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<meta name="description" content="Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots">
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<h1 class="title is-1 publication-title">Minimizing Energy Consumption Leads to the<br />Emergence of Gaits in Legged Robots</h1>
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="https://markfzp.github.io/">Zipeng Fu</a><sup>1</sup>
<a href="https://ashish-kmr.github.io/">Ashish Kumar</a><sup>2</sup>
<a href="https://people.eecs.berkeley.edu/~malik/">Jitendra Malik</a><sup>2</sup>
<a href="https://www.cs.cmu.edu/~dpathak/">Deepak Pathak</a><sup>1</sup>
<br /><sup>1</sup>Carnegie Mellon University <sup>2</sup>UC Berkeley
<span class="brmod">CoRL 2021</span>
</span>
</div>
<div class="column has-text-centered">
<div class="publication-links">
<!-- PDF Link. -->
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<a href="./resources/CoRL-Energy-Locomotion.pdf"
class="external-link button is-normal is-rounded is-dark">
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<i class="fas fa-file-pdf"></i>
</span>
<span>Paper</span>
</a>
</span>
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<a href="#method_video"
class="external-link button is-normal is-rounded is-dark">
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<span>Video</span>
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</div>
</div>
</section>
<section class="hero teaser">
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<video autoplay muted loop playsinline height="100%" src="./resources/teaser.mp4"></video>
</div>
<h2 class="subtitle has-text-centered">
Walking, trotting and bouncing (galloping) gaits in real world emerge from learning fully in simulation by minimizing the energy consumption <strong>without any human priors about gaits</strong>.
</h2>
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<section class="section">
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<!-- Abstract. -->
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<h2 class="title is-2">Abstract</h2>
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<p>
Legged locomotion is commonly studied and expressed as a discrete set of gait patterns, like walk, trot, gallop, which are usually treated as given and pre-programmed in legged robots for efficient locomotion at different speeds. However, fixing a set of pre-programmed gaits limits the generality of locomotion. Recent animal motor studies show that these conventional gaits are only prevalent in ideal flat terrain conditions while real-world locomotion is unstructured and more like bouts of intermittent steps. What principles could lead to both structured and unstructured patterns across mammals and how to synthesize them in robots? In this work, we take an analysis-by-synthesis approach and learn to move by minimizing mechanical energy. We demonstrate that learning to minimize energy consumption is sufficient for the emergence of natural locomotion gaits at different speeds in real quadruped robots. The emergent gaits are structured in ideal terrains and look similar to that of horses and sheep. The same approach leads to unstructured gaits in rough terrains which is consistent with the findings in animal motor control. We validate our hypothesis in both simulation and real hardware across natural terrains.
</p>
</div>
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</div>
<!--/ Abstract. -->
<!-- Paper video. -->
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<h2 class="title is-2">Project Video</h2>
<div class="publication-video">
<iframe src="https://www.youtube.com/embed/OQN5W2IAb9k"
frameborder="0" allow="autoplay; encrypted-media" allowfullscreen></iframe>
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<!--/ Paper video. -->
</section>
<section class="section">
<div class="container">
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<h2 class="title is-2" style="text-align: center;">Gait Transition via a Velocity-Conditioned Policy</h2>
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<td>
<br>
<div class="columns is-centered has-text-centered">
<video autoplay loop muted playsinline src="./resources/gait_transition.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 80%;"></video>
</div>
</td>
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<br><br>
<div class="columns is-centered">
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<h2 class="title is-2" style="text-align: center;">Similar Energy Consumption Trend<br \>between Our Robot and Horses</h2>
<div class="is-vcentered interpolation-panel">
<div class="content has-text-centered">
<!-- <img style="width: 1.5%;" src="./resources/divider.png"> -->
<img style="border: 1px solid #bbb; border-radius: 10px; width: 36.75%;" src="./resources/horse.png"> <img style="border: 1px solid #bbb; border-radius: 10px; width: 40%;" src="./resources/mpc_energy.png">
</div>
<div class="content has-text-centered">
<p>
In Biomechanics, Froude number is a metric characterizing gaits of quadrupeds and bipeds. Animals with a similar morphology but with different sizes tend to use the same gait when moving with equal Froude numbers. Our robot has similar Froude numbers as horses and sheep. The plot on the left <strong>(Hoyt et al. 1981)</strong> analyzes the energy consumption of different horse gaits across different speeds. Shown on the right, the energy consumption plot of our robot has a similar trend, which also validates certain gaits will emerge at certain speeds if we minimize the energy consumption.
</p>
</div>
</div>
<br>
<div class="is-vcentered interpolation-panel">
<div class="content has-text-centered">
<video autoplay loop muted playsinline src="./resources/gait_comparison.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 80%;"></video>
</div>
<div class="content has-text-centered">
<p>
Foot Contact Plots of Walking, Trotting, Bouncing (Galloping)
</p>
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</div>
</div>
<br><br>
<div class="columns is-centered">
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<h2 class="title is-2" style="text-align: center;">More Examples of Emergent Structured Gaits <br> (Walk, Trot & Bounce)</h2>
<tr>
<td>
<br><h3 class="title is-4">Walking Gait (0.375 m/s): </h3><br>
<div class="columns is-centered has-text-centered">
<video autoplay loop muted playsinline src="./resources/walk_trench.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 33%;"></video>
<video autoplay loop muted playsinline src="./resources/walk_payload.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 33%;"></video>
<video autoplay loop muted playsinline src="./resources/walk_brush.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 33%;"></video>
</div>
</td>
</tr>
<tr>
<td>
<br><h3 class="title is-4">Trotting Gait (0.9 m/s): </h3><br>
<div class="columns is-centered has-text-centered">
<video autoplay loop muted playsinline src="./resources/trot_trench.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 33%;"></video>
<video autoplay loop muted playsinline src="./resources/trot_payload.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 33%;"></video>
<video autoplay loop muted playsinline src="./resources/trot_brush.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 33%;"></video>
</div>
</td>
</tr>
<tr>
<td>
<br><h3 class="title is-4">Bouncing (Galloping) Gait (1.5 m/s): </h3><br>
<div class="columns is-centered has-text-centered">
<video autoplay loop muted playsinline src="./resources/bounce_pull.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 50%;"></video>
<video autoplay loop muted playsinline src="./resources/bounce_pull_slomo.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 50%;"></video>
</div>
<br />
<div class="columns is-centered has-text-centered">
<video autoplay loop muted playsinline src="./resources/bounce_slomo.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 50%;"></video>
<video autoplay loop muted playsinline src="./resources/bounce_trench.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 50%;"></video>
</div>
</td>
</tr>
<!-- <tr>
<td>
<br><h3 class="title is-4">Gait Transition via a Velocity-Conditioned Policy: </h3><br>
<div class="columns is-centered has-text-centered">
<video autoplay loop muted playsinline src="./resources/gait_transition.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 80%;"></video>
</div>
</td>
</tr> -->
<br/>
</div>
</div>
<div class="columns is-centered">
<div class="column is-full-width">
<h2 class="title is-2" style="text-align: center;">Emergent Unstructured Gaits</h2>
<tr>
<td>
<br>
<div class="columns is-centered has-text-centered v-divider">
<video autoplay loop muted playsinline src="./resources/rocky.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 50%;"></video>
<video autoplay loop muted playsinline src="./resources/plank.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 50%;"></video>
</div>
<br />
<div class="columns is-centered has-text-centered v-divider">
<video autoplay loop muted playsinline src="./resources/unstructured-indoor-1.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 50%;"></video>
<video autoplay loop muted playsinline src="./resources/unstructured-indoor-2.mp4" style="border: 1px solid #bbb; border-radius: 10px; width: 50%;"></video>
</div>
</td>
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<br><br>
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</section>
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<h2 class="title is-2" style="text-align: center;">Related Work</h2>
<div class="content is-centered has-text-centered">
This work is part of our series of research on learning based control of legged robots. Please check out other works below.
</div>
<br><br>
<div class="container">
<div class="subtitle is-centered">
<table width="100%">
<tr>
<td width="100%">
<div style="float:left;margin-right:30px;margin-left:30px;">
<video autoplay loop muted src="resources/rma-clip.mp4" width="400"></video>
</div>
RMA: Rapid Motor Adaptation for Legged Robots <br/>
Ashish Kumar, Zipeng Fu, Deepak Pathak, Jitendra Malik <br/>
RSS 2021 <br/> <br/> <br/>
<a href="https://ashish-kmr.github.io/rma-legged-robots/rma-locomotion-final.pdf">PDF</a> |
<a href="https://www.youtube.com/watch?v=nBy1piJrq1A">Video</a> |
<a href="https://ashish-kmr.github.io/rma-legged-robots/">Project Page</a>
</tr>
</table>
</div>
<div class="subtitle is-centered">
<table width="100%">
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<div style="float:left;margin-right:30px;margin-left:30px;">
<video autoplay loop muted src="resources/nav-clip.mp4" width="400"></video>
</div>
Coupling Vision and Proprioception for Navigation of Legged Robots <br/>
Zipeng Fu*, Ashish Kumar*, Ananye Agarwal, Haozhi Qi, Jitendra Malik, Deepak Pathak <br/>
CVPR 2022 <br/> <br/> <br/>
<a href="https://navigation-locomotion.github.io/camera-ready/resources/navigation-locomotion.pdf">PDF</a> |
<a href="https://www.youtube.com/watch?v=sZVvutQUAQ4">Video</a> |
<a href="https://navigation-locomotion.github.io/">Project Page</a>
</tr>
</table>
</div>
</div>
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</div>
</section>
<section class="section" id="BibTeX">
<div class="container content">
<h2 class="titile">BibTeX</h2>
<pre><code>@inproceedings{fu2021minimizing,
author = {Fu, Zipeng and Kumar, Ashish and Malik, Jitendra and Pathak, Deepak},
title = {Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots},
booktitle = {Conference on Robot Learning ({CoRL})},
year = {2021},
}</code></pre>
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