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<article role="main">
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<section id="hopper">
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<h1>Hopper<a class="headerlink" href="#hopper" title="Permalink to this heading">#</a></h1>
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<figure class="align-default" id="id1">
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<a class="reference internal image-reference" href="../../../_images/hopper.gif"><img alt="../../../_images/hopper.gif" src="../../../_images/hopper.gif" style="width: 200px;" /></a>
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</figure>
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<p>This environment is part of the Mujoco environments which contains general information about the environment.</p>
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<div class="table-wrapper colwidths-auto docutils container">
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<table class="docutils align-default">
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<thead>
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<tr class="row-odd"><th class="head"><p></p></th>
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<th class="head"><p></p></th>
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</tr>
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</thead>
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<tbody>
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<tr class="row-even"><td><p>Action Space</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">Box(-1.0,</span> <span class="pre">1.0,</span> <span class="pre">(3,),</span> <span class="pre">float32)</span></code></p></td>
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</tr>
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<tr class="row-odd"><td><p>Observation Space</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">Box(-inf,</span> <span class="pre">inf,</span> <span class="pre">(11,),</span> <span class="pre">float64)</span></code></p></td>
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</tr>
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<tr class="row-even"><td><p>import</p></td>
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<td><p><code class="docutils literal notranslate"><span class="pre">gymnasium.make("Hopper-v4")</span></code></p></td>
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</tr>
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</tbody>
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</table>
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</div>
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<section id="description">
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<h2>Description<a class="headerlink" href="#description" title="Permalink to this heading">#</a></h2>
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<p>This environment is based on the work done by Erez, Tassa, and Todorov in
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<a class="reference external" href="http://www.roboticsproceedings.org/rss07/p10.pdf">“Infinite Horizon Model Predictive Control for Nonlinear Periodic Tasks”</a>. The environment aims to
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increase the number of independent state and control variables as compared to
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the classic control environments. The hopper is a two-dimensional
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one-legged figure that consist of four main body parts - the torso at the
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top, the thigh in the middle, the leg in the bottom, and a single foot on
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which the entire body rests. The goal is to make hops that move in the
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forward (right) direction by applying torques on the three hinges
|
|
connecting the four body parts.</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">(3,),</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 thigh rotor</p></td>
|
|
<td><p>-1</p></td>
|
|
<td><p>1</p></td>
|
|
<td><p>thigh_joint</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 leg rotor</p></td>
|
|
<td><p>-1</p></td>
|
|
<td><p>1</p></td>
|
|
<td><p>leg_joint</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 foot rotor</p></td>
|
|
<td><p>-1</p></td>
|
|
<td><p>1</p></td>
|
|
<td><p>foot_joint</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
|
|
hopper, 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 hopper. 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 12 dimensions where the first dimension
|
|
represents the x-coordinate of the hopper.
|
|
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">"x_position"</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">(11,)</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 top (height of hopper)</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 top</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 thigh joint</p></td>
|
|
<td><p>-Inf</p></td>
|
|
<td><p>Inf</p></td>
|
|
<td><p>thigh_joint</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 leg joint</p></td>
|
|
<td><p>-Inf</p></td>
|
|
<td><p>Inf</p></td>
|
|
<td><p>leg_joint</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>angle of the foot joint</p></td>
|
|
<td><p>-Inf</p></td>
|
|
<td><p>Inf</p></td>
|
|
<td><p>foot_joint</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 x-coordinate of the top</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-even"><td><p>6</p></td>
|
|
<td><p>velocity of the z-coordinate (height) of the top</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-odd"><td><p>7</p></td>
|
|
<td><p>angular velocity of the angle of the top</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-even"><td><p>8</p></td>
|
|
<td><p>angular velocity of the thigh hinge</p></td>
|
|
<td><p>-Inf</p></td>
|
|
<td><p>Inf</p></td>
|
|
<td><p>thigh_joint</p></td>
|
|
<td><p>hinge</p></td>
|
|
<td><p>angular velocity (rad/s)</p></td>
|
|
</tr>
|
|
<tr class="row-odd"><td><p>9</p></td>
|
|
<td><p>angular velocity of the leg hinge</p></td>
|
|
<td><p>-Inf</p></td>
|
|
<td><p>Inf</p></td>
|
|
<td><p>leg_joint</p></td>
|
|
<td><p>hinge</p></td>
|
|
<td><p>angular velocity (rad/s)</p></td>
|
|
</tr>
|
|
<tr class="row-even"><td><p>10</p></td>
|
|
<td><p>angular velocity of the foot hinge</p></td>
|
|
<td><p>-Inf</p></td>
|
|
<td><p>Inf</p></td>
|
|
<td><p>foot_joint</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 three parts:</p>
|
|
<ul class="simple">
|
|
<li><p><em>healthy_reward</em>: Every timestep that the hopper is healthy (see definition in section “Episode Termination”), it gets a reward of fixed value <code class="docutils literal notranslate"><span class="pre">healthy_reward</span></code>.</p></li>
|
|
<li><p><em>forward_reward</em>: A reward of hopping 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 4), where the frametime is 0.002 - making the
|
|
default <em>dt = 4 * 0.002 = 0.008</em>. This reward would be positive if the hopper
|
|
hops forward (positive x direction).</p></li>
|
|
<li><p><em>ctrl_cost</em>: A cost for penalising the hopper 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 0.001</p></li>
|
|
</ul>
|
|
<p>The total reward returned is <em><strong>reward</strong></em> <em>=</em> <em>healthy_reward + 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, 1.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) with 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>] added to the values for stochasticity.</p>
|
|
</section>
|
|
<section id="episode-end">
|
|
<h2>Episode End<a class="headerlink" href="#episode-end" title="Permalink to this heading">#</a></h2>
|
|
<p>The hopper is said to be unhealthy if any of the following happens:</p>
|
|
<ol class="arabic simple">
|
|
<li><p>An element of <code class="docutils literal notranslate"><span class="pre">observation[1:]</span></code> (if <code class="docutils literal notranslate"><span class="pre">exclude_current_positions_from_observation=True</span></code>, else <code class="docutils literal notranslate"><span class="pre">observation[2:]</span></code>) is no longer contained in the closed interval specified by the argument <code class="docutils literal notranslate"><span class="pre">healthy_state_range</span></code></p></li>
|
|
<li><p>The height of the hopper (<code class="docutils literal notranslate"><span class="pre">observation[0]</span></code> if <code class="docutils literal notranslate"><span class="pre">exclude_current_positions_from_observation=True</span></code>, else <code class="docutils literal notranslate"><span class="pre">observation[1]</span></code>) is no longer contained in the closed interval specified by the argument <code class="docutils literal notranslate"><span class="pre">healthy_z_range</span></code> (usually meaning that it has fallen)</p></li>
|
|
<li><p>The angle (<code class="docutils literal notranslate"><span class="pre">observation[1]</span></code> if <code class="docutils literal notranslate"><span class="pre">exclude_current_positions_from_observation=True</span></code>, else <code class="docutils literal notranslate"><span class="pre">observation[2]</span></code>) is no longer contained in the closed interval specified by the argument <code class="docutils literal notranslate"><span class="pre">healthy_angle_range</span></code></p></li>
|
|
</ol>
|
|
<p>If <code class="docutils literal notranslate"><span class="pre">terminate_when_unhealthy=True</span></code> is passed during construction (which is the default),
|
|
the episode ends when any of the following happens:</p>
|
|
<ol class="arabic simple">
|
|
<li><p>Truncation: The episode duration reaches a 1000 timesteps</p></li>
|
|
<li><p>Termination: The hopper is unhealthy</p></li>
|
|
</ol>
|
|
<p>If <code class="docutils literal notranslate"><span class="pre">terminate_when_unhealthy=False</span></code> is passed, the episode is ended only when 1000 timesteps are exceeded.</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">'Hopper-v2'</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">'Hopper-v4'</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">"hopper.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">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">0.001</span></code></p></td>
|
|
<td><p>Weight for <em>ctrl_cost</em> reward (see section on reward)</p></td>
|
|
</tr>
|
|
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">healthy_reward</span></code></p></td>
|
|
<td><p><strong>float</strong></p></td>
|
|
<td><p><code class="docutils literal notranslate"><span class="pre">1</span></code></p></td>
|
|
<td><p>Constant reward given if the ant is “healthy” after timestep</p></td>
|
|
</tr>
|
|
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">terminate_when_unhealthy</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>If true, issue a done signal if the hopper is no longer healthy</p></td>
|
|
</tr>
|
|
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">healthy_state_range</span></code></p></td>
|
|
<td><p><strong>tuple</strong></p></td>
|
|
<td><p><code class="docutils literal notranslate"><span class="pre">(-100,</span> <span class="pre">100)</span></code></p></td>
|
|
<td><p>The elements of <code class="docutils literal notranslate"><span class="pre">observation[1:]</span></code> (if <code class="docutils literal notranslate"><span class="pre">exclude_current_positions_from_observation=True</span></code>, else <code class="docutils literal notranslate"><span class="pre">observation[2:]</span></code>) must be in this range for the hopper to be considered healthy</p></td>
|
|
</tr>
|
|
<tr class="row-even"><td><p><code class="docutils literal notranslate"><span class="pre">healthy_z_range</span></code></p></td>
|
|
<td><p><strong>tuple</strong></p></td>
|
|
<td><p><code class="docutils literal notranslate"><span class="pre">(0.7,</span> <span class="pre">float("inf"))</span></code></p></td>
|
|
<td><p>The z-coordinate must be in this range for the hopper to be considered healthy</p></td>
|
|
</tr>
|
|
<tr class="row-odd"><td><p><code class="docutils literal notranslate"><span class="pre">healthy_angle_range</span></code></p></td>
|
|
<td><p><strong>tuple</strong></p></td>
|
|
<td><p><code class="docutils literal notranslate"><span class="pre">(-0.2,</span> <span class="pre">0.2)</span></code></p></td>
|
|
<td><p>The angle given by <code class="docutils literal notranslate"><span class="pre">observation[1]</span></code> (if <code class="docutils literal notranslate"><span class="pre">exclude_current_positions_from_observation=True</span></code>, else <code class="docutils literal notranslate"><span class="pre">observation[2]</span></code>) must be in this range for the hopper to be considered healthy</p></td>
|
|
</tr>
|
|
<tr class="row-even"><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">5e-3</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-odd"><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 >= 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 >= 1.50</p></li>
|
|
<li><p>v1: max_time_steps raised to 1000 for robot based tasks. Added reward_threshold to environments.</p></li>
|
|
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