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Modern Robotics: Mechanics, Planning, and Control

C++ Library

This repository contains the code library accompanying Modern Robotics: Mechanics, Planning, and Control (Kevin Lynch and Frank Park, Cambridge University Press 2017). The user manual is in the doc directory of main repository.

The functions are available in:

Each function has a commented section above it explaining the inputs required for its use as well as an example of how it can be used and what the output will be. This repository also contains a pdf document that provides an overview of the available functions using MATLAB syntax. Functions are organized according to the chapter in which they are introduced in the book. Basic functions, such as functions to calculate the magnitude of a vector, normalize a vector, test if the value is near zero, and perform matrix operations such as multiplication and inverses, are not documented here.

The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness.

Installation

1. Install Eigen library.

  • On Mac
foo@bar:~$ brew install eigen
  • On Linux
foo@bar:~$ sudo apt-get install libeigen3-dev

2. Prepare build

foo@bar:~$ mkdir build &&cd build

By default cmake will install our build into the system directories. To define a custom install directory we simply pass it to cmake:

foo@bar:build $ cmake .. -DCMAKE_INSTALL_PREFIX=../_install

Or just configure with defaults

foo@bar:build $ cmake ..

Building and installing library

foo@bar:build $ make all && make install

Testing the library

foo@bar:build $ ./lib_test

About

Modern Robotics: Mechanics, Planning, and Control C++ Library --- The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness. http://modernrobotics.org/

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all 
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}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

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Repository files navigation
Modern Robotics: Mechanics, Planning, and Control
C++ Library
This repository contains the code library accompanying Modern Robotics:
Mechanics, Planning, and Control (Kevin Lynch
and Frank Park, Cambridge University Press 2017). The
user manual is in the doc directory of main repository.
The functions are available in:
Each function has a commented section above it explaining the inputs required for its use as well as an example of how it can be used and what the output will be. This repository also contains a pdf document that provides an overview of the available functions using MATLAB syntax. Functions are organized according to the chapter in which they are introduced in the book. Basic functions, such as functions to calculate the magnitude of a vector, normalize a vector, test if the value is near zero, and perform matrix operations such as multiplication and inverses, are not documented here.
The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness.
Installation
1. Install Eigen library.
  • On Mac
foo@bar:~$ brew install eigen
  • On Linux
foo@bar:~$ sudo apt-get install libeigen3-dev
2. Prepare build
foo@bar:~$ mkdir build &&cd build
By default cmake will install our build into the system directories.
To define a custom install directory we simply pass it to cmake:
foo@bar:build $ cmake .. -DCMAKE_INSTALL_PREFIX=../_install
Or just configure with defaults
foo@bar:build $ cmake ..
Building and installing library
foo@bar:build $ make all && make install
Testing the library
foo@bar:build $ ./lib_test
About
Modern Robotics: Mechanics, Planning, and Control C++ Library --- The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness. http://modernrobotics.org/
Resources
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Repository files navigation
Modern Robotics: Mechanics, Planning, and Control
C++ Library
This repository contains the code library accompanying Modern Robotics:
Mechanics, Planning, and Control (Kevin Lynch
and Frank Park, Cambridge University Press 2017). The
user manual is in the doc directory of main repository.
The functions are available in:
Each function has a commented section above it explaining the inputs required for its use as well as an example of how it can be used and what the output will be. This repository also contains a pdf document that provides an overview of the available functions using MATLAB syntax. Functions are organized according to the chapter in which they are introduced in the book. Basic functions, such as functions to calculate the magnitude of a vector, normalize a vector, test if the value is near zero, and perform matrix operations such as multiplication and inverses, are not documented here.
The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness.
Installation
1. Install Eigen library.
  • On Mac
foo@bar:~$ brew install eigen
  • On Linux
foo@bar:~$ sudo apt-get install libeigen3-dev
2. Prepare build
foo@bar:~$ mkdir build &&cd build
By default cmake will install our build into the system directories.
To define a custom install directory we simply pass it to cmake:
foo@bar:build $ cmake .. -DCMAKE_INSTALL_PREFIX=../_install
Or just configure with defaults
foo@bar:build $ cmake ..
Building and installing library
foo@bar:build $ make all && make install
Testing the library
foo@bar:build $ ./lib_test
About
Modern Robotics: Mechanics, Planning, and Control C++ Library --- The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness. http://modernrobotics.org/
Resources
Readme
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Repository files navigation
Modern Robotics: Mechanics, Planning, and Control
C++ Library
This repository contains the code library accompanying Modern Robotics:
Mechanics, Planning, and Control (Kevin Lynch
and Frank Park, Cambridge University Press 2017). The
user manual is in the doc directory of main repository.
The functions are available in:
Each function has a commented section above it explaining the inputs required for its use as well as an example of how it can be used and what the output will be. This repository also contains a pdf document that provides an overview of the available functions using MATLAB syntax. Functions are organized according to the chapter in which they are introduced in the book. Basic functions, such as functions to calculate the magnitude of a vector, normalize a vector, test if the value is near zero, and perform matrix operations such as multiplication and inverses, are not documented here.
The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness.
Installation
1. Install Eigen library.
  • On Mac
foo@bar:~$ brew install eigen
  • On Linux
foo@bar:~$ sudo apt-get install libeigen3-dev
2. Prepare build
foo@bar:~$ mkdir build &&cd build
By default cmake will install our build into the system directories.
To define a custom install directory we simply pass it to cmake:
foo@bar:build $ cmake .. -DCMAKE_INSTALL_PREFIX=../_install
Or just configure with defaults
foo@bar:build $ cmake ..
Building and installing library
foo@bar:build $ make all && make install
Testing the library
foo@bar:build $ ./lib_test
About
Modern Robotics: Mechanics, Planning, and Control C++ Library --- The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness. http://modernrobotics.org/
Resources
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

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README.md
Repository files navigation
Modern Robotics: Mechanics, Planning, and Control
C++ Library
This repository contains the code library accompanying Modern Robotics:
Mechanics, Planning, and Control (Kevin Lynch
and Frank Park, Cambridge University Press 2017). The
user manual is in the doc directory of main repository.
The functions are available in:
Each function has a commented section above it explaining the inputs required for its use as well as an example of how it can be used and what the output will be. This repository also contains a pdf document that provides an overview of the available functions using MATLAB syntax. Functions are organized according to the chapter in which they are introduced in the book. Basic functions, such as functions to calculate the magnitude of a vector, normalize a vector, test if the value is near zero, and perform matrix operations such as multiplication and inverses, are not documented here.
The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness.
Installation
1. Install Eigen library.
  • On Mac
foo@bar:~$ brew install eigen
  • On Linux
foo@bar:~$ sudo apt-get install libeigen3-dev
2. Prepare build
foo@bar:~$ mkdir build &&cd build
By default cmake will install our build into the system directories.
To define a custom install directory we simply pass it to cmake:
foo@bar:build $ cmake .. -DCMAKE_INSTALL_PREFIX=../_install
Or just configure with defaults
foo@bar:build $ cmake ..
Building and installing library
foo@bar:build $ make all && make install
Testing the library
foo@bar:build $ ./lib_test
About
Modern Robotics: Mechanics, Planning, and Control C++ Library --- The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness. http://modernrobotics.org/
Resources
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Repository files navigation
Modern Robotics: Mechanics, Planning, and Control
C++ Library
This repository contains the code library accompanying Modern Robotics:
Mechanics, Planning, and Control (Kevin Lynch
and Frank Park, Cambridge University Press 2017). The
user manual is in the doc directory of main repository.
The functions are available in:
Each function has a commented section above it explaining the inputs required for its use as well as an example of how it can be used and what the output will be. This repository also contains a pdf document that provides an overview of the available functions using MATLAB syntax. Functions are organized according to the chapter in which they are introduced in the book. Basic functions, such as functions to calculate the magnitude of a vector, normalize a vector, test if the value is near zero, and perform matrix operations such as multiplication and inverses, are not documented here.
The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness.
Installation
1. Install Eigen library.
  • On Mac
foo@bar:~$ brew install eigen
  • On Linux
foo@bar:~$ sudo apt-get install libeigen3-dev
2. Prepare build
foo@bar:~$ mkdir build &&cd build
By default cmake will install our build into the system directories.
To define a custom install directory we simply pass it to cmake:
foo@bar:build $ cmake .. -DCMAKE_INSTALL_PREFIX=../_install
Or just configure with defaults
foo@bar:build $ cmake ..
Building and installing library
foo@bar:build $ make all && make install
Testing the library
foo@bar:build $ ./lib_test
About
Modern Robotics: Mechanics, Planning, and Control C++ Library --- The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness. http://modernrobotics.org/
Resources
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
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var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Repository files navigation
Modern Robotics: Mechanics, Planning, and Control
C++ Library
This repository contains the code library accompanying Modern Robotics:
Mechanics, Planning, and Control (Kevin Lynch
and Frank Park, Cambridge University Press 2017). The
user manual is in the doc directory of main repository.
The functions are available in:
Each function has a commented section above it explaining the inputs required for its use as well as an example of how it can be used and what the output will be. This repository also contains a pdf document that provides an overview of the available functions using MATLAB syntax. Functions are organized according to the chapter in which they are introduced in the book. Basic functions, such as functions to calculate the magnitude of a vector, normalize a vector, test if the value is near zero, and perform matrix operations such as multiplication and inverses, are not documented here.
The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness.
Installation
1. Install Eigen library.
  • On Mac
foo@bar:~$ brew install eigen
  • On Linux
foo@bar:~$ sudo apt-get install libeigen3-dev
2. Prepare build
foo@bar:~$ mkdir build &&cd build
By default cmake will install our build into the system directories.
To define a custom install directory we simply pass it to cmake:
foo@bar:build $ cmake .. -DCMAKE_INSTALL_PREFIX=../_install
Or just configure with defaults
foo@bar:build $ cmake ..
Building and installing library
foo@bar:build $ make all && make install
Testing the library
foo@bar:build $ ./lib_test
About
Modern Robotics: Mechanics, Planning, and Control C++ Library --- The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness. http://modernrobotics.org/
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode");
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

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Modern Robotics: Mechanics, Planning, and Control
C++ Library
This repository contains the code library accompanying Modern Robotics:
Mechanics, Planning, and Control (Kevin Lynch
and Frank Park, Cambridge University Press 2017). The
user manual is in the doc directory of main repository.
The functions are available in:
Each function has a commented section above it explaining the inputs required for its use as well as an example of how it can be used and what the output will be. This repository also contains a pdf document that provides an overview of the available functions using MATLAB syntax. Functions are organized according to the chapter in which they are introduced in the book. Basic functions, such as functions to calculate the magnitude of a vector, normalize a vector, test if the value is near zero, and perform matrix operations such as multiplication and inverses, are not documented here.
The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness.
Installation
1. Install Eigen library.
  • On Mac
foo@bar:~$ brew install eigen
  • On Linux
foo@bar:~$ sudo apt-get install libeigen3-dev
2. Prepare build
foo@bar:~$ mkdir build &&cd build
By default cmake will install our build into the system directories.
To define a custom install directory we simply pass it to cmake:
foo@bar:build $ cmake .. -DCMAKE_INSTALL_PREFIX=../_install
Or just configure with defaults
foo@bar:build $ cmake ..
Building and installing library
foo@bar:build $ make all && make install
Testing the library
foo@bar:build $ ./lib_test
About
Modern Robotics: Mechanics, Planning, and Control C++ Library --- The primary purpose of the provided software is to be easy to read and educational, reinforcing the concepts in the book. The code is optimized neither for efficiency nor robustness. http://modernrobotics.org/
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