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<article role="main">
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<section class="tex2jax_ignore mathjax_ignore" id="acrobot">
|
||
<h1>Acrobot<a class="headerlink" href="#acrobot" title="Link 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 Classic Control 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">Discrete(3)</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([</span> <span class="pre">-1.</span> <span class="pre">-1.</span> <span class="pre">-1.</span> <span class="pre">-1.</span> <span class="pre">-12.566371</span> <span class="pre">-28.274334],</span> <span class="pre">[</span> <span class="pre">1.</span> <span class="pre">1.</span> <span class="pre">1.</span> <span class="pre">1.</span> <span class="pre">12.566371</span> <span class="pre">28.274334],</span> <span class="pre">(6,),</span> <span class="pre">float32)</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("Acrobot-v1")</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>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="Link 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="Link 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="Link 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="Link 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>
|
||
<section id="episode-end">
|
||
<h2>Episode End<a class="headerlink" href="#episode-end" title="Link to this heading">¶</a></h2>
|
||
<p>The episode ends if one of the following occurs:</p>
|
||
<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>
|
||
<li><p>Truncation: Episode length is greater than 500 (200 for v0)</p></li>
|
||
</ol>
|
||
</section>
|
||
<section id="arguments">
|
||
<h2>Arguments<a class="headerlink" href="#arguments" title="Link to this heading">¶</a></h2>
|
||
<p>Acrobot only has <code class="docutils literal notranslate"><span class="pre">render_mode</span></code> as a keyword for <code class="docutils literal notranslate"><span class="pre">gymnasium.make</span></code>.
|
||
On reset, the <code class="docutils literal notranslate"><span class="pre">options</span></code> parameter allows the user to change the bounds used to determine the new random state.</p>
|
||
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </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="gp">>>> </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">'Acrobot-v1'</span><span class="p">,</span> <span class="n">render_mode</span><span class="o">=</span><span class="s2">"rgb_array"</span><span class="p">)</span>
|
||
<span class="gp">>>> </span><span class="n">env</span>
|
||
<span class="go"><TimeLimit<OrderEnforcing<PassiveEnvChecker<AcrobotEnv<Acrobot-v1>>>>></span>
|
||
<span class="gp">>>> </span><span class="n">env</span><span class="o">.</span><span class="n">reset</span><span class="p">(</span><span class="n">seed</span><span class="o">=</span><span class="mi">123</span><span class="p">,</span> <span class="n">options</span><span class="o">=</span><span class="p">{</span><span class="s2">"low"</span><span class="p">:</span> <span class="o">-</span><span class="mf">0.2</span><span class="p">,</span> <span class="s2">"high"</span><span class="p">:</span> <span class="mf">0.2</span><span class="p">})</span> <span class="c1"># default low=-0.1, high=0.1</span>
|
||
<span class="go">(array([ 0.997341 , 0.07287608, 0.9841162 , -0.17752565, -0.11185605,</span>
|
||
<span class="go"> -0.12625128], dtype=float32), {})</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-python 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">unwrapped</span><span class="o">.</span><span class="n">book_or_nips</span> <span class="o">=</span> <span class="s1">'nips'</span>
|
||
</pre></div>
|
||
</div>
|
||
<p>See the following note 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">
|
||
<h2>Version History<a class="headerlink" href="#version-history" title="Link 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</p></li>
|
||
</ul>
|
||
</section>
|
||
<section id="references">
|
||
<h2>References<a class="headerlink" href="#references" title="Link 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>
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<li><p>Sutton, R. S., Barto, A. G. (2018 ). Reinforcement Learning: An Introduction. The MIT Press.</p></li>
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