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<html>
<head>
<meta charset="utf-8" />
<title>Push Anything</title>
<meta
content="With fast contact-implicit model predictive control, we demonstrate 'pushing anything' -- even multiple things -- with a robot arm in real time."
name="description" />
<meta content="Fast contact-implicit MPC can push anything." property="og:title" />
<meta
content="With fast contact-implicit model predictive control, we demonstrate 'pushing anything' -- even multiple things -- with a robot arm in real time."
name="description" property="og:description" />
<meta content="https://dairlab.github.io/push-anything/static/images/meta.png" property="og:image" />
<meta content="Fast contact-implicit MPC can push anything." property="twitter:title" />
<meta
content="With fast contact-implicit model predictive control, we demonstrate 'pushing anything' -- even multiple things -- with a robot arm in real time."
name="description" property="twitter:description" />
<meta content="https://dairlab.github.io/push-anything/static/images/meta.png" property="twitter:image" />
<meta property="og:type" content="website" />
<meta content="summary_large_image" name="twitter:card" />
<meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1" />
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<script src="https://ajax.googleapis.com/ajax/libs/webfont/1.6.26/webfont.js" type="text/javascript"></script>
<link href="https://fonts.googleapis.com/css?family=Google+Sans|Noto+Sans|Castoro" rel="stylesheet">
<script type="text/javascript">WebFont.load({
google: {
families: [
"Lato:100,100italic,300,300italic,400,400italic,700,700italic,900,900italic",
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</script>
<script src="script.js" type="text/javascript"></script>
<link href="style.css" rel="stylesheet" type="text/css" />
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
<!-- Favicon -->
<link rel="apple-touch-icon" sizes="180x180" href="../shared/images/apple-touch-icon.png">
<link rel="icon" type="image/png" sizes="32x32" href="../shared/images/favicon-32x32.png">
<link rel="icon" type="image/png" sizes="16x16" href="../shared/images/favicon-16x16.png">
<link rel="manifest" href="../shared/images/shared/images/site.webmanifest">
</head>
<body>
<div class="section">
<div class="container">
<br>
<h1 class="title main-title">Push Anything</h1>
<h2 class="title sub-title">Single- and Multi-Object Pushing
From First Sight with Contact-Implicit MPC</h2>
<br>
<br>
<div class="publication-authors" style="font-size:1.25rem;">
<span class="author-block">
<a href="https://hienbui.me" target="_blank">Hien
Bui</a><sup>*</sup>,</span>
<span class="author-block">
<a href="https://www.linkedin.com/in/yufeiyanggao/" target="_blank">Yufeiyang
Gao</a><sup>*</sup>,</span>
<span class="author-block">Haoran Yang<sup>*</sup>,</span>
<br>
<span class="author-block">
<a href="https://www.linkedin.com/in/eric-cui-296565171/" target="_blank">Eric Cui</a>,</span>
<span class="author-block">
<a href="https://www.linkedin.com/in/siddhant-mody/" target="_blank">Siddhant Mody</a>,</span>
<span class="author-block">
<a href="https://brianacosta.me/" target="_blank">Brian Acosta</a>,</span>
<span class="author-block">
<a href="https://meow404.github.io" target="_blank">Thomas Stephen
Felix</a>,</span>
<span class="author-block">
<a href="http://www.bianchini-love.com/bibit" target="_blank">Bibit Bianchini</a>,</span>
<span class="author-block">
<a href="https://dair.seas.upenn.edu" target="_blank">Michael Posa</a></span>
</div>
<br>
<div class="publication-authors" style="font-size:1.1rem; line-height:22px;">
<span class="author-block" style="display:block"><sup>*</sup>The
first three authors contributed equally to this work.</span>
<span class="author-block" style="display:block">University of
Pennsylvania</span>
</div>
<div class="accepted-for-publication"
style="display:block; font-size: x-large; font-weight: bold; margin-top: 1em;">Accepted for publication
in ICRA 2026</div>
<br>
<div class="link-labels base-row">
<div class="base-col icon-col">
<!-- <a href="TBD archive link" target="_blank"
class="link-block"> -->
<img src="https://uploads-ssl.webflow.com/51e0d73d83d06baa7a00000f/5cab99df4998decfbf9e218e_paper-01.png"
alt="paper"
sizes="(max-width: 479px) 12vw, (max-width: 767px) 7vw, (max-width: 991px) 41.8515625px, 56.6953125px"
srcset="https://uploads-ssl.webflow.com/51e0d73d83d06baa7a00000f/5cab99df4998decfbf9e218e_paper-01-p-500.png 500w, https://uploads-ssl.webflow.com/51e0d73d83d06baa7a00000f/5cab99df4998decfbf9e218e_paper-01.png 672w"
class="icon-img" />
<!-- </a> -->
</div>
<div class="base-col icon-col">
<!-- <a href="TBD dairlib branch/examples/sampling_c3#readme"
target="_blank" class="link-block"> -->
<img src="https://uploads-ssl.webflow.com/51e0d73d83d06baa7a00000f/5cae3b53b42ebb3dd4175a82_68747470733a2f2f7777772e69636f6e66696e6465722e636f6d2f646174612f69636f6e732f6f637469636f6e732f313032342f6d61726b2d6769746875622d3235362e706e67.png"
alt="code" class="icon-img github-img-icon" />
<!-- </a> -->
</div>
</div>
<div class="link-labels base-row">
<div class="base-col icon-col">
<strong class="link-labels-text"><a href="https://arxiv.org/abs/2510.19974"
target="_blank">Paper</a></strong>
</div>
<div class="base-col icon-col">
<strong class="link-labels-text">Code (coming soon)</strong>
</div>
</div>
<br>
<br>
<!-- Teaser video -->
<div class="base-row add-top-padding">
<video autobuffer muted autoplay loop preload="metadata">
<source id="mp4" src="./static/images/PushAnything_intro_small.mp4" type="video/mp4">
</video>
</div>
<h1 class="tldr">
<b>TL;DR</b>:
Our enhanced contact-implicit MPC (CI-MPC) algorithm, C3+,
enables contact-rich manipulation of single or multiple diverse
objects modeled with unprecedented numbers of contact pairs.
</h1>
<br>
<!-- Main video -->
<div class="base-row add-top-padding">
<h1 id="abstract">Overview Video</h1>
<video autobuffer controls muted preload="metadata" poster="./static/images/meta.png"
style="border: 1px solid #000000; border-radius: 15px;">
<source id="mp4" src="./static/images/PushAnything_overview_video.mp4" type="video/mp4">
</video>
</div>
<br>
<!-- Abstract -->
<div class="base-row add-top-padding">
<h1 id="abstract">Abstract</h1>
<p class="paragraph">
Non-prehensile manipulation of diverse objects remains a
core challenge in robotics, driven by unknown physical
properties and the complexity of contact-rich interactions.
Recent advances in contact-implicit model predictive control
(CI-MPC), with contact reasoning embedded within the
trajectory optimization, have shown promise in tackling the
task efficiently and robustly, yet demonstrations have been
limited to narrowly-curated examples. In this work, we
showcase the broader capabilities of CI-MPC through precise
planar pushing tasks over a wide range of object geometries,
including multi-object domains. These scenarios demand
reasoning over numerous inter-object and object-environment
contacts to strategically manipulate and de-clutter the
environment, challenges that were intractable for prior
CI-MPC methods. To achieve this, we introduce Consensus
Complementarity Control Plus (C3+), an enhanced CI-MPC
algorithm integrated into a complete pipeline spanning
object scanning, mesh reconstruction, and hardware
execution. Compared to <a href="https://arxiv.org/abs/2304.11259">its predecessor C3
</a>, C3+ achieves
substantially faster solve times, enabling real-time
performance even in multi-object pushing tasks. On hardware,
our system achieves overall 98% success rate across 33
objects, reaching pose goals within tight tolerances. The
average time-to-goal is approximately 0.5, 1.6, 3.2, and
5.3 minutes for 1-, 2-, 3-, and 4-object tasks,
respectively.
</p>
</div>
<br>
<div class="base-row add-top-padding">
<h1 id="abstract">Uncut Single Object Manipulation Videos (1X speed)</h1>
<h2>Tight tolerances: 2cm, 0.1rad (5.7 degrees)</h2>
<br>
<div class="video-section">
<div class="main-video-container">
<video id="main-video" controls autoplay muted playsinline>
<source src="./static/videos/default.mp4" type="video/mp4" />
</video>
<div id="video-title">Push T - 28 consecutive SE(2) goals</div>
</div>
<div class="thumbnail-column">
<div class="thumbnail-grid">
<img loading="lazy" src="./static/images/thumbnails/push_t.gif" class="video-thumb"
data-src="./static/images/single_object/push_t_09_07_25_hwlog000001_compressed.mp4"
data-title="Push T - 28 consecutive SE(2) goals" alt="Push T"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/xbox.gif" class="video-thumb"
data-src="./static/images/single_object/xbox_09_13_25_hwlog000008_compressed.mp4"
data-title="Xbox Controller - 28 consecutive SE(2) goals" alt="Xbox Controller"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/gallon_milk.gif" class="video-thumb"
data-src="./static/images/single_object/gallon_milk_09_07_25_hwlog000010_compressed.mp4"
data-title="Gallon Milk - 28 consecutive SE(2) goals" alt="Gallon Milk"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/baby_toy.gif" class="video-thumb"
data-src="./static/images/single_object/baby_toy_09_03_25_hwlog000021_compressed.mp4"
data-title="Baby Toy - 28 consecutive SE(2) goals" alt="Baby Toy"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/book.gif" class="video-thumb"
data-src="./static/images/single_object/book_09_06_25_hwlog000017_compressed.mp4"
data-title="Book - 28 consecutive SE(2) goals" alt="Book" onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/egg_carton.gif" class="video-thumb"
data-src="./static/images/single_object/egg_09_02_25_hwlog000019_compressed.mp4"
data-title="Egg Carton - 10 consecutive SE(2) goals" alt="Egg Carton"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/chicken_broth.gif" class="video-thumb"
data-src="./static/images/single_object/chicken_broth_09_05_25_hwlog000003_compressed.mp4"
data-title="Chicken Broth - 28 consecutive SE(2) goals" alt="Chicken Broth"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/clamp.gif" class="video-thumb"
data-src="./static/images/single_object/clamp_09_08_25_hwlog000006_compressed.mp4"
data-title="Clamp - 28 consecutive SE(2) goals" alt="Clamp" onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/milk_bottle.gif" class="video-thumb"
data-src="./static/images/single_object/milk_09_02_25_hwlog000040_compressed.mp4"
data-title="Milk Bottle - 28 consecutive SE(2) goals" alt="Milk Bottle"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/eraser.gif" class="video-thumb"
data-src="./static/images/single_object/eraser_09_07_25_hwlog000005_compressed.mp4"
data-title="Eraser - 28 consecutive SE(2) goals" alt="Eraser"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/tape.gif" class="video-thumb"
data-src="./static/images/single_object/tape_09_07_25_hwlog000006_compressed.mp4"
data-title="Tape - 28 consecutive SE(2) goals" alt="Tape" onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/wood_block.gif" class="video-thumb"
data-src="./static/images/single_object/wood_block_09_04_25_hwlog000008_compressed.mp4"
data-title="Wood Block - 28 consecutive SE(2) goals" alt="Wood Block"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/lotion.gif" class="video-thumb"
data-src="./static/images/single_object/lotion_09_04_25_hwlog000012_compressed.mp4"
data-title="Lotion - 19 consecutive SE(2) goals" alt="Lotion"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/expo_box.gif" class="video-thumb"
data-src="./static/images/single_object/expo_09_02_25_hwlog000003_compressed.mp4"
data-title="Expo Box - 28 consecutive SE(2) goals" alt="Expo Box"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_i.gif" class="video-thumb"
data-src="./static/images/single_object/I_09_03_25_hwlog000056_compressed.mp4"
data-title="Letter I - 28 consecutive SE(2) goals" alt="Letter I"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_c.gif" class="video-thumb"
data-src="./static/images/single_object/C_08_31_25_hwlog000006_compressed.mp4"
data-title="Letter C - 28 consecutive SE(2) goals" alt="Letter C"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_r.gif" class="video-thumb"
data-src="./static/images/single_object/R_09_02_25_hwlog000010_compressed.mp4"
data-title="Letter R - 28 consecutive SE(2) goals" alt="Letter R"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_a.gif" class="video-thumb"
data-src="./static/images/single_object/A_09_07_25_hwlog000011_compressed.mp4"
data-title="Letter A - 28 consecutive SE(2) goals" alt="Letter A"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_y.gif" class="video-thumb"
data-src="./static/images/single_object/Y_09_08_25_hwlog000005_compressed.mp4"
data-title="Letter Y - 28 consecutive SE(2) goals" alt="Letter Y"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_g.gif" class="video-thumb"
data-src="./static/images/single_object/G_09_08_25_hwlog000003_compressed.mp4"
data-title="Letter G - 28 consecutive SE(2) goals" alt="Letter G"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_b.gif" class="video-thumb"
data-src="./static/images/single_object/B_09_03_25_hwlog000057_small.mp4"
data-title="Letter B - 28 consecutive SE(2) goals" alt="Letter B"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_h.gif" class="video-thumb"
data-src="./static/images/single_object/H_09_03_25_hwlog000055_compressed.mp4"
data-title="Letter H - 28 consecutive SE(2) goals" alt="Letter H"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_3.gif" class="video-thumb"
data-src="./static/images/single_object/letter_3_09_02_25_hwlog000011_compressed.mp4"
data-title="Letter 3 - 28 consecutive SE(2) goals" alt="Letter 3"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_e.gif" class="video-thumb"
data-src="./static/images/single_object/E_09_02_25_hwlog000031_compressed.mp4"
data-title="Letter E - 28 consecutive SE(2) goals" alt="Letter E"
onclick="loadVideo(this)" />
<img loading="lazy" src="./static/images/thumbnails/letter_s.gif" class="video-thumb"
data-src="./static/images/single_object/S_09_08_25_hwlog000008_compressed.mp4"
data-title="Letter S - 28 consecutive SE(2) goals" alt="Letter S"
onclick="loadVideo(this)" />
</div>
<div class="thumbnail-instruction">Click on a thumbnail to play video</div>
</div>
</div>
</div>
<br>
<!-- Uncut 2-object videos -->
<div class="base-row add-top-padding">
<h1 id="abstract">Uncut Two-Object Manipulation Videos (3X speed)</h1>
<h2>Tight tolerances: 2cm, 0.1rad (5.7 degrees)</h2>
<nav>
<div class="carousel-slider-wrapper">
<div class="carousel-slider">
<div class="video-container">
<h2>Letter B and Letter 3 - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/B_and_3_09_04_25_hwlog000048_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Baby Toy and Letter E - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/baby_toy_and_E_09_04_25_hwlog000045_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Book and Letter S - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/book_and_S_09_05_25_hwlog000031_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Chicken Broth and Expo Box - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/chicken_broth_and_expo_09_05_25_hwlog000008_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Chicken Broth and Wood Block - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/chicken_broth_and_wood_block_09_05_25_hwlog000023_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Clamp and Letter I - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/clamp_and_I_09_05_25_hwlog000027_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Letter G and Xbox Controller - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/G_and_xbox_09_08_25_hwlog000012_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Lotion and Letter R - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/lotion_and_R_09_04_25_hwlog000035_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Letter T and Letter H - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/T_and_H_09_08_25_hwlog000013_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Tape and Letter A - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/two_objects/tape_and_A_09_07_25_hwlog000012_compressed_3X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
</div>
<button class="carousel-button left" type="button"><</button>
<button class="carousel-button right" type="button">></button>
</div>
</nav>
</div>
<br>
<!-- Uncut 3-object videos -->
<div class="base-row add-top-padding">
<h1 id="abstract">Uncut Three-Object Manipulation Videos (10X speed)</h1>
<h2>Tight tolerances: 2cm, 0.1rad (5.7 degrees)</h2>
<nav>
<div class="carousel-slider-wrapper">
<div class="carousel-slider">
<div class="video-container">
<h2>Letter A, Letter N, and Letter Y - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/three_objects/ANY_09_10_25_hwlog000008_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Letter C, Letter 3, and Letter + - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/three_objects/C3+_09_10_25_hwlog000021_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Clamp, Lotion, and Book - 4 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/three_objects/clamp_lotion_book_09_10_25_hwlog000015_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Clamp, Lotion, and Book - 4 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/three_objects/clamp_lotion_book_09_10_25_hwlog000017_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Clamp, Lotion, and Book - 4 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/three_objects/clamp_lotion_book_09_10_25_hwlog000018_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Letter D, Letter I, and Letter Y - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/three_objects/DIY_09_10_25_hwlog000000_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Letter I, Letter N, and Letter G - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/three_objects/ING_09_10_25_hwlog000010_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>Letter R, Letter A, and Letter S - 10 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/three_objects/RAS_09_10_25_hwlog000002_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
</div>
<button class="carousel-button left" type="button"><</button>
<button class="carousel-button right" type="button">></button>
</div>
</nav>
</div>
<br>
<!-- Uncut 4-object videos -->
<div class="base-row add-top-padding">
<h1 id="abstract">Uncut Four-Object Manipulation Videos (10X speed)</h1>
<h2>Tight tolerances: 2cm, 0.1rad (5.7 degrees)</h2>
<nav>
<div class="carousel-slider-wrapper">
<div class="carousel-slider">
<div class="video-container">
<h2>C3PO - 2 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/C3PO_09_13_25_hwlog000002_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>C3PO - 2 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/C3PO_09_13_25_hwlog000003_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>C3PO - 4 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/C3PO_09_13_25_hwlog000004_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>C3PO - 3 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/C3PO_09_13_25_hwlog000007_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>DAY+ - 3 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/DAY+_09_12_25_hwlog000017_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>DAY+ - 3 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/DAY+_09_12_25_hwlog000018_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>DAY+ - 2 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/DAY+_09_12_25_hwlog000019_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>DAY+ - 1 consecutive SE(2) goal</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/DAY+_09_13_25_hwlog000000_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>DAY+ - 1 consecutive SE(2) goal</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/DAY+_09_13_25_hwlog000001_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>ICRA - 5 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/ICRA_09_11_25_hwlog000042_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>ICRA - 4 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/ICRA_09_12_25_hwlog000004_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>ICRA - 1 consecutive SE(2) goal</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/ICRA_09_12_25_hwlog000005_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>PUSH - 3 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/PUSH_09_12_25_hwlog000000_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>PUSH - 3 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/PUSH_09_12_25_hwlog000002_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>PUSH - 4 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/PUSH_09_12_25_hwlog000003_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>URDF - 2 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/URDF_09_12_25_hwlog000006_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>URDF - 5 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/URDF_09_12_25_hwlog000009_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
<div class="video-container">
<h2>URDF - 3 consecutive SE(2) goals</h2>
<video class="lazy-carousel-video"
data-src="./static/images/four_objects/URDF_09_12_25_hwlog000016_compressed_10X.mp4"
preload="none" controls muted loop playsinline height="100%">
<source type="video/mp4">
</video>
</div>
</div>
<button class="carousel-button left" type="button"><</button>
<button class="carousel-button right" type="button">></button>
</div>
</nav>
</div>
<br>
<!-- System Diagram -->
<div class="base-row add-top-padding">
<h1 id="abstract">System Diagram</h1>
<img id="full-img" src="./static/images/system_v5.png" />
<br>
<br>
<p class="paragraph">
We present the <b>Push Anything</b> framework (above), a
pipeline integrating object perception with a novel
controller. Our framework operates in two phases. In the
offline phase, we build an object library by scanning
objects to generate meshes (via <a href="https://bundlesdf.github.io/">BundleSDF</a>) and
URDFs, assuming same mass and inertia. In the online phase,
our controller uses robot and object state estimates (the
latter using <a href="https://nvlabs.github.io/FoundationPose/">
FoundationPose</a>) to compute end effector trajectories.
Following the approach in <a href="https://dynamic-controlled-sliding.github.io/">Yang
and Posa</a>, these trajectories are tracked by a low-level
operational space controller (OSC).
<br>
<br>
Our controller is implemented in C++ within the
<a href="https://drake.mit.edu">Drake systems framework</a>.
We use three computers in our experiments: (i) an Intel Core i9-13900KF (13th-gen, 32
threads) dedicated to the sampling-based controller, (ii) an
Intel Core i7-9700K running the operational-space controller
and robot drivers on a real-time kernel for Franka communication, and
(iii) an Intel Core i9-14900K paired with an NVIDIA GeForce RTX 4090 for <a
href="https://nvlabs.github.io/FoundationPose/">FoundationPose</a>. All
computers communicate via <a href="https://lcm-proj.github.io/lcm/">LCM</a>.
</p>
</div>
<br>
<div class="base-row add-top-padding">
<h1 id="abstract">Sampling-based MPC Controller using Enhanced Local CI-MPC</h1>
<p class="paragraph">
<img src="./static/images/sampling_based_mpc.png" alt="Example Image"
style="float: right; width: 500px; height: auto; margin-right: 20px; margin-bottom: 10px; border-radius: 8px;">
Our controller is built upon the
original framework from <a href="https://approximating-global-ci-mpc.github.io/">
Approximating Global CI-MPC</a>.
In this approach, candidate end effector
positions are sampled and evaluated by solving the CI-MPC
problem, augmented with a travel cost from the current location.
The candidate with the lowest overall cost is selected,
and if it differs from the current pose, the robot first moves
along a collision-free path to that position before executing
CI-MPC. As illustrated in the figure beside, by steering the system
toward configurations that expand the reach of local MPC,
this strategy helps the controller overcome local minima and
achieve goals that require long-horizon reasoning.
<b>The success of the sampling-based CI-MPC framework hinges on two key components: a robust
sampling strategy for selecting candidate end effector locations, and a
fast, effective local CI-MPC. While this approach is effective,
applying it to arbitrary objects, particularly in multi-object
scenarios, requires significant adaptations.</b>
</p>
<br>
<!-- Sampling Strategy -->
<h2 id="abstract" style="text-align: left;">Sampling Strategy: Applicable to Any Mesh</h2>
<p class="paragraph">
We pre-process object meshes by storing body-frame face
locations, areas, and normal vectors. Given world-frame
object pose estimates, we generate a candidate end effector
location by first performing several random sampling steps
in series: 1) select an object uniformly, 2) select a
stored face of this object weighted by area, and 3) sample a
point lying on this face. This surface point is then
projected a fixed distance along the face's outward normal
vector then projected to a fixed world height (see below).
We reject samples which, even after projection away from one
face, are too close to any of the objects. This can occur
due to object non-convexity, the presence of multiple
objects, or the selection of a face whose normal is too
vertical. We repeat this process until the desired number
of end effector candidates is obtained.
</p>
<img id="full-img" src="./static/images/sampling_v2.png" />
<br>
<br>
<p class="paragraph">
Above is a visualization of the sampling strategy for end
effector locations. The gray plane indicates the ground, and
the orange planes represent local tangent planes to the mesh
surfaces. Blue arrows project surface samples outwards from
the mesh along the face normals, then purple arrows project
those to a fixed height in the world, generating candidate
samples (green dots). Samples located too close to object
surfaces (e.g. red dot) are discarded.
</p>
<br>
<h2 id="abstract" style="text-align: left;">C3+ Algorithm: Fast, Effective Local CI-MPC</h2>
<p class="paragraph">
C3+ is an enhanced version of <a href="https://arxiv.org/abs/2304.11259">C3</a>, which leverages
the <a href="https://web.stanford.edu/class/ee364b/lectures/admm_slides.pdf">
Alternating Direction Method of Multipliers (ADMM)</a> to solve a
Quadratic Program with Complementarity Constraints (QPCC), where the system dynamics
are modeled as a <a href="https://epubs.siam.org/doi/10.1137/S0036139997325199">
Linear Complementarity System (LCS)</a>. C3 decouples the contact scheduling problem,
which involves solving the complementarity constraints, across planning steps,
enabling parallelization where each subproblem solves a small-scale
Mixed-Integer Quadratic Program (MIQP).
Building on this idea, our proposed C3+ algorithm introduces a new slack variable
that further decouples the contact problem across individual contacts.
This reformulation makes it equivalent to solving multiple independent
1D MIQPs, each has a simple closed-form solution, thereby transforming the costly,
coupled exponential-time MIQP into a constant-time analytical computation and
achieving a substantial overall speedup. More detailed derivations
can be found in our manuscript.
</p>
</div>
<br>
<!-- Numerical Results -->
<div class="base-row add-top-padding">
<h1 id="abstract">Experimental Results</h1>
<h2 id="abstract" style="text-align: left;">Single-Object Pushing</h2>
<p class="paragraph">
We evaluated our method in <b>701
hardware trials</b>, testing <b>25 objects</b>, with each object run until
<b>28 successful trials</b> were obtained. The system achieved a
<b>99.9% success rate (700/701)</b>, with the only failure occurring
when the large egg carton was pushed out of the robot’s reach. More details can be found
in the plot below.
</p>
<div class="columns is-centered">
<img id="single-object performance" src="./static/images/c3plus_single_object_performance.png"
style="width: 100%; height: auto;" />
</div>
<h2 id="abstract" style="text-align: left;">Multi-Object Pushing</h2>
<p class="paragraph">
We conducted a total of <b>227 trials</b>, comprising 10 experiments for the 2-object case,
6 for the 3-object, and 5 for the 4-object case. Each experiment was run until 10
successful trials were achieved.
Our method achieved a <b>92.5% success rate (210/227)</b>, with detailed results under
both tight and loose tolerances presented in the table below.
All failures occurred when an object moved beyond the robot’s reach.
<b>The mean time-to-goal for these tasks was approximately 96.4s, 191.1s, and 315.7s for
the 2-, 3-, and 4-object settings, respectively</b>. These numbers
do not scale linearly with the number of objects because
goal assignments are permuted across objects in each trial,
requiring object rearrangements that introduce additional time.
</p>
<table
style="min-width: 950px; border-collapse: collapse; text-align: center; font-family: sans-serif; font-size: 14px;">
<thead>
<tr>
<th rowspan="3" style="border: 1px solid black; padding: 6px;"># Objs</th>
<th rowspan="3" style="border: 1px solid black; padding: 6px;">Object Names</th>
<th rowspan="3" style="border: 1px solid black; padding: 6px;">Success Rate</th>
<th rowspan="3" style="border: 1px solid black; padding: 6px;">Control Rate (Hz)</th>
<th colspan="4" style="border: 1px solid black; padding: 6px;">Time to Goal (s) within Pose
Tolerances</th>
</tr>
<tr>
<th colspan="2" style="border: 1px solid black; padding: 6px;">Tight (2cm, 0.1rad)</th>
<th colspan="2" style="border: 1px solid black; padding: 6px;">Loose (5cm, 0.4rad)</th>
</tr>
<tr>
<th style="border: 1px solid black; padding: 6px;">Mean ± σ</th>
<th style="border: 1px solid black; padding: 6px;">Min, Max</th>
<th style="border: 1px solid black; padding: 6px;">Mean ± σ</th>
<th style="border: 1px solid black; padding: 6px;">Min, Max</th>
</tr>
</thead>
<tbody>
<!-- 2 objects -->
<tr>
<td rowspan="10" style="border: 1px solid black; padding: 6px; font-weight: normal;">2</td>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Lotion & Letter
R</td>
<td rowspan="10" style="border: 1px solid black; padding: 6px;">100/102 (98.0%)</td>
<td style="border: 1px solid black; padding: 6px;">14.06</td>
<td style="border: 1px solid black; padding: 6px;">97.01 ± 45.92</td>
<td style="border: 1px solid black; padding: 6px;">47.49, 204.35</td>
<td style="border: 1px solid black; padding: 6px;">74.26 ± 39.33</td>
<td style="border: 1px solid black; padding: 6px;">17.91, 171.49</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Baby toy &
Letter E</td>
<td style="border: 1px solid black; padding: 6px;">14.34</td>
<td style="border: 1px solid black; padding: 6px;">106.91 ± 47.62</td>
<td style="border: 1px solid black; padding: 6px;">60.98, 232.75</td>
<td style="border: 1px solid black; padding: 6px;">54.13 ± 14.28</td>
<td style="border: 1px solid black; padding: 6px;">20.95, 71.86</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Letter B &
Letter 3</td>
<td style="border: 1px solid black; padding: 6px;">14.31</td>
<td style="border: 1px solid black; padding: 6px;">85.31 ± 28.30</td>
<td style="border: 1px solid black; padding: 6px;">41.97, 129.53</td>
<td style="border: 1px solid black; padding: 6px;">53.64 ± 24.39</td>
<td style="border: 1px solid black; padding: 6px;">17.98, 114.74</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Chicken Broth &
Expo Box</td>
<td style="border: 1px solid black; padding: 6px;">13.84</td>
<td style="border: 1px solid black; padding: 6px;">99.35 ± 38.26</td>
<td style="border: 1px solid black; padding: 6px;">63.78, 180.85</td>
<td style="border: 1px solid black; padding: 6px;">75.94 ± 28.79</td>
<td style="border: 1px solid black; padding: 6px;">53.77, 158.16</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Chicken Broth &
Wood Block</td>
<td style="border: 1px solid black; padding: 6px;">14.12</td>
<td style="border: 1px solid black; padding: 6px;">74.43 ± 20.54</td>
<td style="border: 1px solid black; padding: 6px;">41.69, 107.64</td>
<td style="border: 1px solid black; padding: 6px;">54.62 ± 14.29</td>
<td style="border: 1px solid black; padding: 6px;">32.24, 76.12</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Clamp & Letter I
</td>
<td style="border: 1px solid black; padding: 6px;">14.14</td>
<td style="border: 1px solid black; padding: 6px;">87.19 ± 26.44</td>
<td style="border: 1px solid black; padding: 6px;">42.45, 132.87</td>
<td style="border: 1px solid black; padding: 6px;">44.15 ± 15.77</td>
<td style="border: 1px solid black; padding: 6px;">28.52, 80.74</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Book & Letter S
</td>
<td style="border: 1px solid black; padding: 6px;">14.43</td>
<td style="border: 1px solid black; padding: 6px;">92.88 ± 27.27</td>
<td style="border: 1px solid black; padding: 6px;">67.60, 168.00</td>
<td style="border: 1px solid black; padding: 6px;">81.51 ± 27.38</td>
<td style="border: 1px solid black; padding: 6px;">61.09, 154.14</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Tape & Letter A
</td>
<td style="border: 1px solid black; padding: 6px;">14.36</td>
<td style="border: 1px solid black; padding: 6px;">119.07 ± 44.10</td>
<td style="border: 1px solid black; padding: 6px;">69.88, 231.70</td>
<td style="border: 1px solid black; padding: 6px;">73.62 ± 24.24</td>
<td style="border: 1px solid black; padding: 6px;">50.63, 138.86</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Letter T &
Letter H</td>
<td style="border: 1px solid black; padding: 6px;">11.76</td>
<td style="border: 1px solid black; padding: 6px;">79.63 ± 21.47</td>
<td style="border: 1px solid black; padding: 6px;">44.14, 119.52</td>
<td style="border: 1px solid black; padding: 6px;">47.17 ± 11.19</td>
<td style="border: 1px solid black; padding: 6px;">34.06, 69.34</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Letter G & Xbox
</td>
<td style="border: 1px solid black; padding: 6px;">13.93</td>
<td style="border: 1px solid black; padding: 6px;">104.37 ± 23.78</td>
<td style="border: 1px solid black; padding: 6px;">75.97, 149.74</td>
<td style="border: 1px solid black; padding: 6px;">64.50 ± 14.89</td>
<td style="border: 1px solid black; padding: 6px;">45.15, 89.71</td>
</tr>
<!-- 3 objects -->
<tr>
<td rowspan="6" style="border: 1px solid black; padding: 6px; font-weight: normal;">3</td>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Letter R &
Letter A & Letter S</td>
<td rowspan="6" style="border: 1px solid black; padding: 6px;">60/62 (96.8%)</td>
<td style="border: 1px solid black; padding: 6px;">14.70</td>
<td style="border: 1px solid black; padding: 6px;">185.94 ± 63.01</td>
<td style="border: 1px solid black; padding: 6px;">113.44, 299.09</td>
<td style="border: 1px solid black; padding: 6px;">141.28 ± 48.89</td>
<td style="border: 1px solid black; padding: 6px;">94.30, 227.94</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Letter C &
Letter 3 & Letter +</td>
<td style="border: 1px solid black; padding: 6px;">14.85</td>
<td style="border: 1px solid black; padding: 6px;">173.43 ± 29.56</td>
<td style="border: 1px solid black; padding: 6px;">135.00, 219.33</td>
<td style="border: 1px solid black; padding: 6px;">116.54 ± 21.72</td>
<td style="border: 1px solid black; padding: 6px;">80.66, 148.72</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Letter A &
Letter N & Letter Y</td>
<td style="border: 1px solid black; padding: 6px;">14.72</td>
<td style="border: 1px solid black; padding: 6px;">159.63 ± 37.27</td>
<td style="border: 1px solid black; padding: 6px;">111.57, 237.65</td>
<td style="border: 1px solid black; padding: 6px;">121.65 ± 26.65</td>
<td style="border: 1px solid black; padding: 6px;">92.85, 175.08</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Letter I &
Letter N & Letter G</td>
<td style="border: 1px solid black; padding: 6px;">14.84</td>
<td style="border: 1px solid black; padding: 6px;">173.98 ± 46.20</td>
<td style="border: 1px solid black; padding: 6px;">115.48, 275.02</td>
<td style="border: 1px solid black; padding: 6px;">120.18 ± 40.28</td>
<td style="border: 1px solid black; padding: 6px;">68.20, 189.52</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Letter D &
Letter I & Letter Y</td>
<td style="border: 1px solid black; padding: 6px;">14.72</td>
<td style="border: 1px solid black; padding: 6px;">188.96 ± 38.93</td>
<td style="border: 1px solid black; padding: 6px;">139.52, 247.20</td>
<td style="border: 1px solid black; padding: 6px;">137.41 ± 19.84</td>
<td style="border: 1px solid black; padding: 6px;">106.46, 173.66</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">Clamp & Lotion
& Book</td>
<td style="border: 1px solid black; padding: 6px;">15.19</td>
<td style="border: 1px solid black; padding: 6px;">224.03 ± 53.01</td>
<td style="border: 1px solid black; padding: 6px;">148.22, 307.58</td>
<td style="border: 1px solid black; padding: 6px;">157.98 ± 41.55</td>
<td style="border: 1px solid black; padding: 6px;">97.30, 228.89</td>
</tr>
<!-- 4 objects -->
<tr>
<td rowspan="5" style="border: 1px solid black; padding: 6px; font-weight: normal;">4</td>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">PUSH</td>
<td rowspan="5" style="border: 1px solid black; padding: 6px;">50/63 (79.3%)</td>
<td style="border: 1px solid black; padding: 6px;">9.32</td>
<td style="border: 1px solid black; padding: 6px;">312.34 ± 60.07</td>
<td style="border: 1px solid black; padding: 6px;">160.34, 394.28</td>
<td style="border: 1px solid black; padding: 6px;">248.64 ± 60.06</td>
<td style="border: 1px solid black; padding: 6px;">159.82, 366.18</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">ICRA</td>
<td style="border: 1px solid black; padding: 6px;">8.63</td>
<td style="border: 1px solid black; padding: 6px;">267.85 ± 59.80</td>
<td style="border: 1px solid black; padding: 6px;">176.62, 396.33</td>
<td style="border: 1px solid black; padding: 6px;">208.86 ± 44.50</td>
<td style="border: 1px solid black; padding: 6px;">126.65, 278.78</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">URDF</td>
<td style="border: 1px solid black; padding: 6px;">9.10</td>
<td style="border: 1px solid black; padding: 6px;">269.01 ± 93.90</td>
<td style="border: 1px solid black; padding: 6px;">149.50, 465.47</td>
<td style="border: 1px solid black; padding: 6px;">204.92 ± 84.96</td>
<td style="border: 1px solid black; padding: 6px;">121.98, 401.88</td>
</tr>
<tr>
<td style="border: 1px solid black; padding: 6px; font-weight: normal;">C3PO</td>
<td style="border: 1px solid black; padding: 6px;">9.31</td>
<td style="border: 1px solid black; padding: 6px;">281.66 ± 85.97</td>
<td style="border: 1px solid black; padding: 6px;">120.23, 458.00</td>
<td style="border: 1px solid black; padding: 6px;">192.54 ± 38.75</td>
<td style="border: 1px solid black; padding: 6px;">120.23, 246.98</td>