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<article role="main">
<section id="half-cheetah">
<h1>Half Cheetah<a class="headerlink" href="#half-cheetah" title="Permalink to this heading">#</a></h1>
<figure class="align-default" id="id1">
<a class="reference internal image-reference" href="../../../_images/half_cheetah.gif"><img alt="../../../_images/half_cheetah.gif" src="../../../_images/half_cheetah.gif" style="width: 200px;" /></a>
</figure>
<p>This environment is part of the <a href='..'>Mujoco 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>Box(-1.0, 1.0, (6,), float32)</p></td>
</tr>
<tr class="row-odd"><td><p>Observation Shape</p></td>
<td><p>(17,)</p></td>
</tr>
<tr class="row-even"><td><p>Observation High</p></td>
<td><p>inf</p></td>
</tr>
<tr class="row-odd"><td><p>Observation Low</p></td>
<td><p>[-inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf]</p></td>
</tr>
<tr class="row-even"><td><p>Import</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">gymnasium.make(&quot;HalfCheetah-v4&quot;)</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>This environment is based on the work by P. Wawrzyński in
<a class="reference external" href="http://staff.elka.pw.edu.pl/~pwawrzyn/pub-s/0812_LSCLRR.pdf">“A Cat-Like Robot Real-Time Learning to Run”</a>.
The HalfCheetah is a 2-dimensional robot consisting of 9 links and 8
joints connecting them (including two paws). The goal is to apply a torque
on the joints to make the cheetah run forward (right) as fast as possible,
with a positive reward allocated based on the distance moved forward and a
negative reward allocated for moving backward. The torso and head of the
cheetah are fixed, and the torque can only be applied on the other 6 joints
over the front and back thighs (connecting to the torso), shins
(connecting to the thighs) and feet (connecting to the shins).</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 space is a <code class="docutils literal notranslate"><span class="pre">Box(-1,</span> <span class="pre">1,</span> <span class="pre">(6,),</span> <span class="pre">float32)</span></code>. An action represents the torques applied between <em>links</em>.</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>Unit</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>0</p></td>
<td><p>Torque applied on the back thigh rotor</p></td>
<td><p>-1</p></td>
<td><p>1</p></td>
<td><p>bthigh</p></td>
<td><p>hinge</p></td>
<td><p>torque (N m)</p></td>
</tr>
<tr class="row-odd"><td><p>1</p></td>
<td><p>Torque applied on the back shin rotor</p></td>
<td><p>-1</p></td>
<td><p>1</p></td>
<td><p>bshin</p></td>
<td><p>hinge</p></td>
<td><p>torque (N m)</p></td>
</tr>
<tr class="row-even"><td><p>2</p></td>
<td><p>Torque applied on the back foot rotor</p></td>
<td><p>-1</p></td>
<td><p>1</p></td>
<td><p>bfoot</p></td>
<td><p>hinge</p></td>
<td><p>torque (N m)</p></td>
</tr>
<tr class="row-odd"><td><p>3</p></td>
<td><p>Torque applied on the front thigh rotor</p></td>
<td><p>-1</p></td>
<td><p>1</p></td>
<td><p>fthigh</p></td>
<td><p>hinge</p></td>
<td><p>torque (N m)</p></td>
</tr>
<tr class="row-even"><td><p>4</p></td>
<td><p>Torque applied on the front shin rotor</p></td>
<td><p>-1</p></td>
<td><p>1</p></td>
<td><p>fshin</p></td>
<td><p>hinge</p></td>
<td><p>torque (N m)</p></td>
</tr>
<tr class="row-odd"><td><p>5</p></td>
<td><p>Torque applied on the front foot rotor</p></td>
<td><p>-1</p></td>
<td><p>1</p></td>
<td><p>ffoot</p></td>
<td><p>hinge</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>Observations consist of positional values of different body parts of the
cheetah, followed by the velocities of those individual parts (their derivatives) with all the positions ordered before all the velocities.</p>
<p>By default, observations do not include the x-coordinate of the cheetahs center of mass. It may
be included by passing <code class="docutils literal notranslate"><span class="pre">exclude_current_positions_from_observation=False</span></code> during construction.
In that case, the observation space will have 18 dimensions where the first dimension
represents the x-coordinate of the cheetahs center of mass.
Regardless of whether <code class="docutils literal notranslate"><span class="pre">exclude_current_positions_from_observation</span></code> was set to true or false, the x-coordinate
will be returned in <code class="docutils literal notranslate"><span class="pre">info</span></code> with key <code class="docutils literal notranslate"><span class="pre">&quot;x_position&quot;</span></code>.</p>
<p>However, by default, 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">(17,)</span></code> where the elements correspond to the following:</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>Unit</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>0</p></td>
<td><p>z-coordinate of the front tip</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>rootz</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>angle of the front tip</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>rooty</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>angle of the second rotor</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>bthigh</p></td>
<td><p>hinge</p></td>
<td><p>angle (rad)</p></td>
</tr>
<tr class="row-odd"><td><p>3</p></td>
<td><p>angle of the second rotor</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>bshin</p></td>
<td><p>hinge</p></td>
<td><p>angle (rad)</p></td>
</tr>
<tr class="row-even"><td><p>4</p></td>
<td><p>velocity of the tip along the x-axis</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>bfoot</p></td>
<td><p>hinge</p></td>
<td><p>angle (rad)</p></td>
</tr>
<tr class="row-odd"><td><p>5</p></td>
<td><p>velocity of the tip along the y-axis</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>fthigh</p></td>
<td><p>hinge</p></td>
<td><p>angle (rad)</p></td>
</tr>
<tr class="row-even"><td><p>6</p></td>
<td><p>angular velocity of front tip</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>fshin</p></td>
<td><p>hinge</p></td>
<td><p>angle (rad)</p></td>
</tr>
<tr class="row-odd"><td><p>7</p></td>
<td><p>angular velocity of second rotor</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>ffoot</p></td>
<td><p>hinge</p></td>
<td><p>angle (rad)</p></td>
</tr>
<tr class="row-even"><td><p>8</p></td>
<td><p>x-coordinate of the front tip</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>rootx</p></td>
<td><p>slide</p></td>
<td><p>velocity (m/s)</p></td>
</tr>
<tr class="row-odd"><td><p>9</p></td>
<td><p>y-coordinate of the front tip</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>rootz</p></td>
<td><p>slide</p></td>
<td><p>velocity (m/s)</p></td>
</tr>
<tr class="row-even"><td><p>10</p></td>
<td><p>angle of the front tip</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>rooty</p></td>
<td><p>hinge</p></td>
<td><p>angular velocity (rad/s)</p></td>
</tr>
<tr class="row-odd"><td><p>11</p></td>
<td><p>angle of the second rotor</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>bthigh</p></td>
<td><p>hinge</p></td>
<td><p>angular velocity (rad/s)</p></td>
</tr>
<tr class="row-even"><td><p>12</p></td>
<td><p>angle of the second rotor</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>bshin</p></td>
<td><p>hinge</p></td>
<td><p>angular velocity (rad/s)</p></td>
</tr>
<tr class="row-odd"><td><p>13</p></td>
<td><p>velocity of the tip along the x-axis</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>bfoot</p></td>
<td><p>hinge</p></td>
<td><p>angular velocity (rad/s)</p></td>
</tr>
<tr class="row-even"><td><p>14</p></td>
<td><p>velocity of the tip along the y-axis</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>fthigh</p></td>
<td><p>hinge</p></td>
<td><p>angular velocity (rad/s)</p></td>
</tr>
<tr class="row-odd"><td><p>15</p></td>
<td><p>angular velocity of front tip</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>fshin</p></td>
<td><p>hinge</p></td>
<td><p>angular velocity (rad/s)</p></td>
</tr>
<tr class="row-even"><td><p>16</p></td>
<td><p>angular velocity of second rotor</p></td>
<td><p>-Inf</p></td>
<td><p>Inf</p></td>
<td><p>ffoot</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="Permalink to this heading">#</a></h2>
<p>The reward consists of two parts:</p>
<ul class="simple">
<li><p><em>forward_reward</em>: A reward of moving forward which is measured
as <em><code class="docutils literal notranslate"><span class="pre">forward_reward_weight</span></code> * (x-coordinate before action - x-coordinate after action)/dt</em>. <em>dt</em> is
the time between actions and is dependent on the frame_skip parameter
(fixed to 5), where the frametime is 0.01 - making the
default <em>dt = 5 * 0.01 = 0.05</em>. This reward would be positive if the cheetah
runs forward (right).</p></li>
<li><p><em>ctrl_cost</em>: A cost for penalising the cheetah if it takes
actions that are too large. It is measured as <em><code class="docutils literal notranslate"><span class="pre">ctrl_cost_weight</span></code> *
sum(action<sup>2</sup>)</em> where <em><code class="docutils literal notranslate"><span class="pre">ctrl_cost_weight</span></code></em> is a parameter set for the
control and has a default value of 0.1</p></li>
</ul>
<p>The total reward returned is <em><strong>reward</strong></em> <em>=</em> <em>forward_reward - ctrl_cost</em> and <code class="docutils literal notranslate"><span class="pre">info</span></code> will also contain the individual reward terms</p>
</section>
<section id="starting-state">
<h2>Starting State<a class="headerlink" href="#starting-state" title="Permalink to this heading">#</a></h2>
<p>All observations start in state (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,) with a noise added to the
initial state for stochasticity. As seen before, the first 8 values in the
state are positional and the last 9 values are velocity. A uniform noise in
the range of [-<code class="docutils literal notranslate"><span class="pre">reset_noise_scale</span></code>, <code class="docutils literal notranslate"><span class="pre">reset_noise_scale</span></code>] is added to the positional values while a standard
normal noise with a mean of 0 and standard deviation of <code class="docutils literal notranslate"><span class="pre">reset_noise_scale</span></code> is added to the
initial velocity values of all zeros.</p>
</section>
<section id="episode-end">
<h2>Episode End<a class="headerlink" href="#episode-end" title="Permalink to this heading">#</a></h2>
<p>The episode truncates when the episode length is greater than 1000.</p>
</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 in v2 and lower.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">gymnasium</span> <span class="k">as</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">&#39;HalfCheetah-v2&#39;</span><span class="p">)</span>
</pre></div>
</div>
<p>v3 and v4 take <code class="docutils literal notranslate"><span class="pre">gymnasium.make</span></code> kwargs such as <code class="docutils literal notranslate"><span class="pre">xml_file</span></code>, <code class="docutils literal notranslate"><span class="pre">ctrl_cost_weight</span></code>, <code class="docutils literal notranslate"><span class="pre">reset_noise_scale</span></code>, etc.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">gymnasium</span> <span class="k">as</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">&#39;HalfCheetah-v4&#39;</span><span class="p">,</span> <span class="n">ctrl_cost_weight</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="o">....</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">&quot;half_cheetah.xml&quot;</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">forward_reward_weight</span></code></p></td>
<td><p><strong>float</strong></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">1.0</span></code></p></td>
<td><p>Weight for <em>forward_reward</em> term (see section on reward)</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">ctrl_cost_weight</span></code></p></td>
<td><p><strong>float</strong></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">0.1</span></code></p></td>
<td><p>Weight for <em>ctrl_cost</em> weight (see section on reward)</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">0.1</span></code></p></td>
<td><p>Scale of random perturbations of initial position and velocity (see section on Starting State)</p></td>
</tr>
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">exclude_current_positions_from_observation</span></code></p></td>
<td><p><strong>bool</strong></p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">True</span></code></p></td>
<td><p>Whether or not to omit the x-coordinate from observations. Excluding the position can serve as an inductive bias to induce position-agnostic behavior in policies</p></td>
</tr>
</tbody>
</table>
</div>
</section>
<section id="version-history">
<h2>Version History<a class="headerlink" href="#version-history" title="Permalink to this heading">#</a></h2>
<ul class="simple">
<li><p>v4: all mujoco environments now use the mujoco bindings in mujoco&gt;=2.1.3</p></li>
<li><p>v3: support for <code class="docutils literal notranslate"><span class="pre">gymnasium.make</span></code> kwargs such as <code class="docutils literal notranslate"><span class="pre">xml_file</span></code>, <code class="docutils literal notranslate"><span class="pre">ctrl_cost_weight</span></code>, <code class="docutils literal notranslate"><span class="pre">reset_noise_scale</span></code>, etc. rgb rendering comes from tracking camera (so agent does not run away from screen)</p></li>
<li><p>v2: All continuous control environments now use mujoco_py &gt;= 1.50</p></li>
<li><p>v1: max_time_steps raised to 1000 for robot based tasks. Added reward_threshold to environments.</p></li>
<li><p>v0: Initial versions release (1.0.0)</p></li>
</ul>
</section>
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<li><a class="reference internal" href="#">Half Cheetah</a><ul>
<li><a class="reference internal" href="#description">Description</a></li>
<li><a class="reference internal" href="#action-space">Action Space</a></li>
<li><a class="reference internal" href="#observation-space">Observation Space</a></li>
<li><a class="reference internal" href="#rewards">Rewards</a></li>
<li><a class="reference internal" href="#starting-state">Starting State</a></li>
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