Top

Published in:

2015 | OriginalPaper | Chapter

5. Foundation: Rigid Motions and Image Formation

Authors : Takeshi Hatanaka, Nikhil Chopra, Masayuki Fujita, Mark W. Spong

Published in: Passivity-Based Control and Estimation in Networked Robotics

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This chapter provides foundations not only for visual feedback control and estimation, but also for all the subsequent chapters. Here, the bases of rigid motions and image formations are introduced. In particular, inherent passivity in the 3-D rigid body motion is highlighted.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Synchronization of Bilateral Teleoperators

next chapter Passivity-Based Visual Feedback Estimation

A frame \(\varSigma \), whose \(x,y,z\)-axes are denoted by \(x\), \(y\) and \(z\), is said to be right-handed if \(x \times y = z\) holds. Throughout this book, all the coordinate frames are assumed to be right-handed.

Physically, the angular velocity \(\omega _{ab}^s\) is the instantaneous angular velocity of \(\varSigma _b\) as viewed in the fixed (spatial) frame \(\varSigma _a\), and the linear velocity \(v^s_{ab}\) is the velocity of a point on the body traveling the origin of \(\varSigma _a\). Please refer to [192, 219] for more details.

The notation \({\mathbb S}^{n\times n}\) represents the set of all symmetric matrices in \({\mathbb R}^{n \times n}\).

Title: Foundation: Rigid Motions and Image Formation
Authors: Takeshi Hatanaka
Nikhil Chopra
Masayuki Fujita
Mark W. Spong
Publisher: Springer International Publishing
Book: Passivity-Based Control and Estimation in Networked Robotics
Print ISBN: 978-3-319-15170-0

Electronic ISBN: 978-3-319-15171-7

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-319-15171-7_5