flykhan/maths-cs-ai-compendium-zh
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
Files
gh-pages
maths-cs-ai-compendium-zh/chapter 11: autonomous systems/05. space and extreme robotics/index.html
T

5645 lines
144 KiB
HTML
Raw Permalink Blame History

This file contains ambiguous Unicode characters
This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.
<!doctype html>
<html lang="zh" class="no-js">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
<meta name="description" content="一本开源的直觉优先教科书，从零开始覆盖数学、计算机科学和人工智能（中文翻译版）。">
<meta name="author" content="Henry Ndubuaku (flykhan 译)">
<link rel="canonical" href="https://flykhan.github.io/maths-cs-ai-compendium-zh/chapter%2011%3A%20autonomous%20systems/05.%20space%20and%20extreme%20robotics/">
<link rel="prev" href="../04.%20self-driving/">
<link rel="next" href="../../chapter%2012%3A%20graph%20neural%20networks/01.%20geometric%20deep%20learning/">
<link rel="icon" href="../../assets/images/favicon.png">
<meta name="generator" content="mkdocs-1.6.1, mkdocs-material-9.7.6">
<title>太空与极端机器人 - 数学、计算机科学与 AI 百科全书</title>
<link rel="stylesheet" href="../../assets/stylesheets/main.484c7ddc.min.css">
<link rel="stylesheet" href="../../assets/stylesheets/palette.ab4e12ef.min.css">
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Roboto:300,300i,400,400i,700,700i%7CRoboto+Mono:400,400i,700,700i&display=fallback">
<style>:root{--md-text-font:"Roboto";--md-code-font:"Roboto Mono"}</style>
<script>__md_scope=new URL("../..",location),__md_hash=e=>[...e].reduce(((e,_)=>(e<<5)-e+_.charCodeAt(0)),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
</head>
<body dir="ltr" data-md-color-scheme="default" data-md-color-primary="slate" data-md-color-accent="indigo">
<input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
<input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
<label class="md-overlay" for="__drawer"></label>
<div data-md-component="skip">
<a href="#_1" class="md-skip">
跳转至
</a>
</div>
<div data-md-component="announce">
</div>
<header class="md-header" data-md-component="header">
<nav class="md-header__inner md-grid" aria-label="页眉">
<a href="../.." title="数学、计算机科学与 AI 百科全书" class="md-header__button md-logo" aria-label="数学、计算机科学与 AI 百科全书" data-md-component="logo">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
</a>
<label class="md-header__button md-icon" for="__drawer">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3zm0 5h18v2H3zm0 5h18v2H3z"/></svg>
</label>
<div class="md-header__title" data-md-component="header-title">
<div class="md-header__ellipsis">
<div class="md-header__topic">
<span class="md-ellipsis">
数学、计算机科学与 AI 百科全书
</span>
</div>
<div class="md-header__topic" data-md-component="header-topic">
<span class="md-ellipsis">
太空与极端机器人
</span>
</div>
</div>
</div>
<form class="md-header__option" data-md-component="palette">
<input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="slate" data-md-color-accent="indigo" aria-label="切换到深色模式" type="radio" name="__palette" id="__palette_0">
<label class="md-header__button md-icon" title="切换到深色模式" for="__palette_1" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a4 4 0 0 0-4 4 4 4 0 0 0 4 4 4 4 0 0 0 4-4 4 4 0 0 0-4-4m0 10a6 6 0 0 1-6-6 6 6 0 0 1 6-6 6 6 0 0 1 6 6 6 6 0 0 1-6 6m8-9.31V4h-4.69L12 .69 8.69 4H4v4.69L.69 12 4 15.31V20h4.69L12 23.31 15.31 20H20v-4.69L23.31 12z"/></svg>
</label>
<input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="slate" data-md-color-accent="indigo" aria-label="切换到浅色模式" type="radio" name="__palette" id="__palette_1">
<label class="md-header__button md-icon" title="切换到浅色模式" for="__palette_0" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 18c-.89 0-1.74-.2-2.5-.55C11.56 16.5 13 14.42 13 12s-1.44-4.5-3.5-5.45C10.26 6.2 11.11 6 12 6a6 6 0 0 1 6 6 6 6 0 0 1-6 6m8-9.31V4h-4.69L12 .69 8.69 4H4v4.69L.69 12 4 15.31V20h4.69L12 23.31 15.31 20H20v-4.69L23.31 12z"/></svg>
</label>
</form>
<script>var palette=__md_get("__palette");if(palette&&palette.color){if("(prefers-color-scheme)"===palette.color.media){var media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']");palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent")}for(var[key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
<label class="md-header__button md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
</label>
<div class="md-search" data-md-component="search" role="dialog">
<label class="md-search__overlay" for="__search"></label>
<div class="md-search__inner" role="search">
<form class="md-search__form" name="search">
<input type="text" class="md-search__input" name="query" aria-label="搜索" placeholder="搜索" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
<label class="md-search__icon md-icon" for="__search">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.52 6.52 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5"/></svg>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</label>
<nav class="md-search__options" aria-label="查找">
<button type="reset" class="md-search__icon md-icon" title="清空当前内容" aria-label="清空当前内容" tabindex="-1">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12z"/></svg>
</button>
</nav>
<div class="md-search__suggest" data-md-component="search-suggest"></div>
</form>
<div class="md-search__output">
<div class="md-search__scrollwrap" tabindex="0" data-md-scrollfix>
<div class="md-search-result" data-md-component="search-result">
<div class="md-search-result__meta">
正在初始化搜索引擎
</div>
<ol class="md-search-result__list" role="presentation"></ol>
</div>
</div>
</div>
</div>
</div>
<div class="md-header__source">
<a href="https://github.com/flykhan/maths-cs-ai-compendium-zh" title="前往仓库" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
</div>
<div class="md-source__repository">
flykhan/maths-cs-ai-compendium-zh
</div>
</a>
</div>
</nav>
</header>
<div class="md-container" data-md-component="container">
<nav class="md-tabs" aria-label="标签" data-md-component="tabs">
<div class="md-grid">
<ul class="md-tabs__list">
<li class="md-tabs__item">
<a href="../.." class="md-tabs__link">
首页
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2001%3A%20vectors/01.%20vector%20spaces/" class="md-tabs__link">
向量
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2002%3A%20matrices/01.%20matrix%20properties/" class="md-tabs__link">
矩阵
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2003%3A%20calculus/01.%20differential%20calculus/" class="md-tabs__link">
微积分
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2004%3A%20statistics/01.%20fundamentals/" class="md-tabs__link">
统计学
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2005%3A%20probability/01.%20counting/" class="md-tabs__link">
概率论
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2006%3A%20machine%20learning/01.%20classical%20machine%20learning/" class="md-tabs__link">
机器学习
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2007%3A%20computational%20linguistics/01.%20linguistic%20foundations/" class="md-tabs__link">
计算语言学
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2008%3A%20computer%20vision/01.%20image%20fundamentals/" class="md-tabs__link">
计算机视觉
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2009%3A%20audio%20and%20speech/01.%20digital%20signal%20processing/" class="md-tabs__link">
音频与语音
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2010%3A%20multimodal%20learning/01.%20multimodal%20representations/" class="md-tabs__link">
多模态学习
</a>
</li>
<li class="md-tabs__item md-tabs__item--active">
<a href="../01.%20perception/" class="md-tabs__link">
自主系统
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2012%3A%20graph%20neural%20networks/01.%20geometric%20deep%20learning/" class="md-tabs__link">
图神经网络
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2013%3A%20computing%20and%20OS/01.%20discrete%20maths/" class="md-tabs__link">
计算机与操作系统
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/00.%20foundations/" class="md-tabs__link">
数据结构与算法
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2015%3A%20production%20software%20engineering/01.%20linux%20and%20CMD/" class="md-tabs__link">
生产级软件工程
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/00.%20why%20C%2B%2B%20and%20how%20ML%20frameworks%20work/" class="md-tabs__link">
SIMD 与 GPU 编程
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2017%3A%20AI%20inference/01.%20quantisation/" class="md-tabs__link">
AI 推理
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2018%3A%20ML%20systems%20design/01.%20systems%20design%20fundamentals/" class="md-tabs__link">
ML 系统设计
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2019%3A%20applied%20AI/01.%20AI%20for%20finance/" class="md-tabs__link">
应用 AI
</a>
</li>
<li class="md-tabs__item">
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/01.%20quantum%20machine%20learning/" class="md-tabs__link">
前沿 AI
</a>
</li>
</ul>
</div>
</nav>
<main class="md-main" data-md-component="main">
<div class="md-main__inner md-grid">
<div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
<div class="md-sidebar__scrollwrap">
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--primary md-nav--lifted" aria-label="导航栏" data-md-level="0">
<label class="md-nav__title" for="__drawer">
<a href="../.." title="数学、计算机科学与 AI 百科全书" class="md-nav__button md-logo" aria-label="数学、计算机科学与 AI 百科全书" data-md-component="logo">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 8a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3 3 3 0 0 0 3 3m0 3.54C9.64 9.35 6.5 8 3 8v11c3.5 0 6.64 1.35 9 3.54 2.36-2.19 5.5-3.54 9-3.54V8c-3.5 0-6.64 1.35-9 3.54"/></svg>
</a>
数学、计算机科学与 AI 百科全书
</label>
<div class="md-nav__source">
<a href="https://github.com/flykhan/maths-cs-ai-compendium-zh" title="前往仓库" class="md-source" data-md-component="source">
<div class="md-source__icon md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M439.6 236.1 244 40.5c-5.4-5.5-12.8-8.5-20.4-8.5s-15 3-20.4 8.4L162.5 81l51.5 51.5c27.1-9.1 52.7 16.8 43.4 43.7l49.7 49.7c34.2-11.8 61.2 31 35.5 56.7-26.5 26.5-70.2-2.9-56-37.3L240.3 199v121.9c25.3 12.5 22.3 41.8 9.1 55-6.4 6.4-15.2 10.1-24.3 10.1s-17.8-3.6-24.3-10.1c-17.6-17.6-11.1-46.9 11.2-56v-123c-20.8-8.5-24.6-30.7-18.6-45L142.6 101 8.5 235.1C3 240.6 0 247.9 0 255.5s3 15 8.5 20.4l195.6 195.7c5.4 5.4 12.7 8.4 20.4 8.4s15-3 20.4-8.4l194.7-194.7c5.4-5.4 8.4-12.8 8.4-20.4s-3-15-8.4-20.4"/></svg>
</div>
<div class="md-source__repository">
flykhan/maths-cs-ai-compendium-zh
</div>
</a>
</div>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../.." class="md-nav__link">
<span class="md-ellipsis">
首页
</span>
</a>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_2" >
<label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
<span class="md-ellipsis">
向量
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_2">
<span class="md-nav__icon md-icon"></span>
向量
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2001%3A%20vectors/01.%20vector%20spaces/" class="md-nav__link">
<span class="md-ellipsis">
向量空间
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2001%3A%20vectors/02.%20vector%20properties/" class="md-nav__link">
<span class="md-ellipsis">
向量性质
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2001%3A%20vectors/03.%20norms%20and%20metrics/" class="md-nav__link">
<span class="md-ellipsis">
范数与度量
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2001%3A%20vectors/04.%20products/" class="md-nav__link">
<span class="md-ellipsis">
向量积
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2001%3A%20vectors/05.%20basis%20and%20duality/" class="md-nav__link">
<span class="md-ellipsis">
基与对偶性
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_3" >
<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
<span class="md-ellipsis">
矩阵
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
矩阵
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2002%3A%20matrices/01.%20matrix%20properties/" class="md-nav__link">
<span class="md-ellipsis">
矩阵性质
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2002%3A%20matrices/02.%20matrix%20types/" class="md-nav__link">
<span class="md-ellipsis">
矩阵类型
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2002%3A%20matrices/03.%20operations/" class="md-nav__link">
<span class="md-ellipsis">
矩阵运算
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2002%3A%20matrices/04.%20linear%20transformations/" class="md-nav__link">
<span class="md-ellipsis">
线性变换
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2002%3A%20matrices/05.%20decompositions/" class="md-nav__link">
<span class="md-ellipsis">
矩阵分解
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_4" >
<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
<span class="md-ellipsis">
微积分
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_4">
<span class="md-nav__icon md-icon"></span>
微积分
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2003%3A%20calculus/01.%20differential%20calculus/" class="md-nav__link">
<span class="md-ellipsis">
微分
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2003%3A%20calculus/02.%20integral%20calculus/" class="md-nav__link">
<span class="md-ellipsis">
积分
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2003%3A%20calculus/03.%20multivariate%20calculus/" class="md-nav__link">
<span class="md-ellipsis">
多元微积分
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2003%3A%20calculus/04.%20function%20approximation/" class="md-nav__link">
<span class="md-ellipsis">
函数逼近
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2003%3A%20calculus/05.%20optimisation/" class="md-nav__link">
<span class="md-ellipsis">
优化
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_5" >
<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
<span class="md-ellipsis">
统计学
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_5">
<span class="md-nav__icon md-icon"></span>
统计学
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2004%3A%20statistics/01.%20fundamentals/" class="md-nav__link">
<span class="md-ellipsis">
基础
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2004%3A%20statistics/02.%20measures/" class="md-nav__link">
<span class="md-ellipsis">
统计量
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2004%3A%20statistics/03.%20sampling/" class="md-nav__link">
<span class="md-ellipsis">
抽样
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2004%3A%20statistics/04.%20hypothesis%20testing/" class="md-nav__link">
<span class="md-ellipsis">
假设检验
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2004%3A%20statistics/05.%20inference/" class="md-nav__link">
<span class="md-ellipsis">
推断
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_6" >
<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
<span class="md-ellipsis">
概率论
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_6">
<span class="md-nav__icon md-icon"></span>
概率论
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2005%3A%20probability/01.%20counting/" class="md-nav__link">
<span class="md-ellipsis">
计数
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2005%3A%20probability/02.%20probability%20concepts/" class="md-nav__link">
<span class="md-ellipsis">
概率概念
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2005%3A%20probability/03.%20distributions/" class="md-nav__link">
<span class="md-ellipsis">
分布
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2005%3A%20probability/04.%20bayesian/" class="md-nav__link">
<span class="md-ellipsis">
贝叶斯
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2005%3A%20probability/05.%20information%20theory/" class="md-nav__link">
<span class="md-ellipsis">
信息论
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_7" >
<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
<span class="md-ellipsis">
机器学习
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_7">
<span class="md-nav__icon md-icon"></span>
机器学习
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2006%3A%20machine%20learning/01.%20classical%20machine%20learning/" class="md-nav__link">
<span class="md-ellipsis">
经典机器学习
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2006%3A%20machine%20learning/02.%20gradient%20machine%20learning/" class="md-nav__link">
<span class="md-ellipsis">
梯度机器学习
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2006%3A%20machine%20learning/03.%20deep%20learning/" class="md-nav__link">
<span class="md-ellipsis">
深度学习
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2006%3A%20machine%20learning/04.%20reinforcement%20learning/" class="md-nav__link">
<span class="md-ellipsis">
强化学习
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2006%3A%20machine%20learning/05.%20distributed%20deep%20learning/" class="md-nav__link">
<span class="md-ellipsis">
分布式深度学习
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_8" >
<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
<span class="md-ellipsis">
计算语言学
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_8">
<span class="md-nav__icon md-icon"></span>
计算语言学
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2007%3A%20computational%20linguistics/01.%20linguistic%20foundations/" class="md-nav__link">
<span class="md-ellipsis">
语言学基础
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2007%3A%20computational%20linguistics/02.%20text%20processing%20and%20classic%20NLP/" class="md-nav__link">
<span class="md-ellipsis">
文本处理与经典 NLP
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2007%3A%20computational%20linguistics/03.%20embeddings%20and%20sequence%20models/" class="md-nav__link">
<span class="md-ellipsis">
嵌入与序列模型
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2007%3A%20computational%20linguistics/04.%20transformers%20and%20language%20models/" class="md-nav__link">
<span class="md-ellipsis">
Transformer 与语言模型
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2007%3A%20computational%20linguistics/05.%20advanced%20text%20generation/" class="md-nav__link">
<span class="md-ellipsis">
高级文本生成
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_9" >
<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
<span class="md-ellipsis">
计算机视觉
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_9">
<span class="md-nav__icon md-icon"></span>
计算机视觉
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2008%3A%20computer%20vision/01.%20image%20fundamentals/" class="md-nav__link">
<span class="md-ellipsis">
图像基础
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2008%3A%20computer%20vision/02.%20convolutional%20networks/" class="md-nav__link">
<span class="md-ellipsis">
卷积网络
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2008%3A%20computer%20vision/03.%20object%20detection%20and%20segmentation/" class="md-nav__link">
<span class="md-ellipsis">
目标检测与分割
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2008%3A%20computer%20vision/04.%20vision%20transformers%20and%20generation/" class="md-nav__link">
<span class="md-ellipsis">
ViT 与生成模型
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2008%3A%20computer%20vision/05.%20video%20and%203D%20vision/" class="md-nav__link">
<span class="md-ellipsis">
视频与 3D 视觉
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_10" >
<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
<span class="md-ellipsis">
音频与语音
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_10">
<span class="md-nav__icon md-icon"></span>
音频与语音
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2009%3A%20audio%20and%20speech/01.%20digital%20signal%20processing/" class="md-nav__link">
<span class="md-ellipsis">
数字信号处理
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2009%3A%20audio%20and%20speech/02.%20automatic%20speech%20recognition/" class="md-nav__link">
<span class="md-ellipsis">
自动语音识别
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2009%3A%20audio%20and%20speech/03.%20text%20to%20speech%20and%20voice/" class="md-nav__link">
<span class="md-ellipsis">
语音合成
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2009%3A%20audio%20and%20speech/04.%20speaker%20and%20audio%20analysis/" class="md-nav__link">
<span class="md-ellipsis">
说话人与音频分析
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2009%3A%20audio%20and%20speech/05.%20source%20separation%20and%20noise/" class="md-nav__link">
<span class="md-ellipsis">
源分离与降噪
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_11" >
<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
<span class="md-ellipsis">
多模态学习
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_11">
<span class="md-nav__icon md-icon"></span>
多模态学习
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2010%3A%20multimodal%20learning/01.%20multimodal%20representations/" class="md-nav__link">
<span class="md-ellipsis">
多模态表征
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2010%3A%20multimodal%20learning/02.%20vision%20language%20models/" class="md-nav__link">
<span class="md-ellipsis">
视觉语言模型
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2010%3A%20multimodal%20learning/03.%20image%20and%20video%20tokenisation/" class="md-nav__link">
<span class="md-ellipsis">
图像与视频 Token 化
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2010%3A%20multimodal%20learning/04.%20cross-modal%20generation/" class="md-nav__link">
<span class="md-ellipsis">
跨模态生成
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2010%3A%20multimodal%20learning/05.%20unified%20multimodal%20architectures/" class="md-nav__link">
<span class="md-ellipsis">
统一多模态架构
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="">
<span class="md-ellipsis">
自主系统
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
<label class="md-nav__title" for="__nav_12">
<span class="md-nav__icon md-icon"></span>
自主系统
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../01.%20perception/" class="md-nav__link">
<span class="md-ellipsis">
感知
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../02.%20robot%20learning/" class="md-nav__link">
<span class="md-ellipsis">
机器人学习
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../03.%20vision-language-action%20models/" class="md-nav__link">
<span class="md-ellipsis">
视觉-语言-动作模型
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../04.%20self-driving/" class="md-nav__link">
<span class="md-ellipsis">
自动驾驶
</span>
</a>
</li>
<li class="md-nav__item md-nav__item--active">
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
<label class="md-nav__link md-nav__link--active" for="__toc">
<span class="md-ellipsis">
太空与极端机器人
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<a href="./" class="md-nav__link md-nav__link--active">
<span class="md-ellipsis">
太空与极端机器人
</span>
</a>
<nav class="md-nav md-nav--secondary" aria-label="目录">
<label class="md-nav__title" for="__toc">
<span class="md-nav__icon md-icon"></span>
目录
</label>
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
<li class="md-nav__item">
<a href="#_2" class="md-nav__link">
<span class="md-ellipsis">
太空机器人
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_3" class="md-nav__link">
<span class="md-ellipsis">
通信约束
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_4" class="md-nav__link">
<span class="md-ellipsis">
抗辐射计算
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_5" class="md-nav__link">
<span class="md-ellipsis">
非结构化地形中的自主导航
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_6" class="md-nav__link">
<span class="md-ellipsis">
水下机器人
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_7" class="md-nav__link">
<span class="md-ellipsis">
搜索救援机器人
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_8" class="md-nav__link">
<span class="md-ellipsis">
群体机器人
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_9" class="md-nav__link">
<span class="md-ellipsis">
人机交互
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#colabnotebook" class="md-nav__link">
<span class="md-ellipsis">
编程任务（使用CoLab或notebook）
</span>
</a>
</li>
</ul>
</nav>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_13" >
<label class="md-nav__link" for="__nav_13" id="__nav_13_label" tabindex="0">
<span class="md-ellipsis">
图神经网络
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_13">
<span class="md-nav__icon md-icon"></span>
图神经网络
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2012%3A%20graph%20neural%20networks/01.%20geometric%20deep%20learning/" class="md-nav__link">
<span class="md-ellipsis">
几何深度学习
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2012%3A%20graph%20neural%20networks/02.%20graph%20theory/" class="md-nav__link">
<span class="md-ellipsis">
图论
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2012%3A%20graph%20neural%20networks/03.%20graph%20neural%20networks/" class="md-nav__link">
<span class="md-ellipsis">
图神经网络
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2012%3A%20graph%20neural%20networks/04.%20graph%20attention%20networks/" class="md-nav__link">
<span class="md-ellipsis">
图注意力网络
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2012%3A%20graph%20neural%20networks/05.%203d%20graph%20networks/" class="md-nav__link">
<span class="md-ellipsis">
3D 图网络
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_14" >
<label class="md-nav__link" for="__nav_14" id="__nav_14_label" tabindex="0">
<span class="md-ellipsis">
计算机与操作系统
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_14">
<span class="md-nav__icon md-icon"></span>
计算机与操作系统
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2013%3A%20computing%20and%20OS/01.%20discrete%20maths/" class="md-nav__link">
<span class="md-ellipsis">
离散数学
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2013%3A%20computing%20and%20OS/02.%20computer%20architecture/" class="md-nav__link">
<span class="md-ellipsis">
计算机体系结构
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2013%3A%20computing%20and%20OS/03.%20operating%20systems/" class="md-nav__link">
<span class="md-ellipsis">
操作系统
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2013%3A%20computing%20and%20OS/04.%20concurrency%20and%20parallelism/" class="md-nav__link">
<span class="md-ellipsis">
并发与并行
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2013%3A%20computing%20and%20OS/05.%20programming%20languages/" class="md-nav__link">
<span class="md-ellipsis">
编程语言
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_15" >
<label class="md-nav__link" for="__nav_15" id="__nav_15_label" tabindex="0">
<span class="md-ellipsis">
数据结构与算法
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_15">
<span class="md-nav__icon md-icon"></span>
数据结构与算法
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/00.%20foundations/" class="md-nav__link">
<span class="md-ellipsis">
基础
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/01.%20arrays%20and%20hashing/" class="md-nav__link">
<span class="md-ellipsis">
数组与哈希
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/02.%20linked%20lists%2C%20stacks%2C%20and%20queues/" class="md-nav__link">
<span class="md-ellipsis">
链表、栈与队列
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/03.%20trees/" class="md-nav__link">
<span class="md-ellipsis">
树
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/04.%20graphs/" class="md-nav__link">
<span class="md-ellipsis">
图
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2014%3A%20data%20structures%20and%20algorithms/05.%20sorting%20and%20search/" class="md-nav__link">
<span class="md-ellipsis">
排序与搜索
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_16" >
<label class="md-nav__link" for="__nav_16" id="__nav_16_label" tabindex="0">
<span class="md-ellipsis">
生产级软件工程
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_16">
<span class="md-nav__icon md-icon"></span>
生产级软件工程
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2015%3A%20production%20software%20engineering/01.%20linux%20and%20CMD/" class="md-nav__link">
<span class="md-ellipsis">
Linux 与命令行
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2015%3A%20production%20software%20engineering/02.%20git%20and%20repository%20management/" class="md-nav__link">
<span class="md-ellipsis">
Git 与仓库管理
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2015%3A%20production%20software%20engineering/03.%20codebase%20design/" class="md-nav__link">
<span class="md-ellipsis">
代码设计
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2015%3A%20production%20software%20engineering/04.%20testing%20and%20quality%20assurance/" class="md-nav__link">
<span class="md-ellipsis">
测试与质量保障
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2015%3A%20production%20software%20engineering/05.%20deployment%20and%20devops/" class="md-nav__link">
<span class="md-ellipsis">
部署与 DevOps
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_17" >
<label class="md-nav__link" for="__nav_17" id="__nav_17_label" tabindex="0">
<span class="md-ellipsis">
SIMD 与 GPU 编程
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_17">
<span class="md-nav__icon md-icon"></span>
SIMD 与 GPU 编程
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/00.%20why%20C%2B%2B%20and%20how%20ML%20frameworks%20work/" class="md-nav__link">
<span class="md-ellipsis">
为什么是 C++ 及 ML 框架原理
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/01.%20hardware%20fundamentals/" class="md-nav__link">
<span class="md-ellipsis">
硬件基础
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/02.%20ARM%20and%20NEON/" class="md-nav__link">
<span class="md-ellipsis">
ARM 与 NEON
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/03.%20x86%20and%20AVX/" class="md-nav__link">
<span class="md-ellipsis">
x86 与 AVX
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/04.%20GPU%20architecture%20and%20CUDA/" class="md-nav__link">
<span class="md-ellipsis">
GPU 架构与 CUDA
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/05.%20triton%2C%20TPUs%20and%20pallax/" class="md-nav__link">
<span class="md-ellipsis">
Triton、TPU 与 Pallas
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/06.%20RISC-V%20and%20embedded%20systems/" class="md-nav__link">
<span class="md-ellipsis">
RISC-V 与嵌入式系统
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2016%3A%20SIMD%20and%20GPU%20programming/07.%20vulkan%20compute%20and%20cross-platform%20GPU/" class="md-nav__link">
<span class="md-ellipsis">
Vulkan Compute 与跨平台 GPU
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_18" >
<label class="md-nav__link" for="__nav_18" id="__nav_18_label" tabindex="0">
<span class="md-ellipsis">
AI 推理
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_18">
<span class="md-nav__icon md-icon"></span>
AI 推理
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2017%3A%20AI%20inference/01.%20quantisation/" class="md-nav__link">
<span class="md-ellipsis">
量化
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2017%3A%20AI%20inference/02.%20efficient%20architectures/" class="md-nav__link">
<span class="md-ellipsis">
高效架构
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2017%3A%20AI%20inference/03.%20serving%20and%20batching/" class="md-nav__link">
<span class="md-ellipsis">
服务与批处理
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2017%3A%20AI%20inference/04.%20edge%20inference/" class="md-nav__link">
<span class="md-ellipsis">
边缘推理
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2017%3A%20AI%20inference/05.%20scaling%20and%20deployment/" class="md-nav__link">
<span class="md-ellipsis">
扩缩与部署
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_19" >
<label class="md-nav__link" for="__nav_19" id="__nav_19_label" tabindex="0">
<span class="md-ellipsis">
ML 系统设计
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_19">
<span class="md-nav__icon md-icon"></span>
ML 系统设计
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2018%3A%20ML%20systems%20design/01.%20systems%20design%20fundamentals/" class="md-nav__link">
<span class="md-ellipsis">
系统设计基础
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2018%3A%20ML%20systems%20design/02.%20cloud%20computing/" class="md-nav__link">
<span class="md-ellipsis">
云计算
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2018%3A%20ML%20systems%20design/03.%20large%20scale%20infrastructure/" class="md-nav__link">
<span class="md-ellipsis">
大规模基础设施
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2018%3A%20ML%20systems%20design/04.%20ML%20systems%20design/" class="md-nav__link">
<span class="md-ellipsis">
ML 系统设计
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2018%3A%20ML%20systems%20design/05.%20ML%20design%20examples/" class="md-nav__link">
<span class="md-ellipsis">
ML 设计案例
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_20" >
<label class="md-nav__link" for="__nav_20" id="__nav_20_label" tabindex="0">
<span class="md-ellipsis">
应用 AI
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_20_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_20">
<span class="md-nav__icon md-icon"></span>
应用 AI
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2019%3A%20applied%20AI/01.%20AI%20for%20finance/" class="md-nav__link">
<span class="md-ellipsis">
AI 金融
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2019%3A%20applied%20AI/02.%20protein%20design/" class="md-nav__link">
<span class="md-ellipsis">
蛋白质设计
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2019%3A%20applied%20AI/03.%20drug%20discovery/" class="md-nav__link">
<span class="md-ellipsis">
药物发现
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2019%3A%20applied%20AI/04.%20agentic%20systems/" class="md-nav__link">
<span class="md-ellipsis">
智能体系统
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2019%3A%20applied%20AI/05.%20healthcare/" class="md-nav__link">
<span class="md-ellipsis">
医疗健康
</span>
</a>
</li>
</ul>
</nav>
</li>
<li class="md-nav__item md-nav__item--nested">
<input class="md-nav__toggle md-toggle md-toggle--indeterminate" type="checkbox" id="__nav_21" >
<label class="md-nav__link" for="__nav_21" id="__nav_21_label" tabindex="0">
<span class="md-ellipsis">
前沿 AI
</span>
<span class="md-nav__icon md-icon"></span>
</label>
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_21_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_21">
<span class="md-nav__icon md-icon"></span>
前沿 AI
</label>
<ul class="md-nav__list" data-md-scrollfix>
<li class="md-nav__item">
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/01.%20quantum%20machine%20learning/" class="md-nav__link">
<span class="md-ellipsis">
量子机器学习
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/02.%20neuromorphic%20computing/" class="md-nav__link">
<span class="md-ellipsis">
神经形态计算
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/03.%20datacentres%20in%20space/" class="md-nav__link">
<span class="md-ellipsis">
太空数据中心
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/04.%20decentralised%20AI/" class="md-nav__link">
<span class="md-ellipsis">
去中心化 AI
</span>
</a>
</li>
<li class="md-nav__item">
<a href="../../chapter%2020%3A%20bleeding%20edge%20AI/05.%20brain%20machine%20interfaces/" class="md-nav__link">
<span class="md-ellipsis">
脑机接口
</span>
</a>
</li>
</ul>
</nav>
</li>
</ul>
</nav>
</div>
</div>
</div>
<div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
<div class="md-sidebar__scrollwrap">
<div class="md-sidebar__inner">
<nav class="md-nav md-nav--secondary" aria-label="目录">
<label class="md-nav__title" for="__toc">
<span class="md-nav__icon md-icon"></span>
目录
</label>
<ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
<li class="md-nav__item">
<a href="#_2" class="md-nav__link">
<span class="md-ellipsis">
太空机器人
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_3" class="md-nav__link">
<span class="md-ellipsis">
通信约束
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_4" class="md-nav__link">
<span class="md-ellipsis">
抗辐射计算
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_5" class="md-nav__link">
<span class="md-ellipsis">
非结构化地形中的自主导航
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_6" class="md-nav__link">
<span class="md-ellipsis">
水下机器人
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_7" class="md-nav__link">
<span class="md-ellipsis">
搜索救援机器人
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_8" class="md-nav__link">
<span class="md-ellipsis">
群体机器人
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#_9" class="md-nav__link">
<span class="md-ellipsis">
人机交互
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#colabnotebook" class="md-nav__link">
<span class="md-ellipsis">
编程任务（使用CoLab或notebook）
</span>
</a>
</li>
</ul>
</nav>
</div>
</div>
</div>
<div class="md-content" data-md-component="content">
<article class="md-content__inner md-typeset">
<h1 id="_1">太空与极端环境机器人<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
<p><em>太空和极端环境机器人将自主性推向极限——通信延迟、辐射和非结构化地形要求机器人自己思考。本章涵盖行星漫游车、在轨服务、通信受限自主性、抗辐射计算、水下机器人、搜索救援、群体机器人和人机交互。</em></p>
<ul>
<li>
<p>在本章中，我们研究了在相对温和环境中运行的自主系统：有车道标线的道路、有平坦地板的地板、有已知物体类别的厨房。但机器人技术的一些最具影响力的应用是在人类无法到达的环境，或者人类存在的成本极高的环境：火星表面、深海海底、核灾难现场和燃烧的建筑。</p>
</li>
<li>
<p>这些<strong>极端环境</strong>面临着共同的挑战：通信受限或有延迟、地形非结构化且不可预测、硬件必须在恶劣条件下生存、而且附近没有人能在出现问题时修理。机器人必须真正自主，而不仅仅是"有人在屏幕前监控的自主"。</p>
</li>
</ul>
<h2 id="_2">太空机器人<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>太空是终极的极端环境。没有空气，温度在-170°C到+120°C之间摆动，辐射轰击电子设备，而援助在数百万公里之外。太空机器人必须异常可靠、节能且自主。</p>
</li>
<li>
<p><strong>行星漫游车</strong>是在其他世界表面探索的移动机器人。NASA的火星漫游车（勇气号、机遇号、好奇号、毅力号）是最著名的例子。每一代都比上一代更加自主。</p>
</li>
</ul>
<p><img alt="地球-火星通信延迟：单向4-24分钟，往返8-48分钟，使得实时控制不可能" src="../../images/earth_mars_delay.svg" /></p>
<ul>
<li>
<p>根本限制是<strong>通信延迟</strong>。火星距地球4-24分钟的无线电距离（取决于轨道位置），因此往返通信需要8-48分钟。漫游车不能实时操控。如果遇到岩石，它不能向地球求助并等待回应。它必须自己决定。</p>
</li>
<li>
<p>早期的漫游车（勇气号、机遇号）严重依赖地面参与的规划：人类研究图像、规划路径、上传命令，漫游车执行命令。一个驾驶周期需要一个完整的火星日。漫游车每天大约能行进50-100米。</p>
</li>
<li>
<p>好奇号和毅力号上的<strong>AutoNav</strong>（自主导航）极大地提高了自主性。漫游车使用立体相机构建局部3D地图（回顾第8章的立体深度），评估地形可通过性（坡度、粗糙度、岩石大小），并使用基于网格的规划器和可通过性代价图规划安全路径。漫游车在人类团队睡眠时自主行驶，将每日行进距离提高到100米以上。</p>
</li>
<li>
<p>火星漫游车上的感知流程受到抗辐射处理器的限制，这些处理器比消费级硬件慢几个数量级（下文讨论）。算法必须计算节俭：经典的立体匹配而非深度神经网络，简单的代价图规划器而非学习型策略。</p>
</li>
<li>
<p><strong>在轨服务</strong>涉及在轨道上检查、修理、加油或使卫星脱离轨道的机器人。随着太空变得更加拥挤，这是一个不断增长的领域。<strong>OSAM-1</strong>（NASA）和商业企业（Astroscale、Northrop Grumman MEV）等任务使用机械臂和对接机构来服务卫星。</p>
</li>
<li>
<p>挑战在于<strong>近距离操作</strong>：服务航天器必须接近目标卫星（可能正在翻滚、不合作且缺乏对接接口），并在微重力下执行精确操作。基于视觉的位姿估计（从相机图像确定目标的3D位置和方向）至关重要。这使用了第8章的技术：特征检测、PnP（透视n点）求解，以及最近基于深度学习的位姿估计器。</p>
</li>
<li>
<p><strong>卫星检查</strong>使用小型航天器目视检查其他卫星是否有损坏或异常。检查者必须自主绕目标导航、避免碰撞并从最佳视角捕获高分辨率图像。这是一个规划问题：找到覆盖所有检查点且满足燃料约束、光照条件和避碰要求的轨迹。</p>
</li>
</ul>
<h2 id="_3">通信约束<a class="headerlink" href="#_3" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>在太空中，通信受到光速、可用带宽和轨道几何的限制（火星背面的漫游车在没有中继卫星的情况下根本无法与地球通信）。</p>
</li>
<li>
<p>这些限制从根本上改变了自主性架构。在地球上，机器人可以将高清视频流传输到云服务器，在GPU集群上运行推理，并在毫秒内接收指令。在太空中，机器人必须在飞行器上完成所有工作。</p>
</li>
<li>
<p><strong>高延迟</strong>意味着机器人必须在没有实时人类指导的情况下规划和行动。自主软件必须处理常规操作、检测异常并响应危险，而无需等待人类输入。这需要鲁棒的板载状态估计、故障检测和应急规划。</p>
</li>
<li>
<p><strong>有限带宽</strong>意味着机器人无法传输原始传感器数据。一张高分辨率图像可能有几兆字节，但火星到地球的数据速率通过直接对地链路只有每秒几千比特（通过轨道中继更高，但仍然有限）。机器人必须积极压缩数据、优先决定发送哪些数据，并在本地做出大部分决策。</p>
</li>
<li>
<p><strong>通信窗口</strong>是间歇性的。火星漫游车只能在特定轨道几何形状期间与地球通信，通常每个火星日通过中继卫星只有几小时。在这些窗口之外，漫游车完全靠自己。</p>
</li>
<li>
<p>对AI的影响是<strong>板载自主性</strong>必须非常可靠。系统需要检测是否出了问题（轮子卡住了、传感器故障了、前方地形无法通行），决定安全响应，并继续运行直到下一个通信窗口，届时它可以报告并接收更新指令。</p>
</li>
</ul>
<h2 id="_4">抗辐射计算<a class="headerlink" href="#_4" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>太空中充满了电离辐射：宇宙射线、太阳粒子事件以及行星磁场中的捕获辐射。高能粒子可以翻转存储器中的比特（<strong>单粒子翻转，SEU</strong>），永久损坏晶体管（<strong>总电离剂量，TID</strong>），或在电路中引起破坏性闩锁。</p>
</li>
<li>
<p><strong>抗辐射处理器</strong>被设计为承受这种环境。它们使用更大的晶体管几何尺寸、冗余逻辑（三模冗余：每个电路有三个副本对输出进行投票）和专门的制造工艺。代价是性能：最先进的抗辐射处理器可能提供200 MIPS，而消费级GPU每秒可执行数十亿次操作。</p>
</li>
<li>
<p><strong>RAD750</strong>（BAE Systems）为好奇号和许多其他航天器提供动力。它以200 MHz运行，约400 MIPS的处理能力，相当于1990年代中期的台式电脑。毅力号使用类似等级的处理器。在现代神经网络上运行（数百万参数、数十亿次乘加运算）在这样的硬件上是不可行的。</p>
</li>
<li>
<p><strong>模型压缩</strong>变得至关重要。第6章的技术（量化、剪枝、知识蒸馏）用于缩小神经网络以适应极端的计算预算。在笔记本电脑GPU上毫秒级运行的模型可能在抗辐射处理器上需要数分钟，或者根本无法装入内存。</p>
</li>
<li>
<p>另一种方法使用<strong>商用现货</strong>处理器，配合软件中的辐射缓解措施：纠错码、看门狗定时器、定期内存清理和优雅降级策略。一些现代任务使用这种方法以获得更强大的计算能力，代价是增加了软件复杂性和风险。</p>
</li>
<li>
<p>未来的行星任务正在探索<strong>FPGA</strong>和专门的AI加速器，它们可以具有耐辐射性，同时提供比传统抗辐射CPU多得多的计算能力，可能首次实现板载深度学习。</p>
</li>
</ul>
<h2 id="_5">非结构化地形中的自主导航<a class="headerlink" href="#_5" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>在地球上，道路平坦、标记清晰且有地图。在火星、月球或灾难现场，没有道路。地形是非结构化的：岩石、斜坡、沙地、裂缝和可能无法支撑机器人重量的表面。</p>
</li>
<li>
<p><strong>地形分类</strong>评估每块地面是否安全通行。特征包括坡度（来自3D重建）、粗糙度（表面法线的方差）、岩石密度和土壤类型。经典方法从立体深度图计算这些特征；现代方法在视觉和几何特征上使用学习型分类器。</p>
</li>
<li>
<p><strong>视觉-惯性里程计（VIO）</strong>通过跟踪跨相机帧的视觉特征并与IMU测量融合来估计机器人的运动。这是SLAM的核心组件（第8章），针对极端条件进行了调整。在火星上，VIO必须处理：无特征的沙地地形（几乎没有可跟踪的视觉特征）、强烈的光照（极端阴影）和有限的计算能力。</p>
</li>
<li>
<p>估计过程使用<strong>扩展卡尔曼滤波（EKF）</strong>或因子图优化融合视觉和惯性数据。状态向量包括位置、速度、方向和IMU偏差。预测步骤使用IMU积分：</p>
</li>
</ul>
<div class="arithmatex">\[\\mathbf{x}_{t+1} = f(\\mathbf{x}_t, \\mathbf{u}_t)\]</div>
<ul>
<li>
<p>其中<span class="arithmatex">\(\\mathbf{u}_t\)</span>是IMU测量值（加速度和角速度）。更新步骤使用视觉特征观测来校正预测。这是贝叶斯估计（第5章）：IMU提供先验，视觉观测更新信念。</p>
</li>
<li>
<p><strong>危险规避</strong>在行星着陆过程中至关重要。当航天器下降向表面时，它必须使用板载相机或LiDAR实时识别安全的着陆区。NASA毅力号上的<strong>地形相对导航（TRN）</strong>系统将板载相机图像与预加载的轨道地图进行比较，以确定下降过程中的位置，然后避开危险地形。这使得在Jezero陨石坑着陆成为可能——一个科学丰富但地形危险的站点，对于以前的 missions 来说风险太大。</p>
</li>
</ul>
<h2 id="_6">水下机器人<a class="headerlink" href="#_6" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>深海与太空一样陌生：压碎性压力（全海深1000+个大气压）、接近零能见度、无GPS和有限的通信。水下机器人对海洋科学、近海基础设施检查、深海采矿和搜索操作至关重要。</p>
</li>
<li>
<p><strong>AUV</strong>（自主水下航行器）无缆运行，携带自己的电力和计算资源。它们遵循预设的测量模式或使用板载智能来适应发现。AUV用于海底测绘、管道检查和环境监测。</p>
</li>
<li>
<p><strong>ROV</strong>（遥控水下航行器）通过电缆连接到水面船只，提供电力和通信。它们用于需要实时人类控制的任务：深海操作、建造和修理。缆线消除了通信限制，但限制了范围并增加了操作复杂性。</p>
</li>
<li>
<p><strong>声学通信</strong>是主要的水下通信方法（无线电波在水中迅速衰减）。声学调制解调器在几公里范围内达到1-10 kbps的数据速率，而陆地上无线电可达吉比特每秒。这甚至比火星通信更加受限，迫使AUV高度自主。</p>
</li>
<li>
<p><strong>水下SLAM</strong>尤其具有挑战性。声纳提供距离测量，但角分辨率差且噪声大（来自海底和水面的多径反射）。相机只能在非常短的距离内工作（清澈水中几米，浑浊条件下更短）。基于特征的可视SLAM（第8章）必须针对水下场景的独特视觉特征进行调整：颜色衰减（红光首先被吸收）、反向散射以及产生亮斑和深影的人工照明。</p>
</li>
<li>
<p>无GPS导航使用<strong>航位推算</strong>（积分来自多普勒测速仪DVL的速度，该仪器利用声学多普勒频移测量相对于海底的速度），辅以偶尔浮出水面获取GPS定位或来自水面应答器的声学定位。这与仅IMU导航相同的漂移问题：小的速度误差在长任务中累积。</p>
</li>
</ul>
<h2 id="_7">搜索救援机器人<a class="headerlink" href="#_7" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p>在地震、建筑物倒塌或工业事故后，机器人可以进入对人类救援人员太危险的区域：结构不稳定的建筑物、有毒环境、火场或密闭空间。</p>
</li>
<li>
<p>需求是：快速部署（几分钟而非几小时）、在GPS受限环境中运行（建筑物内部、地下）、通过墙壁和瓦砾的鲁棒通信，以及导航高度杂乱、部分坍塌空间的能力，这些空间充满碎片、灰尘和不良照明。</p>
</li>
<li>
<p><strong>多机器人协调</strong>在搜索救援中很有价值，因为一支机器人团队可以比单个机器人更快地覆盖大面积。挑战在于协调：机器人必须划分搜索区域、避免重复工作并共享发现。</p>
</li>
<li>
<p><strong>前沿探索</strong>将机器人分配到已探索和未探索空间之间的边界（"前沿"）。每个机器人导航到最近的未探索前沿、绘制地图并继续前进。中央或分布式规划器将前沿分配给机器人以最小化总探索时间。这是一个覆盖优化问题。</p>
</li>
<li>
<p>通过瓦砾的通信不可靠。机器人可能失去与控制台和彼此的联系。系统必须对间歇通信具有鲁棒性：每个机器人应能独立运行，构建自己的局部地图并做出自己的决策，然后在通信恢复时合并信息。</p>
</li>
</ul>
<h2 id="_8">群体机器人<a class="headerlink" href="#_8" title="Permanent link">&para;</a></h2>
<ul>
<li>
<p><strong>群体机器人</strong>使用大量简单、低成本的机器人，通过局部交互实现复杂的集体行为。没有单个机器人单独具备能力，但整个群体可以执行单个机器人无法完成的任务。</p>
</li>
<li>
<p>灵感来自生物群体：蚂蚁用身体搭桥、蜜蜂集体决定巢穴位置、鱼群通过协调运动躲避捕食者。在每种情况下，简单的局部规则（跟随邻居、避免碰撞、向食物移动）产生复杂的全局行为。</p>
</li>
<li>
<p><strong>去中心化控制</strong>意味着没有中央指挥官。每个机器人遵循相同的局部规则，仅对其邻居和即时环境作出反应。全局行为从这些局部交互中<strong>涌现</strong>。这使得群体具有固有的鲁棒性：如果一个机器人失效，群体继续运行。没有单点故障。</p>
</li>
<li>
<p><strong>共识算法</strong>使群体能够仅通过局部通信就集体决策达成一致（例如，向哪个方向移动、优先处理哪个任务）。一个简单的共识协议让每个机器人与其邻居平均其值：</p>
</li>
</ul>
<div class="arithmatex">\[x_i(t+1) = \\frac{1}{|N_i| + 1} \\left( x_i(t) + \\sum_{j \\in N_i} x_j(t) \\right)\]</div>
<p><img alt="群体共识：机器人从分散开始，迭代地与邻居平均，收敛到共享位置" src="../../images/swarm_consensus.svg" /></p>
<ul>
<li>其中<span class="arithmatex">\(N_i\)</span>是机器人<span class="arithmatex">\(i\)</span>的邻居集合。这一过程迭代直到所有机器人收敛到相同的值（全局平均值）。收敛速度取决于通信图的拓扑结构，特别是其代数连通性（图拉普拉斯矩阵的第二小特征值，与第2章的特征值相关）。</li>
</ul>
<p><img alt="Reynolds三个群集规则：分离避免碰撞，对齐匹配航向，内聚保持群体" src="../../images/reynolds_flocking.svg" /></p>
<ul>
<li>
<p><strong>群集算法</strong>（Reynolds规则）通过每个机器人的三个简单规则产生协调的群体运动：</p>
<ul>
<li><strong>分离</strong>：远离太近的邻居（避免碰撞）。</li>
<li><strong>对齐</strong>：朝向邻居的平均航向（朝相同方向移动）。</li>
<li><strong>内聚</strong>：朝向邻居的平均位置（与群体在一起）。</li>
</ul>
</li>
<li>
<p>每个规则是机器人速度的一个向量贡献。这些向量的加权和产生自然主义的群集行为。这是一个向量的线性组合（第1章），其中权重控制每个行为的相对重要性。</p>
</li>
<li>
<p>群体机器人的应用包括环境监测（在大范围内分布传感器）、精准农业（协调无人机进行作物喷洒）、建造（机器人集体组装结构）和搜索操作（高效覆盖大面积）。</p>
</li>
</ul>
<h2 id="_9">人机交互<a class="headerlink" href="#_9" title="Permanent link">&para;</a></h2>
<ul>
<li>大多数真实的自主系统是与人类并肩运行，而非孤立运行。人与机器人之间的交互——他们如何沟通、共享控制和建立信任——与机器人的技术能力同样重要。</li>
</ul>
<p><img alt="共享自主光谱：从完全人类遥控操作（alpha=1）经混合控制到完全机器人自主（alpha=0）" src="../../images/shared_autonomy_spectrum.svg" /></p>
<ul>
<li>
<p><strong>共享自主</strong>混合了人和机器人的控制。不是完全遥控操作（人类控制一切）或完全自主（机器人控制一切），而是共享自主让人类提供高层意图，同时机器人处理底层执行。例如，人类可能指向一个物体说"捡起来"，然后机器人自主规划抓取和手臂运动。</p>
</li>
<li>
<p>数学上，共享自主可以建模为人类输入<span class="arithmatex">\(\\mathbf{u}_h\)</span>和机器人自主动作<span class="arithmatex">\(\\mathbf{u}_r\)</span>的混合：</p>
</li>
</ul>
<div class="arithmatex">\[\\mathbf{u} = \\alpha \\mathbf{u}_h + (1 - \\alpha) \\mathbf{u}_r\]</div>
<ul>
<li>
<p>其中<span class="arithmatex">\(\\alpha \\in [0, 1]\)</span>是混合参数。当<span class="arithmatex">\(\\alpha = 1\)</span>时，人类完全控制（遥控操作）。当<span class="arithmatex">\(\\alpha = 0\)</span>时，机器人完全自主。自适应共享自主根据情况调整<span class="arithmatex">\(\\alpha\)</span>：机器人在自信时接管更多控制，在不确定或情况新颖时让出控制。</p>
</li>
<li>
<p><strong>遥控操作</strong>对于超出当前自主能力的任务仍然很重要。人类操作员通过机器人的相机远程查看场景并控制机器人。挑战是<strong>延迟</strong>：即使100毫秒的延迟也会使遥控操作变得困难，而太空中的多秒延迟使其对精细操作几乎不可能。预测显示（显示机器人预测的未来状态）和虚拟夹具（防止操作员命令危险运动的软件引导）有助于弥补。</p>
</li>
<li>
<p><strong>信任校准</strong>是确保人类对机器人有适当信任的问题：不要太多（过度信任导致自满，在需要时未能干预），也不要太少（信任不足导致不必要干预和利用不足）。信任应该校准到机器人的实际能力：在它处理得好的情况下信任它，在接近其能力边缘的情况下保持怀疑。</p>
</li>
<li>
<p>研究表明，信任受以下因素的影响：机器人的透明度（它是否解释其决策？）、可靠性（它是可预测地失败还是随机地失败？）以及沟通（它是否表达不确定性？）。一个说"我对此路径只有40%的置信度，是否继续？"的机器人比一个默默向前驾驶的机器人能做出更好的人类决策。</p>
</li>
<li>
<p>机器人运动中的<strong>可读性</strong>意味着机器人以传达其意图的方式运动给附近的人类。如果机器人伸手去拿一个物体，它的路径应该使其目标对象显而易见，即使它还未到达。这涉及规划最大化观察者早期推断目标的轨迹，可以形式化为给定观察到的部分轨迹时真实目标的后验概率最大化：</p>
</li>
</ul>
<div class="arithmatex">\[\\pi^* = \\arg\\max_\\pi P(G \\mid \\xi_{0:t})\]</div>
<ul>
<li>其中<span class="arithmatex">\(G\)</span>是目标，<span class="arithmatex">\(\\xi_{0:t}\)</span>是到目前为止观察到的轨迹。这使用了贝叶斯推理（第5章）：观察者对可能的目标有先验，机器人的轨迹提供了更新此信念的证据。</li>
</ul>
<h2 id="colabnotebook">编程任务（使用CoLab或notebook）<a class="headerlink" href="#colabnotebook" title="Permanent link">&para;</a></h2>
<ol>
<li>
<p>模拟机器人群体就目标位置达成一致的共识算法。从随机初始位置开始，观察收敛过程。
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">n_robots</span> <span class="o">=</span> <span class="mi">10</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">rng</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">positions</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">rng</span><span class="p">,</span> <span class="p">(</span><span class="n">n_robots</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">minval</span><span class="o">=-</span><span class="mi">5</span><span class="p">,</span> <span class="n">maxval</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="c1"># 通信图：每个机器人与最近的3个邻居通信</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">get_neighbours</span><span class="p">(</span><span class="n">positions</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">3</span><span class="p">):</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">dists</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">positions</span><span class="p">[:,</span> <span class="kc">None</span><span class="p">]</span> <span class="o">-</span> <span class="n">positions</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="p">:],</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a> <span class="c1"># 对每个机器人，找最近的k个（排除自身）</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="n">neighbours</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="n">dists</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">:</span><span class="n">k</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="k">return</span> <span class="n">neighbours</span>
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="n">history</span> <span class="o">=</span> <span class="p">[</span><span class="n">positions</span><span class="o">.</span><span class="n">copy</span><span class="p">()]</span>
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="k">for</span> <span class="n">step</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">30</span><span class="p">):</span>
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a> <span class="n">neighbours</span> <span class="o">=</span> <span class="n">get_neighbours</span><span class="p">(</span><span class="n">positions</span><span class="p">)</span>
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a> <span class="n">new_positions</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">positions</span><span class="p">)</span>
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_robots</span><span class="p">):</span>
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a> <span class="n">nbr_pos</span> <span class="o">=</span> <span class="n">positions</span><span class="p">[</span><span class="n">neighbours</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a> <span class="n">new_positions</span> <span class="o">=</span> <span class="n">new_positions</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span>
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a> <span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="n">nbr_pos</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">neighbours</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="p">)</span>
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a> <span class="n">positions</span> <span class="o">=</span> <span class="n">new_positions</span>
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a> <span class="n">history</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">positions</span><span class="o">.</span><span class="n">copy</span><span class="p">())</span>
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="c1"># 绘制收敛过程</span>
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="k">for</span> <span class="n">ax</span><span class="p">,</span> <span class="n">step_idx</span><span class="p">,</span> <span class="n">title</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">axes</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">29</span><span class="p">],</span> <span class="p">[</span><span class="s2">&quot;初始&quot;</span><span class="p">,</span> <span class="s2">&quot;第10步&quot;</span><span class="p">,</span> <span class="s2">&quot;最终&quot;</span><span class="p">]):</span>
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a> <span class="n">h</span> <span class="o">=</span> <span class="n">history</span><span class="p">[</span><span class="n">step_idx</span><span class="p">]</span>
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a> <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">h</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">h</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="o">-</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">);</span> <span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">);</span> <span class="n">ax</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">);</span> <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s2">&quot;群体共识：机器人收敛到一致性&quot;</span><span class="p">)</span>
<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</code></pre></div></p>
</li>
<li>
<p>实现Reynolds群集规则（分离、对齐、内聚）并模拟一个群体一起移动。
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">n</span> <span class="o">=</span> <span class="mi">30</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">rng</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">k1</span><span class="p">,</span> <span class="n">k2</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="n">rng</span><span class="p">)</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">pos</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">k1</span><span class="p">,</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">minval</span><span class="o">=-</span><span class="mi">5</span><span class="p">,</span> <span class="n">maxval</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">vel</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="n">k2</span><span class="p">,</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">minval</span><span class="o">=-</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">maxval</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="n">dt</span> <span class="o">=</span> <span class="mf">0.1</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="n">separation_radius</span> <span class="o">=</span> <span class="mf">1.0</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="n">neighbour_radius</span> <span class="o">=</span> <span class="mf">3.0</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="n">trajectories</span> <span class="o">=</span> <span class="p">[</span><span class="n">pos</span><span class="o">.</span><span class="n">copy</span><span class="p">()]</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">200</span><span class="p">):</span>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a> <span class="n">new_vel</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">vel</span><span class="p">)</span>
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a> <span class="n">diffs</span> <span class="o">=</span> <span class="n">pos</span> <span class="o">-</span> <span class="n">pos</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a> <span class="n">dists</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">diffs</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a>
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a> <span class="c1"># 半径内的邻居（排除自身）</span>
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a> <span class="n">nbr_mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">dists</span> <span class="o">&lt;</span> <span class="n">neighbour_radius</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="n">dists</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a> <span class="n">sep_mask</span> <span class="o">=</span> <span class="p">(</span><span class="n">dists</span> <span class="o">&lt;</span> <span class="n">separation_radius</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="n">dists</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a>
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a> <span class="c1"># 分离：远离非常近的邻居</span>
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a> <span class="k">if</span> <span class="n">sep_mask</span><span class="o">.</span><span class="n">any</span><span class="p">():</span>
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a> <span class="n">sep</span> <span class="o">=</span> <span class="o">-</span><span class="n">diffs</span><span class="p">[</span><span class="n">sep_mask</span><span class="p">]</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a> <span class="n">sep</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a>
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a> <span class="c1"># 对齐：匹配邻居的平均速度</span>
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a> <span class="k">if</span> <span class="n">nbr_mask</span><span class="o">.</span><span class="n">any</span><span class="p">():</span>
<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a> <span class="n">align</span> <span class="o">=</span> <span class="n">vel</span><span class="p">[</span><span class="n">nbr_mask</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="o">-</span> <span class="n">vel</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a> <span class="n">align</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a>
<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a> <span class="c1"># 内聚：朝向邻居的平均位置</span>
<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a> <span class="k">if</span> <span class="n">nbr_mask</span><span class="o">.</span><span class="n">any</span><span class="p">():</span>
<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a> <span class="n">cohesion</span> <span class="o">=</span> <span class="n">pos</span><span class="p">[</span><span class="n">nbr_mask</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="o">-</span> <span class="n">pos</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a> <span class="n">cohesion</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a>
<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a> <span class="n">new_vel</span> <span class="o">=</span> <span class="n">new_vel</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">vel</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="mf">1.5</span> <span class="o">*</span> <span class="n">sep</span> <span class="o">+</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="n">align</span> <span class="o">+</span> <span class="mf">0.3</span> <span class="o">*</span> <span class="n">cohesion</span><span class="p">)</span>
<a id="__codelineno-1-46" name="__codelineno-1-46" href="#__codelineno-1-46"></a>
<a id="__codelineno-1-47" name="__codelineno-1-47" href="#__codelineno-1-47"></a> <span class="c1"># 限制速度</span>
<a id="__codelineno-1-48" name="__codelineno-1-48" href="#__codelineno-1-48"></a> <span class="n">speeds</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">new_vel</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<a id="__codelineno-1-49" name="__codelineno-1-49" href="#__codelineno-1-49"></a> <span class="n">vel</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">speeds</span> <span class="o">&gt;</span> <span class="mf">2.0</span><span class="p">,</span> <span class="n">new_vel</span> <span class="o">/</span> <span class="n">speeds</span> <span class="o">*</span> <span class="mf">2.0</span><span class="p">,</span> <span class="n">new_vel</span><span class="p">)</span>
<a id="__codelineno-1-50" name="__codelineno-1-50" href="#__codelineno-1-50"></a> <span class="n">pos</span> <span class="o">=</span> <span class="n">pos</span> <span class="o">+</span> <span class="n">vel</span> <span class="o">*</span> <span class="n">dt</span>
<a id="__codelineno-1-51" name="__codelineno-1-51" href="#__codelineno-1-51"></a> <span class="n">trajectories</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pos</span><span class="o">.</span><span class="n">copy</span><span class="p">())</span>
<a id="__codelineno-1-52" name="__codelineno-1-52" href="#__codelineno-1-52"></a>
<a id="__codelineno-1-53" name="__codelineno-1-53" href="#__codelineno-1-53"></a><span class="c1"># 绘制快照</span>
<a id="__codelineno-1-54" name="__codelineno-1-54" href="#__codelineno-1-54"></a><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<a id="__codelineno-1-55" name="__codelineno-1-55" href="#__codelineno-1-55"></a><span class="k">for</span> <span class="n">ax</span><span class="p">,</span> <span class="n">idx</span><span class="p">,</span> <span class="n">title</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">axes</span><span class="p">,</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">50</span><span class="p">,</span> <span class="mi">199</span><span class="p">],</span> <span class="p">[</span><span class="s2">&quot;开始&quot;</span><span class="p">,</span> <span class="s2">&quot;第50步&quot;</span><span class="p">,</span> <span class="s2">&quot;第200步&quot;</span><span class="p">]):</span>
<a id="__codelineno-1-56" name="__codelineno-1-56" href="#__codelineno-1-56"></a> <span class="n">p</span> <span class="o">=</span> <span class="n">trajectories</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
<a id="__codelineno-1-57" name="__codelineno-1-57" href="#__codelineno-1-57"></a> <span class="n">v</span> <span class="o">=</span> <span class="n">vel</span> <span class="k">if</span> <span class="n">idx</span> <span class="o">==</span> <span class="mi">199</span> <span class="k">else</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">vel</span><span class="p">)</span>
<a id="__codelineno-1-58" name="__codelineno-1-58" href="#__codelineno-1-58"></a> <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">p</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">p</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">s</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s2">&quot;blue&quot;</span><span class="p">)</span>
<a id="__codelineno-1-59" name="__codelineno-1-59" href="#__codelineno-1-59"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">);</span> <span class="n">ax</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">);</span> <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
<a id="__codelineno-1-60" name="__codelineno-1-60" href="#__codelineno-1-60"></a> <span class="n">lim</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">p</span><span class="p">)</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<a id="__codelineno-1-61" name="__codelineno-1-61" href="#__codelineno-1-61"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="o">-</span><span class="n">lim</span><span class="p">,</span> <span class="n">lim</span><span class="p">);</span> <span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">-</span><span class="n">lim</span><span class="p">,</span> <span class="n">lim</span><span class="p">)</span>
<a id="__codelineno-1-62" name="__codelineno-1-62" href="#__codelineno-1-62"></a><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s2">&quot;Reynolds群集：分离+对齐+内聚&quot;</span><span class="p">)</span>
<a id="__codelineno-1-63" name="__codelineno-1-63" href="#__codelineno-1-63"></a><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<a id="__codelineno-1-64" name="__codelineno-1-64" href="#__codelineno-1-64"></a><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</code></pre></div></p>
</li>
<li>
<p>模拟共享自主混合：人类提供带噪声的方向输入，机器人的自主系统提供到目标的平滑路径。用不同的alpha值进行混合。
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">goal</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">10.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">])</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">pos</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">])</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">dt</span> <span class="o">=</span> <span class="mf">0.1</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">rng</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">PRNGKey</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="n">fig</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">15</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="k">for</span> <span class="n">ax</span><span class="p">,</span> <span class="n">alpha</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">axes</span><span class="p">,</span> <span class="p">[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]):</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a> <span class="n">pos</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">])</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a> <span class="n">path</span> <span class="o">=</span> <span class="p">[</span><span class="n">pos</span><span class="o">.</span><span class="n">copy</span><span class="p">()]</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a> <span class="k">for</span> <span class="n">step</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">150</span><span class="p">):</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a> <span class="c1"># 机器人自主：到目标的平滑路径</span>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a> <span class="n">direction</span> <span class="o">=</span> <span class="n">goal</span> <span class="o">-</span> <span class="n">pos</span>
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a> <span class="n">u_robot</span> <span class="o">=</span> <span class="n">direction</span> <span class="o">/</span> <span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">direction</span><span class="p">)</span> <span class="o">+</span> <span class="mf">1e-6</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1.0</span>
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a>
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a> <span class="c1"># 人类输入：大致正确的方向但有噪声</span>
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a> <span class="n">noise</span> <span class="o">=</span> <span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">jax</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">fold_in</span><span class="p">(</span><span class="n">rng</span><span class="p">,</span> <span class="n">step</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,))</span> <span class="o">*</span> <span class="mf">0.5</span>
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a> <span class="n">u_human</span> <span class="o">=</span> <span class="n">u_robot</span> <span class="o">+</span> <span class="n">noise</span>
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a>
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a> <span class="c1"># 混合</span>
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a> <span class="n">u</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">u_human</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">alpha</span><span class="p">)</span> <span class="o">*</span> <span class="n">u_robot</span>
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a> <span class="n">pos</span> <span class="o">=</span> <span class="n">pos</span> <span class="o">+</span> <span class="n">u</span> <span class="o">*</span> <span class="n">dt</span>
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a> <span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pos</span><span class="o">.</span><span class="n">copy</span><span class="p">())</span>
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a>
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a> <span class="k">if</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">pos</span> <span class="o">-</span> <span class="n">goal</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mf">0.3</span><span class="p">:</span>
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a> <span class="k">break</span>
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a>
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a> <span class="n">path</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">path</span><span class="p">)</span>
<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">path</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">path</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">&quot;b-&quot;</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="o">*</span><span class="n">goal</span><span class="p">,</span> <span class="s2">&quot;r*&quot;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;go&quot;</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">10</span><span class="p">)</span>
<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;α=</span><span class="si">{</span><span class="n">alpha</span><span class="si">:</span><span class="s2">.1f</span><span class="si">}</span><span class="s2"> (</span><span class="si">{</span><span class="s1">&#39;人类&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">alpha</span><span class="o">==</span><span class="mi">1</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;机器人&#39;</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">alpha</span><span class="o">==</span><span class="mi">0</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="s1">&#39;共享&#39;</span><span class="si">}</span><span class="s2">)&quot;</span><span class="p">)</span>
<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">12</span><span class="p">);</span> <span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">8</span><span class="p">)</span>
<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a> <span class="n">ax</span><span class="o">.</span><span class="n">set_aspect</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">);</span> <span class="n">ax</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a>
<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s2">&quot;共享自主：混合人类与机器人控制&quot;</span><span class="p">)</span>
<a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</code></pre></div></p>
</li>
</ol>
</article>
</div>
<script>var target=document.getElementById(location.hash.slice(1));target&&target.name&&(target.checked=target.name.startsWith("__tabbed_"))</script>
</div>
<button type="button" class="md-top md-icon" data-md-component="top" hidden>
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8z"/></svg>
回到页面顶部
</button>
</main>
<footer class="md-footer">
<nav class="md-footer__inner md-grid" aria-label="页脚" >
<a href="../04.%20self-driving/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 自动驾驶">
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11z"/></svg>
</div>
<div class="md-footer__title">
<span class="md-footer__direction">
上一页
</span>
<div class="md-ellipsis">
自动驾驶
</div>
</div>
</a>
<a href="../../chapter%2012%3A%20graph%20neural%20networks/01.%20geometric%20deep%20learning/" class="md-footer__link md-footer__link--next" aria-label="下一页: 几何深度学习">
<div class="md-footer__title">
<span class="md-footer__direction">
下一页
</span>
<div class="md-ellipsis">
几何深度学习
</div>
</div>
<div class="md-footer__button md-icon">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11z"/></svg>
</div>
</a>
</nav>
<div class="md-footer-meta md-typeset">
<div class="md-footer-meta__inner md-grid">
<div class="md-copyright">
Made with
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
Material for MkDocs
</a>
</div>
<div class="md-social">
<a href="https://github.com/flykhan/maths-cs-ai-compendium-zh" target="_blank" rel="noopener" title="github.com" class="md-social__link">
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 7.1.0 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2025 Fonticons, Inc.--><path d="M173.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6m-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3m44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9M252.8 8C114.1 8 8 113.3 8 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C436.2 457.8 504 362.9 504 252 504 113.3 391.5 8 252.8 8M105.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1m-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7m32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1m-11.4-14.7c-1.6 1-1.6 3.6 0 5.9s4.3 3.3 5.6 2.3c1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2"/></svg>
</a>
</div>
</div>
</div>
</footer>
</div>
<div class="md-dialog" data-md-component="dialog">
<div class="md-dialog__inner md-typeset"></div>
</div>
<script id="__config" type="application/json">{"annotate": null, "base": "../..", "features": ["navigation.tabs", "navigation.sections", "navigation.expand", "navigation.top", "navigation.footer", "search.suggest", "search.highlight", "content.code.copy", "toc.follow"], "search": "../../assets/javascripts/workers/search.2c215733.min.js", "tags": null, "translations": {"clipboard.copied": "\u5df2\u590d\u5236", "clipboard.copy": "\u590d\u5236", "search.result.more.one": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.more.other": "\u5728\u8be5\u9875\u4e0a\u8fd8\u6709 # \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.none": "\u6ca1\u6709\u627e\u5230\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.one": "\u627e\u5230 1 \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.other": "# \u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u7ed3\u679c", "search.result.placeholder": "\u952e\u5165\u4ee5\u5f00\u59cb\u641c\u7d22", "search.result.term.missing": "\u7f3a\u5c11", "select.version": "\u9009\u62e9\u5f53\u524d\u7248\u672c"}, "version": null}</script>
<script src="../../assets/javascripts/bundle.79ae519e.min.js"></script>
<script src="../../javascripts/mathjax.js"></script>
<script src="https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js"></script>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink