Cayley-Hamilton for Roboticists

Martijn Visser, Stefano Stramigioli, Cock Heemskerk

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    10 Citations (Scopus)
    671 Downloads (Pure)

    Abstract

    The Cayley-Hamilton theorem is an important theorem of linear algebra which is well known and used in system theory. Unfortunately, this powerful result is practically never used in robotics even though it is of extreme relevance. This article is a review of the use of this result for the calculation of general matrix functions which are very common in robotics. It will be shown how any analytic matrix function like exponential, logarithm and more complicated expressions in robotics, can be easily and analytically calculated in an explicit form. Examples are given for the exponential map, inverse of the exponential map, and the derivative of the exponential map. For the first two examples there exist well known expressions in the literature, but the last one is not as easy to compute without the presented methods
    Original languageEnglish
    Title of host publicationIEEE/RSJ International Conference on Intelligent Robots and Systems 2006
    PublisherIEEE
    Pages4187-4192
    Number of pages6
    ISBN (Electronic)1-4244-0259-X
    ISBN (Print)1-4244-0259-X
    DOIs
    Publication statusPublished - Oct 2006
    Event2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2006 - Beijing, China
    Duration: 9 Oct 200615 Oct 2006

    Conference

    Conference2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2006
    Abbreviated titleIROS
    CountryChina
    CityBeijing
    Period9/10/0615/10/06

    Keywords

    • IR-62279
    • CE-Advanced Robotics
    • EWI-12668
    • METIS-248246

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