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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<!-- Meta tags for social media banners, these should be filled in appropriatly as they are your "business card" -->
<!-- Replace the content tag with appropriate information -->
<meta name="description" content="DESCRIPTION META TAG">
<meta property="og:title" content="SOCIAL MEDIA TITLE TAG"/>
<meta property="og:description" content="SOCIAL MEDIA DESCRIPTION TAG TAG"/>
<meta property="og:url" content="URL OF THE WEBSITE"/>
<!-- Path to banner image, should be in the path listed below. Optimal dimenssions are 1200X630-->
<meta property="og:image" content="static/image/your_banner_image.png" />
<meta property="og:image:width" content="1200"/>
<meta property="og:image:height" content="630"/>
<meta name="twitter:title" content="TWITTER BANNER TITLE META TAG">
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<meta name="twitter:image" content="static/images/your_twitter_banner_image.png">
<meta name="twitter:card" content="summary_large_image">
<!-- Keywords for your paper to be indexed by-->
<meta name="keywords" content="KEYWORDS SHOULD BE PLACED HERE">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Academic Project Page</title>
<link rel="icon" type="image/x-icon" href="static/images/favicon.ico">
<link href="https://fonts.googleapis.com/css?family=Google+Sans|Noto+Sans|Castoro"
rel="stylesheet">
<link rel="stylesheet" href="static/css/bulma.min.css">
<link rel="stylesheet" href="static/css/bulma-carousel.min.css">
<link rel="stylesheet" href="static/css/bulma-slider.min.css">
<link rel="stylesheet" href="static/css/fontawesome.all.min.css">
<link rel="stylesheet"
href="https://cdn.jsdelivr.net/gh/jpswalsh/academicons@1/css/academicons.min.css">
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<script src="static/js/index.js"></script>
</head>
<body>
<section class="hero">
<div class="hero-body">
<div class="container is-max-desktop">
<div class="columns is-centered">
<div class="column has-text-centered">
<h1 class="title is-1 publication-title">Learning-based Bayesian Inference for Testing of Autonomous Systems</h1>
<div class="is-size-5 publication-authors">
<!-- Paper authors -->
<span class="author-block">
<a href="FIRST AUTHOR PERSONAL LINK" target="_blank">Anjali Parashar</a><sup>1</sup>,</span>
<span class="author-block">
<a href="SECOND AUTHOR PERSONAL LINK" target="_blank">Ji Yin</a><sup>2</sup>,</span>
<span class="author-block">
<a href="THIRD AUTHOR PERSONAL LINK" target="_blank">Charles Dawson</a><sup>1</sup>,
</span>
<span class="author-block">
<a href="FOURTH AUTHOR PERSONAL LINK" target="_blank">Panagiotis Tsiotras</a><sup>2</sup>,
</span><span class="author-block">
<a href="FIFTH AUTHOR PERSONAL LINK" target="_blank">Chuchu Fan</a><sup>1</sup>,
</span>
</div>
<div class="is-size-5 publication-authors">
<span class="author-block"><br><sup>1</sup>MIT</span>
<span class="author-block"><br><sup>2</sup>Georgia Tech</span>
</div>
<div class="column has-text-centered">
<div class="publication-links">
<!-- Arxiv PDF link -->
<span class="link-block">
<a href="https://arxiv.org/pdf/<ARXIV PAPER ID>.pdf" target="_blank"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<i class="fas fa-file-pdf"></i>
</span>
<span>Paper</span>
</a>
</span>
<!-- Supplementary PDF link -->
<span class="link-block">
<a href="static/pdfs/supplementary_material.pdf" target="_blank"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<i class="fas fa-file-pdf"></i>
</span>
<span>Supplementary</span>
</a>
</span>
<!-- ArXiv abstract Link -->
<span class="link-block">
<a href="https://arxiv.org/abs/<ARXIV PAPER ID>" target="_blank"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<i class="ai ai-arxiv"></i>
</span>
<span>arXiv</span>
</a>
</span>
</div>
</div>
</div>
</div>
</div>
</div>
</section>
<!-- Image carousel -->
<section class="hero is-small">
<div class="hero-body">
<div class="container">
<div id="results-carousel" class="carousel results-carousel">
<div class="item">
<!-- Your image here -->
<img src="static/images/intro.png" alt="Method Description"/>
<h2 class="subtitle has-text-centered">
Overview of our approach. We use learning-based Bayesian inference to find failure modes of a robotic system by finding environmental agents such as obstacles, reference paths that lead to failure.
</h2>
</div>
</div>
</div>
</div>
</section>
<!-- End image carousel -->
<!-- Teaser video-->
<section class="hero teaser">
<div class="container is-max-desktop">
<div class="hero-body">
<video poster="" id="tree" autoplay controls muted loop height="100%">
<!-- Your video here -->
<source src="static/videos/banner_video.mp4"
type="video/mp4">
</video>
<h2 class="subtitle has-text-centered">
Aliquam vitae elit ullamcorper tellus egestas pellentesque. Ut lacus tellus, maximus vel lectus at, placerat pretium mi. Maecenas dignissim tincidunt vestibulum. Sed consequat hendrerit nisl ut maximus.
</h2>
</div>
</div>
</section>
<!-- End teaser video -->
<!-- Paper abstract -->
<section class="section hero is-light">
<div class="container is-max-desktop">
<div class="columns is-centered has-text-centered">
<div class="column is-four-fifths">
<h2 class="title is-3">Abstract</h2>
<div class="content has-text-justified">
<p>For safe operation of robotic systems, it is important to accurately understand its failure modes using prior testing. Hardware testing of robotic infrastructure is known to be extremely slow and costly. Instead, failure prediction in simulation can help in analyzing the system before deployment. Conventionally, large-scale na\"ive Monte Carlo simulations are used for testing; however, this method is only suitable for testing average system performance. For safety-critical systems, worst-case performance is more crucial as failures are often rare events, and the size of test batches increases substantially to discover rare occurrences of failures. Rare-event sampling methods can be helpful; however, they exhibit slow convergence and cannot handle constraints.
This research introduces a novel sampling-based testing framework for autonomous systems which bridges these gaps by utilizing a discretized gradient-based second-order Langevin algorithm combined with learning-based techniques for constrained sampling of failure modes. Our method can predict more diverse failures by exploring the search space efficiently and ensures feasibility with respect to temporal and implicit constraints. We demonstrate the application of our testing methodology on two categories of testing problems, via simulations and hardware experiments. Our method discovers upto 2X failures compared to naive Random Walk sampling, with only half of the sample size. </p>
</div>
</div>
</div>
</div>
</section>
<!-- End paper abstract -->
<!-- Image carousel -->
<section class="hero is-small">
<div class="hero-body">
<div class="container">
<div id="results-carousel" class="carousel results-carousel">
<div class="item">
<!-- Your image here -->
<img src="static/images/NPO.png" width='400', height ='400' alt="Neural Projection Operator"/>
<h2 class="subtitle has-text-centered">
Neural Projection Operator (NPO): We use binary classifier to learn decision boundaries alongwith gradient-based projection for ensuring constraint feasibility of low dimensional environment variable. Fig shows the application of NPO on static obstacles that should be present around a given racetrack
</h2>
</div>
<div class="item">
<!-- Your image here -->
<img src="static/images/Latent_VAE.png" width='400', height ='400' alt="Learning Sequence EVs using AutoEncoder"/>
<h2 class="subtitle has-text-centered">
Latent Variable Encoding: We use this approach for desigining sequences that must be temporally consistent and represent realistic environment variables using an AutoEncoder that learns the frequency-domain representation of control input signals.
</h2>
</div>
<div class="item">
<!-- Your image here -->
<img src="static/images/carousel3.jpg" alt="MY ALT TEXT"/>
<h2 class="subtitle has-text-centered">
Third image description.
</h2>
</div>
<div class="item">
<!-- Your image here -->
<img src="static/images/carousel4.jpg" alt="MY ALT TEXT"/>
<h2 class="subtitle has-text-centered">
Fourth image description.
</h2>
</div>
</div>
</div>
</div>
</section>
<!-- End image carousel -->
<!--BibTex citation -->
<section class="section" id="BibTeX">
<div class="container is-max-desktop content">
<h2 class="title">BibTeX</h2>
<pre><code>BibTex Code Here</code></pre>
</div>
</section>
<!--End BibTex citation -->
<footer class="footer">
<div class="container">
<div class="columns is-centered">
<div class="column is-8">
<div class="content">
<p>
This page was built using the <a href="https://github.com/eliahuhorwitz/Academic-project-page-template" target="_blank">Academic Project Page Template</a> which was adopted from the <a href="https://nerfies.github.io" target="_blank">Nerfies</a> project page.
You are free to borrow the of this website, we just ask that you link back to this page in the footer. <br> This website is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/" target="_blank">Creative
Commons Attribution-ShareAlike 4.0 International License</a>.
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