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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<meta name="description" content="SPI-Active">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Sampling-Based System Identification with Active Exploration for Legged Robot Sim2Real Learning</title>
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<section class="hero">
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<h1 class="title is-1 publication-title">Sampling-Based System Identification with Active Exploration for Legged Robot Sim2Real Learning </h1>
<div class="is-size-4 publication-authors">
<span class="author-block" style="font-size: 95%;">
<a href="https://nike353.github.io/">Nikhil Sobanbabu*</a>
<a href="https://guanqihe.github.io/">Guanqi He*</a>
<a href="https://tairanhe.com/">Tairan He</a>
<a href="https://yxyang.github.io/">Yuxiang Yang</a>
<a href="https://www.gshi.me/">Guanya Shi</a>
</span>
</div>
<div class="is-size-3 publication-authors">
<!-- make a Italic font -->
<i style="color:rgb(0, 0, 0);">Conference on Robot Learning (CoRL) 2025 (ORAL)</i>
</div>
<div class="column">
<image src="./static/images/ip.png" style="width: 60%;"></image>
</div>
<!-- <div class="is-size-4 publication-authors">
<b style="color:rgb(255, 100, 100);">Best Systems Paper Award Finalist (top 3)</b>
</div> -->
<div class="column has-text-centered">
<div class="publication-links">
<!-- PDF Link. -->
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<a href="./static/pdf/spi_active_arxiv.pdf"
class="external-link button is-normal is-rounded is-dark" target="_blank">
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<i class="fas fa-file-pdf"></i>
</span>
<span>Paper</span>
</a>
</span>
<!-- arXiv Link. -->
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<a href="https://arxiv.org/abs/2505.14266"
class="external-link button is-normal is-rounded is-dark" target="_blank">
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<i class="ai ai-arxiv"></i>
</span>
<span>ArXiv</span>
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<a href=""
class="external-link button is-normal is-rounded is-dark" target="_blank">
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</span>
<span>Summary</span>
</a>
</span>
<!-- Video Link. -->
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<a href="https://youtu.be/pxyig4D1ZFs"
class="external-link button is-normal is-rounded is-dark" target="_blank">
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</span>
<span>Video</span>
</a>
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<!-- Code Link. -->
<span class="link-block">
<a href="https://github.com/LeCAR-Lab/SPI-Active"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<i class="fab fa-github"></i>
</span>
<span>Code</span>
</a>
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</div>
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</div>
</div>
</section>
<!-- <section class="section"> -->
<!-- add video -->
<!-- <div class="container is-max-desktop">
<video controls autoplay loop muted playsinline
src="./static/videos/teaser.mp4" poster="./resources/loading-icon.gif"
style="border: 1px solid #bbb; border-radius: 10px; margin: 1.0%;"
type="video/mp4">
</video>
</div>
</section> -->
<section class="section">
<div class="container is-max-desktop">
<!-- Abstract. -->
<div class="columns is-centered has-text-centered">
<div class="column is-12">
<h2 class="title is-2">Abstract</h2>
<div class="content has-text-justified">
<p> Sim-to-real discrepancies hinder learning-based policies from achieving high-precision tasks in the real world.
While Domain Randomization (DR) is commonly used to bridge this gap,
it often relies on heuristics and can lead to overly conservative policies with degrading performance when not properly tuned.
System Identification (Sys-ID) offers a targeted approach, but standard techniques rely on differentiable dynamics and/or direct torque measurement,
assumptions that rarely hold for contact-rich legged systems. To this end, we present Sampling-based Parameter Identification with Active Exploration (SPI-Active),
a two-stage framework that estimates physical parameters of legged robots to minimize the sim-to-real gap.
SPI-Active robustly identifies key physical parameters through massive parallel sampling,
minimizing state prediction errors between simulated and real-world trajectories.
To further improve the informativeness of collected data,
we introduce an active exploration strategy that maximizes the Fisher Information of the collected real-world trajectories via optimizing the input commands of an exploration policy.
This targeted exploration leads to accurate identification and better generalization across diverse tasks.
Experimental results demonstrate that SPI-Active enables precise sim-to-real transfer of learned policies to the real world,
outperforming baselines by 42-63% in various locomotion tasks.
</p>
</div>
</div>
</div>
<!--/ Abstract. -->
</section>
<section class="section">
<div class="container">
<h2 class="title is-2" style="text-align: center;">Method</h2>
<div class="columns is-centered has-text-centered">
<div class="column is-two-thirds">
<div class="content has-text-justified">
<p>
<span class="method" style="color: green;">SPI-Active</span> is a two-stage framework that estimates physical parameters of legged robots to minimize the sim-to-real gap. It involves data collection of real-world trajectories using RL policies or motion priors and subsequently estimating the desired parameters using sampling-based optimization. Further, the stage 1 parameters are refined by optimizing input commands of a multi-behavioral policy to maximize Fisher Information and gather informative data. Training with identified parameters from <span class="method" style="color: green;">SPI-Active</span> leads to improved sim-to-real transfer in downstream tasks.
</p>
</div>
</div>
</div>
<!-- <h2 class="title is-4" style="text-align: center;">Training Framework</h2> -->
<div class="columns is-centered has-text-centered">
<div class="column is-three-thirds">
<div class="content has-text-justified">
<!-- <ol type="a">
There are two steps within the <span class="method" style="color: darkred;">FALCON</span> framework:
<ol>
<li><strong>Two-Agent Joint Training with Whole-Body Proprioception</strong>: <br>Two agents, each assigned distinct sub-tasks, are jointly trained using shared whole-body proprioception signals. During training, randomized 3D external forces—bounded by the upper-body joint torque limits—are applied to the end-effectors to encourage robust coordination;</li>
<li><strong>External Disturbance Handling via Force Perturbation</strong><br> The agents learn to maintain task performance under force perturbations, developing complementary behaviors to counteract disturbances and achieve stable loco-manipulation.</li>
</ol> -->
</div>
</div>
</div>
<div class="columns is-centered">
<div class="column is-two-thirds has-text-centered">
<img src="./static/images/pipeline_1.png" alt="" style="width: 100%;" />
</div>
</div>
<!-- <h2 class="title is-2" style="text-align: center;">Experiment Results</h2> -->
<section class="section">
<div class="container">
<div class="columns is-centered">
<div class="column is-full-width">
<h2 class="title is-2" style="text-align: center; padding-bottom: 10px;">
Performance in Sim-to-real Locomotion Tasks
</h2>
<p class="content is-medium" style="text-align: center; padding-bottom: 20px;">
We compare the real-world performance of <strong style="color: green; font-weight: 800;">SPI-Active</strong> with <strong style="color: #e63946; font-weight: 800;">Vanilla</strong> baseline on the following tasks: <b>Forward Jump</b>, <b>Yaw Jump</b>, <b>Velocity Tracking</b>and <b>Attitude Tracking</b>.
</p>
<tr>
<td>
<div class="columns">
<div class="column">
<h3 class="title is-3" style="text-align: center; margin-bottom: 10px; font-size: x-large;">Forward Jump (Vanilla)</h3>
<video autoplay muted loop playsinline controls preload="auto" src="./static/videos/fj_vanilla.mp4" width="100%" style="border-radius:10px; border: 5px solid rgb(236, 136, 134);"></video>
</div>
<div class="column">
<h3 class="title is-3" style="text-align: center; margin-bottom: 10px; font-size: x-large;">Forward Jump (SPI-Active)</h3>
<video autoplay muted loop playsinline controls preload="auto" src="./static/videos/fj_spi-active.mp4" width="100%" style="border-radius:10px; border: 5px solid rgb(56, 182, 60);"></video>
</div>
</div>
<div class="columns">
<div class="column" style="text-align: center;">
<h3 class="title is-3" style="margin-bottom: 10px; font-size: x-large;">Yaw Jump (vanilla)</h3>
<video autoplay muted loop playsinline controls preload="auto"
src="./static/videos/yj_vanilla.mp4"
width="100%"
style="border-radius:10px; border: 5px solid rgb(236, 136, 134);">
</video>
</div>
<div class="column" style="text-align: center;">
<h3 class="title is-3" style="margin-bottom: 10px; font-size: x-large;">Yaw Jump (SPI-Active)</h3>
<video autoplay muted loop playsinline controls preload="auto"
src="./static/videos/yj_spi-active.mp4"
width="100%"
style="border-radius:10px; border: 5px solid rgb(56, 182, 60);">
</video>
</div>
</div>
<br>
<div class="columns is-desktop">
<!-- Column 1: Two vertically stacked videos -->
<div class="column">
<h3 class="title is-4" style="text-align: center;">Velocity Tracking (Vanilla)</h3>
<video class="sync-group-1" autoplay muted loop playsinline controls preload="auto"
src="./static/videos/vt_vanilla.mp4"
width="100%" style="border-radius:10px; border: 5px solid rgb(255, 114, 112); margin-bottom: 10px;"></video>
<!-- <h3 class="title is-4" style="text-align: center;">Task B (Baseline)</h3> -->
<!-- Second video: 80% width, centered -->
<div style="display: flex; justify-content: center;">
<video class="sync-group-2" autoplay muted loop playsinline controls preload="auto"
src="./static/videos/vt_vanilla_anim.mp4"
width="60%"
style="border-radius:10px; border: 5px solid rgb(255, 114, 112);">
</video>
</div>
</div>
<!-- Column 2: Two vertically stacked videos -->
<div class="column">
<h3 class="title is-4" style="text-align: center;">Velocity Tracking (SPI-Active)</h3>
<!-- First video: full width -->
<video class="sync-group-2" autoplay muted loop playsinline controls preload="auto"
src="./static/videos/vt_spi-active.mp4"
width="100%"
style="border-radius:10px; border: 5px solid rgb(134, 236, 137); margin-bottom: 10px;">
</video>
<!-- Second video: 80% width, centered -->
<div style="display: flex; justify-content: center;">
<video class="sync-group-2" autoplay muted loop playsinline controls preload="auto"
src="./static/videos/vt_spi-active_anim.mp4"
width="60%"
style="border-radius:10px; border: 5px solid rgb(134, 236, 137);">
</video>
</div>
</div>
</div>
<div class="columns is-desktop">
<!-- Column 1: Two vertically stacked videos -->
<div class="column">
<h3 class="title is-4" style="text-align: center;">Attitude Tracking (Vanilla)</h3>
<video class="sync-group-1" autoplay muted loop playsinline controls preload="auto"
src="./static/videos/rp_vanilla.mp4"
width="100%" style="border-radius:10px; border: 5px solid rgb(255, 114, 112); margin-bottom: 10px;"></video>
<!-- <h3 class="title is-4" style="text-align: center;">Task B (Baseline)</h3> -->
<div style="display: flex; justify-content: center;">
<video class="sync-group-2" autoplay muted loop playsinline controls preload="auto"
src="./static/videos/rp_vanilla (online-video-cutter.com).mp4"
width="80%"
style="border-radius:10px; border: 5px solid rgb(255, 114, 112);">
</video>
</div>
</div>
<!-- Column 2: Two vertically stacked videos -->
<div class="column">
<h3 class="title is-4" style="text-align: center;">Attitude Tracking (SPI-Active)</h3>
<video class="sync-group-2" autoplay muted loop playsinline controls preload="auto"
src="./static/videos/rp_spi-active.mp4"
width="100%" style="border-radius:10px; border: 5px solid rgb(134, 236, 137); margin-bottom: 10px;"></video>
<!-- <h3 class="title is-4" style="text-align: center;">Task B (FALCON)</h3> -->
<div style="display: flex; justify-content: center;">
<video class="sync-group-2" autoplay muted loop playsinline controls preload="auto"
src="./static/videos/rp_spi-active (online-video-cutter.com) (1).mp4"
width="80%"
style="border-radius:10px; border: 5px solid rgb(134, 236, 137);">
</video>
</div>
</div>
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</td>
</tr>
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</section>
<section class="section">
<div class="container">
<div class="columns is-centered">
<div class="column is-full-width">
<h2 class="title is-2" style="text-align: center; padding-bottom: 10px;">
Generalization to Humanoids
</h2>
<tr>
<td>
<div class="columns">
<div class="column">
<h3 class="title is-3" style="text-align: center; margin-bottom: 10px; font-size: x-large;">Velocity Tracking (Vanilla)</h3>
<div style="display: flex; justify-content: center;">
<video autoplay muted loop playsinline controls preload="auto" src="./static/videos/vanilla.mp4" width="60%" style="border-radius:10px; border: 5px solid rgb(236, 136, 134);"></video>
</div>
</div>
<div class="column">
<h3 class="title is-3" style="text-align: center; margin-bottom: 10px; font-size: x-large;">Velocity Tracking (SPI-Active)</h3>
<div style="display: flex; justify-content: center;">
<video autoplay muted loop playsinline controls preload="auto" src="./static/videos/spi-active.mp4" width="60%" style="border-radius:10px; border: 5px solid rgb(56, 182, 60);"></video>
</div>
</div>
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</td>
</tr>
</div>
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</section>
<section class="section">
<div class="container">
<div class="columns is-centered">
<div class="column is-full-width">
<h2 class="title is-2" style="text-align: center; padding-bottom: 10px;">
Open-Loop Weave Pole Navigation
</h2>
<tr>
<td>
<div class="columns">
<div class="column">
<h3 class="title is-3" style="text-align: center; margin-bottom: 10px; font-size: x-large;">Vanilla</h3>
<div style="display: flex; justify-content: center;">
<video autoplay muted loop playsinline controls preload="auto" src="./static/videos/wpn_vanilla.mp4" width="100%" style="border-radius:10px; border: 5px solid rgb(236, 136, 134);"></video>
</div>
</div>
<div class="column">
<h3 class="title is-3" style="text-align: center; margin-bottom: 10px; font-size: x-large;">SPI-Active</h3>
<div style="display: flex; justify-content: center;">
<video autoplay muted loop playsinline controls preload="auto" src="./static/videos/wpn_spi-active.mp4" width="100%" style="border-radius:10px; border: 5px solid rgb(56, 182, 60);"></video>
</div>
</div>
</div>
</td>
</tr>
</div>
</div>
</div>
</section>
<section class="section">
<div class="container">
<div class="columns is-centered">
<div class="column is-full-width">
<h2 class="title is-2" style="text-align: center; padding-bottom: 10px;">
Data Collection with Active Exploration
</h2>
<!-- <p class="content is-medium" style="text-align: center; padding-bottom: 20px;">
Accurate parameter identification using <strong style="color: green; font-weight: 800;">SPI-Active</strong> enables the quadruped to perform high-speed open-loop navigation across narrow poles.
</p> -->
<tr>
<td>
<div class="columns is-vcentered">
<!-- Left: Centered video -->
<div class="column is-half" style="display: flex; justify-content: center; align-items: center;">
<video autoplay muted loop playsinline controls preload="auto"
src="./static/videos/active exploration.mp4"
style="border-radius:10px; border: 5px solid rgb(56, 182, 60); width: 100%; max-width: 640px; height: auto;">
</video>
</div>
<!-- Right: Two plots, no white spacing -->
<div class="column is-half" style="display: flex; flex-direction: column; justify-content: space-between;">
<img src="./static/images/velocity_variation.png"
alt="Velocity Commands Plot"
style="width: 100%; height: 350px; object-fit: contain; margin-bottom: 10px; border-radius: 10px;" />
<img src="./static/images/gait_variation.png"
alt="Gait Variation Plot"
style="width: 100%; height: 220px; object-fit: contain; border-radius: 10px;" />
</div>
</div>
</td>
</tr>
</div>
</div>
</div>
</section>
<section class="section" id="BibTeX">
<div class="container content">
<h2 class="titile">BibTeX</h2>
<pre><code>@InProceedings{pmlr-v305-sobanbabu25a,
title = {Sampling-based System Identification with Active Exploration for Legged Sim2Real Learning},
author = {Sobanbabu, Nikhil and He, Guanqi and He, Tairan and Yang, Yuxiang and Shi, Guanya},
booktitle = {Proceedings of The 9th Conference on Robot Learning},
pages = {578--598},
year = {2025},
editor = {Lim, Joseph and Song, Shuran and Park, Hae-Won},
volume = {305},
series = {Proceedings of Machine Learning Research},
month = {27--30 Sep},
publisher = {PMLR},
pdf = {https://raw.githubusercontent.com/mlresearch/v305/main/assets/sobanbabu25a/sobanbabu25a.pdf},
url = {https://proceedings.mlr.press/v305/sobanbabu25a.html},
}
}</code></pre>
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