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<li class="toctree-l1 has-children"><a class="reference internal" href="../../atari/">Atari</a><input class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" role="switch" type="checkbox"/><label for="toctree-checkbox-1"><div class="visually-hidden">Toggle child pages in navigation</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="../../atari/adventure/">Adventure</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/air_raid/">Air Raid</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/beam_rider/">Beam Rider</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/centipede/">Centipede</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/chopper_command/">Chopper Command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/crazy_climber/">Crazy Climber</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/defender/">Defender</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/demon_attack/">Demon Attack</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/double_dunk/">Double Dunk</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/elevator_action/">Elevator Action</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/enduro/">Enduro</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/fishing_derby/">FishingDerby</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/freeway/">Freeway</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/kangaroo/">Kangaroo</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/ms_pacman/">Ms Pacman</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/pitfall/">Pitfall</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/qbert/">Qbert</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/riverraid/">Riverraid</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../atari/seaquest/">Seaquest</a></li>
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<li class="toctree-l1 current has-children"><a class="reference internal" href="../">Classic Control</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-4" name="toctree-checkbox-4" role="switch" type="checkbox"/><label for="toctree-checkbox-4"><div class="visually-hidden">Toggle child pages in navigation</div><i class="icon"><svg><use href="#svg-arrow-right"></use></svg></i></label><ul class="current">
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<li class="toctree-l2 current current-page"><a class="current reference internal" href="#">Acrobot</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../cart_pole/">Cart Pole</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../mountain_car_continuous/">Mountain Car Continuous</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../pendulum/">Pendulum</a></li>
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<li class="toctree-l1 has-children"><a class="reference internal" href="../../box2d/">Box2D</a><input class="toctree-checkbox" id="toctree-checkbox-5" name="toctree-checkbox-5" role="switch" type="checkbox"/><label for="toctree-checkbox-5"><div class="visually-hidden">Toggle child pages in navigation</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="../../box2d/bipedal_walker/">Bipedal Walker</a></li>
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<li class="toctree-l2"><a class="reference internal" href="../../box2d/lunar_lander/">Lunar Lander</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../../third_party_environments/">Third Party 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-l1"><a class="reference internal" href="../../../content/environment_creation/">Make your own custom environment</a></li>
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<li class="toctree-l1"><a class="reference internal" href="../../../content/vectorising/">Vectorising your environments</a></li>
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<p class="caption" role="heading"><span class="caption-text">Development</span></p>
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<ul>
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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://farama.org/donations">Donate</a></li>
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</aside>
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<div class="main">
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<div class="content">
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<div class="article-container">
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<a href="#" class="back-to-top muted-link">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24">
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<path d="M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8v12z"></path>
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</svg>
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<span>Back to top</span>
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<label class="toc-overlay-icon toc-content-icon" for="__toc">
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<div class="visually-hidden">Toggle table of contents sidebar</div>
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</label>
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</div>
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<article role="main">
|
|||
|
|
<section id="acrobot">
|
|||
|
|
<h1>Acrobot<a class="headerlink" href="#acrobot" title="Permalink to this heading">#</a></h1>
|
|||
|
|
<figure class="align-default" id="id1">
|
|||
|
|
<a class="reference internal image-reference" href="../../../_images/acrobot.gif"><img alt="../../../_images/acrobot.gif" src="../../../_images/acrobot.gif" style="width: 200px;" /></a>
|
|||
|
|
</figure>
|
|||
|
|
<p>This environment is part of the <a href='..'>Classic Control environments</a>. Please read that page first for general information.</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>Discrete(3)</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td><p>Observation Shape</p></td>
|
|||
|
|
<td><p>(6,)</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td><p>Observation High</p></td>
|
|||
|
|
<td><p>[ 1. 1. 1. 1. 12.57 28.27]</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td><p>Observation Low</p></td>
|
|||
|
|
<td><p>[ -1. -1. -1. -1. -12.57 -28.27]</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td><p>Import</p></td>
|
|||
|
|
<td><p><code class="docutils literal notranslate"><span class="pre">gymnasium.make("Acrobot-v1")</span></code></p></td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</div>
|
|||
|
|
<section id="description">
|
|||
|
|
<h2>Description<a class="headerlink" href="#description" title="Permalink to this heading">#</a></h2>
|
|||
|
|
<p>The Acrobot environment is based on Sutton’s work in
|
|||
|
|
<a class="reference external" href="https://papers.nips.cc/paper/1995/hash/8f1d43620bc6bb580df6e80b0dc05c48-Abstract.html">“Generalization in Reinforcement Learning: Successful Examples Using Sparse Coarse Coding”</a>
|
|||
|
|
and <a class="reference external" href="http://www.incompleteideas.net/book/the-book-2nd.html">Sutton and Barto’s book</a>.
|
|||
|
|
The system consists of two links connected linearly to form a chain, with one end of
|
|||
|
|
the chain fixed. The joint between the two links is actuated. The goal is to apply
|
|||
|
|
torques on the actuated joint to swing the free end of the linear chain above a
|
|||
|
|
given height while starting from the initial state of hanging downwards.</p>
|
|||
|
|
<p>As seen in the <strong>Gif</strong>: two blue links connected by two green joints. The joint in
|
|||
|
|
between the two links is actuated. The goal is to swing the free end of the outer-link
|
|||
|
|
to reach the target height (black horizontal line above system) by applying torque on
|
|||
|
|
the actuator.</p>
|
|||
|
|
</section>
|
|||
|
|
<section id="action-space">
|
|||
|
|
<h2>Action Space<a class="headerlink" href="#action-space" title="Permalink to this heading">#</a></h2>
|
|||
|
|
<p>The action is discrete, deterministic, and represents the torque applied on the actuated
|
|||
|
|
joint between the two links.</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>Unit</p></th>
|
|||
|
|
</tr>
|
|||
|
|
</thead>
|
|||
|
|
<tbody>
|
|||
|
|
<tr class="row-even"><td><p>0</p></td>
|
|||
|
|
<td><p>apply -1 torque to the actuated joint</p></td>
|
|||
|
|
<td><p>torque (N m)</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td><p>1</p></td>
|
|||
|
|
<td><p>apply 0 torque to the actuated joint</p></td>
|
|||
|
|
<td><p>torque (N m)</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td><p>2</p></td>
|
|||
|
|
<td><p>apply 1 torque to the actuated joint</p></td>
|
|||
|
|
<td><p>torque (N m)</p></td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</div>
|
|||
|
|
</section>
|
|||
|
|
<section id="observation-space">
|
|||
|
|
<h2>Observation Space<a class="headerlink" href="#observation-space" title="Permalink to this heading">#</a></h2>
|
|||
|
|
<p>The observation is a <code class="docutils literal notranslate"><span class="pre">ndarray</span></code> with shape <code class="docutils literal notranslate"><span class="pre">(6,)</span></code> that provides information about the
|
|||
|
|
two rotational joint angles as well as their angular velocities:</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>
|
|||
|
|
</tr>
|
|||
|
|
</thead>
|
|||
|
|
<tbody>
|
|||
|
|
<tr class="row-even"><td><p>0</p></td>
|
|||
|
|
<td><p>Cosine of <code class="docutils literal notranslate"><span class="pre">theta1</span></code></p></td>
|
|||
|
|
<td><p>-1</p></td>
|
|||
|
|
<td><p>1</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td><p>1</p></td>
|
|||
|
|
<td><p>Sine of <code class="docutils literal notranslate"><span class="pre">theta1</span></code></p></td>
|
|||
|
|
<td><p>-1</p></td>
|
|||
|
|
<td><p>1</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td><p>2</p></td>
|
|||
|
|
<td><p>Cosine of <code class="docutils literal notranslate"><span class="pre">theta2</span></code></p></td>
|
|||
|
|
<td><p>-1</p></td>
|
|||
|
|
<td><p>1</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td><p>3</p></td>
|
|||
|
|
<td><p>Sine of <code class="docutils literal notranslate"><span class="pre">theta2</span></code></p></td>
|
|||
|
|
<td><p>-1</p></td>
|
|||
|
|
<td><p>1</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-even"><td><p>4</p></td>
|
|||
|
|
<td><p>Angular velocity of <code class="docutils literal notranslate"><span class="pre">theta1</span></code></p></td>
|
|||
|
|
<td><p>~ -12.567 (-4 * pi)</p></td>
|
|||
|
|
<td><p>~ 12.567 (4 * pi)</p></td>
|
|||
|
|
</tr>
|
|||
|
|
<tr class="row-odd"><td><p>5</p></td>
|
|||
|
|
<td><p>Angular velocity of <code class="docutils literal notranslate"><span class="pre">theta2</span></code></p></td>
|
|||
|
|
<td><p>~ -28.274 (-9 * pi)</p></td>
|
|||
|
|
<td><p>~ 28.274 (9 * pi)</p></td>
|
|||
|
|
</tr>
|
|||
|
|
</tbody>
|
|||
|
|
</table>
|
|||
|
|
</div>
|
|||
|
|
<p>where</p>
|
|||
|
|
<ul class="simple">
|
|||
|
|
<li><p><code class="docutils literal notranslate"><span class="pre">theta1</span></code> is the angle of the first joint, where an angle of 0 indicates the first link is pointing directly
|
|||
|
|
downwards.</p></li>
|
|||
|
|
<li><p><code class="docutils literal notranslate"><span class="pre">theta2</span></code> is <em><strong>relative to the angle of the first link.</strong></em>
|
|||
|
|
An angle of 0 corresponds to having the same angle between the two links.</p></li>
|
|||
|
|
</ul>
|
|||
|
|
<p>The angular velocities of <code class="docutils literal notranslate"><span class="pre">theta1</span></code> and <code class="docutils literal notranslate"><span class="pre">theta2</span></code> are bounded at ±4π, and ±9π rad/s respectively.
|
|||
|
|
A state of <code class="docutils literal notranslate"><span class="pre">[1,</span> <span class="pre">0,</span> <span class="pre">1,</span> <span class="pre">0,</span> <span class="pre">...,</span> <span class="pre">...]</span></code> indicates that both links are pointing downwards.</p>
|
|||
|
|
</section>
|
|||
|
|
<section id="rewards">
|
|||
|
|
<h2>Rewards<a class="headerlink" href="#rewards" title="Permalink to this heading">#</a></h2>
|
|||
|
|
<p>The goal is to have the free end reach a designated target height in as few steps as possible,
|
|||
|
|
and as such all steps that do not reach the goal incur a reward of -1.
|
|||
|
|
Achieving the target height results in termination with a reward of 0. The reward threshold is -100.</p>
|
|||
|
|
</section>
|
|||
|
|
<section id="starting-state">
|
|||
|
|
<h2>Starting State<a class="headerlink" href="#starting-state" title="Permalink to this heading">#</a></h2>
|
|||
|
|
<p>Each parameter in the underlying state (<code class="docutils literal notranslate"><span class="pre">theta1</span></code>, <code class="docutils literal notranslate"><span class="pre">theta2</span></code>, and the two angular velocities) is initialized
|
|||
|
|
uniformly between -0.1 and 0.1. This means both links are pointing downwards with some initial stochasticity.</p>
|
|||
|
|
</section>
|
|||
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<section id="episode-end">
|
|||
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<h2>Episode End<a class="headerlink" href="#episode-end" title="Permalink to this heading">#</a></h2>
|
|||
|
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<p>The episode ends if one of the following occurs:</p>
|
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<ol class="arabic simple">
|
|||
|
|
<li><p>Termination: The free end reaches the target height, which is constructed as:
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">-cos(theta1)</span> <span class="pre">-</span> <span class="pre">cos(theta2</span> <span class="pre">+</span> <span class="pre">theta1)</span> <span class="pre">></span> <span class="pre">1.0</span></code></p></li>
|
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|
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<li><p>Truncation: Episode length is greater than 500 (200 for v0)</p></li>
|
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|
|
</ol>
|
|||
|
|
</section>
|
|||
|
|
<section id="arguments">
|
|||
|
|
<h2>Arguments<a class="headerlink" href="#arguments" title="Permalink to this heading">#</a></h2>
|
|||
|
|
<p>No additional arguments are currently supported.</p>
|
|||
|
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">env</span> <span class="o">=</span> <span class="n">gymnasium</span><span class="o">.</span><span class="n">make</span><span class="p">(</span><span class="s1">'Acrobot-v1'</span><span class="p">)</span>
|
|||
|
|
</pre></div>
|
|||
|
|
</div>
|
|||
|
|
<p>By default, the dynamics of the acrobot follow those described in Sutton and Barto’s book
|
|||
|
|
<a class="reference external" href="http://incompleteideas.net/book/11/node4.html">Reinforcement Learning: An Introduction</a>.
|
|||
|
|
However, a <code class="docutils literal notranslate"><span class="pre">book_or_nips</span></code> parameter can be modified to change the pendulum dynamics to those described
|
|||
|
|
in the original <a class="reference external" href="https://papers.nips.cc/paper/1995/hash/8f1d43620bc6bb580df6e80b0dc05c48-Abstract.html">NeurIPS paper</a>.</p>
|
|||
|
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># To change the dynamics as described above</span>
|
|||
|
|
<span class="n">env</span><span class="o">.</span><span class="n">env</span><span class="o">.</span><span class="n">book_or_nips</span> <span class="o">=</span> <span class="s1">'nips'</span>
|
|||
|
|
</pre></div>
|
|||
|
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</div>
|
|||
|
|
<p>See the following note and
|
|||
|
|
the <a class="reference external" href="https://github.com/Farama-Foundation/gymnasium/blob/master/gymnasium/envs/classic_control/acrobot.py">implementation</a> for details:</p>
|
|||
|
|
<blockquote>
|
|||
|
|
<div><p>The dynamics equations were missing some terms in the NIPS paper which
|
|||
|
|
are present in the book. R. Sutton confirmed in personal correspondence
|
|||
|
|
that the experimental results shown in the paper and the book were
|
|||
|
|
generated with the equations shown in the book.
|
|||
|
|
However, there is the option to run the domain with the paper equations
|
|||
|
|
by setting <code class="docutils literal notranslate"><span class="pre">book_or_nips</span> <span class="pre">=</span> <span class="pre">'nips'</span></code></p>
|
|||
|
|
</div></blockquote>
|
|||
|
|
</section>
|
|||
|
|
<section id="version-history">
|
|||
|
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<h2>Version History<a class="headerlink" href="#version-history" title="Permalink to this heading">#</a></h2>
|
|||
|
|
<ul class="simple">
|
|||
|
|
<li><p>v1: Maximum number of steps increased from 200 to 500. The observation space for v0 provided direct readings of
|
|||
|
|
<code class="docutils literal notranslate"><span class="pre">theta1</span></code> and <code class="docutils literal notranslate"><span class="pre">theta2</span></code> in radians, having a range of <code class="docutils literal notranslate"><span class="pre">[-pi,</span> <span class="pre">pi]</span></code>. The v1 observation space as described here provides the
|
|||
|
|
sine and cosine of each angle instead.</p></li>
|
|||
|
|
<li><p>v0: Initial versions release (1.0.0) (removed from gymnasium for v1)</p></li>
|
|||
|
|
</ul>
|
|||
|
|
</section>
|
|||
|
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<section id="references">
|
|||
|
|
<h2>References<a class="headerlink" href="#references" title="Permalink to this heading">#</a></h2>
|
|||
|
|
<ul class="simple">
|
|||
|
|
<li><p>Sutton, R. S. (1996). Generalization in Reinforcement Learning: Successful Examples Using Sparse Coarse Coding.
|
|||
|
|
In D. Touretzky, M. C. Mozer, & M. Hasselmo (Eds.), Advances in Neural Information Processing Systems (Vol. 8).
|
|||
|
|
MIT Press. https://proceedings.neurips.cc/paper/1995/file/8f1d43620bc6bb580df6e80b0dc05c48-Paper.pdf</p></li>
|
|||
|
|
<li><p>Sutton, R. S., Barto, A. G. (2018 ). Reinforcement Learning: An Introduction. The MIT Press.</p></li>
|
|||
|
|
</ul>
|
|||
|
|
</section>
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<ul>
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<li><a class="reference internal" href="#">Acrobot</a><ul>
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<li><a class="reference internal" href="#description">Description</a></li>
|
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<li><a class="reference internal" href="#action-space">Action Space</a></li>
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<li><a class="reference internal" href="#starting-state">Starting State</a></li>
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<li><a class="reference internal" href="#episode-end">Episode End</a></li>
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<li><a class="reference internal" href="#arguments">Arguments</a></li>
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