for specifying the observation space compose (e.g. <code class="docutils literal notranslate"><span class="pre">qpos</span></code>, <code class="docutils literal notranslate"><span class="pre">qvel</span></code>), useful for building tooling and wrappers for the MuJoCo environments.</p></li>
|
||
<li><p>Added <code class="docutils literal notranslate"><span class="pre">frame_skip</span></code> argument, used to configure the <code class="docutils literal notranslate"><span class="pre">dt</span></code> (duration of <code class="docutils literal notranslate"><span class="pre">step()</span></code>), default varies by environment check environment documentation pages.</p></li>
|
||
<li><p>Fixed bug: <code class="docutils literal notranslate"><span class="pre">healthy_reward</span></code> was given on every step (even if the Pendulum is unhealthy), now it is only given if the Pendulum is healthy (not terminated) (related <a class="reference external" href="https://github.com/Farama-Foundation/Gymnasium/issues/500">GitHub issue</a>).</p></li>
|
||
<li><p>Added <code class="docutils literal notranslate"><span class="pre">xml_file</span></code> argument.</p></li>
|
||
<li><p>Added <code class="docutils literal notranslate"><span class="pre">reset_noise_scale</span></code> argument to set the range of initial states.</p></li>
|
||
<li><p>Added <code class="docutils literal notranslate"><span class="pre">info["reward_survive"]</span></code> which contains the reward.</p></li>
|
||
</ul>
|
||
</li>
|
||
<li><p>v4: All MuJoCo environments now use the MuJoCo bindings in mujoco >= 2.1.3.</p></li>
|
||
<li><p>v3: This environment does not have a v3 release.</p></li>
|
||
<li><p>v2: All continuous control environments now use mujoco-py >= 1.5.</p></li>
|
||
<li><p>v1: max_time_steps raised to 1000 for robot based tasks (including inverted pendulum).</p></li>
|
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<li><p>v0: Initial versions release.</p></li>
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