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Coordinate System and Attitude Representation

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Introduction to Multicopter Design and Control
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Abstract

In order to describe the attitude and position of a multicopter, it is necessary to establish appropriate coordinate frames.

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Notes

  1. 1.

    It reads: “Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication \(i^{2} =j^{2}=k^{2}=ijk=-1\) & cut it on a stone of this bridge.”

References

  1. Goldstein H, Poole C, Safko J (2001) Classical mechanics, 3rd edn. Addison-Wesley, San Francisco

    Google Scholar 

  2. Wu ST, Fei YH (2005) Flight control system. Beihang University Press, Beijing (In Chinese)

    Google Scholar 

  3. Ducard GJ (2009) Fault-tolerant flight control and guidance systems: practical methods for small unmanned aerial vehicles. Springer-Verlag, London

    Google Scholar 

  4. Murray RM, Li Z, Sastry SS et al (1994) A mathematical introduction to robotic manipulation. CRC Press, Boca Raton

    Google Scholar 

  5. Hamilton WR (1866) Elements of quaternions. Longmans, Green & Company, London

    Google Scholar 

  6. Altmann SL (1989) Hamilton, Rodrigues, and the quaternion scandal. Math Mag 62(5): 291–308

    Google Scholar 

  7. Shoemake K (1994) Quaternions. Department of Computer and Information Science, University of Pennsylvania, USA. http://www.cs.ucr.edu/~vbz/resources/quatut.pdf. Accessed 06 July 2016

  8. Sola J (2015) Quaternion kinematics for the error-state KF. Technical Report. Laboratoire d’Analyse et d’Architecture des Systemes-Centre national de la recherche scientifique (LAAS-CNRS), France. http://www.iri.upc.edu/people/jsola/JoanSola/objectes/notes/kinematics.pdf. Accessed 24 July 2016

  9. Kuipers JB (1999) Quaternions and rotation sequences. Princeton University Press, Princeton

    Google Scholar 

  10. Euler angles, quaternions, and transformation matrices. NASA. http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf. Accessed 06 July 2016

  11. Corke P (2011) Robotics, vision and control: fundamental algorithms in MATLAB. Springer-Verlag, Berlin Heidelberg

    Google Scholar 

  12. Massey WS (1983) Cross products of vectors in higher dimensional Euclidean spaces. Am Math Mon 90(10):697–701

    Google Scholar 

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Correspondence to Quan Quan .

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Quan, Q. (2017). Coordinate System and Attitude Representation. In: Introduction to Multicopter Design and Control. Springer, Singapore. https://doi.org/10.1007/978-981-10-3382-7_5

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  • DOI: https://doi.org/10.1007/978-981-10-3382-7_5

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3381-0

  • Online ISBN: 978-981-10-3382-7

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