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Logarithm-Based Methods for Interpolating Quaternion Time Series

Author

Listed:
  • Joshua Parker

    (Geospatial Research Lab, US Army Corps of Engineers, 7701 Telegraph Rd, Alexandria, VA 22307, USA
    These authors contributed equally to this work.)

  • Dionne Ibarra

    (School of Mathematics, Clayton Campus, Monash University, Melbourne, VIC 3800, Australia)

  • David Ober

    (Geospatial Research Lab, US Army Corps of Engineers, 7701 Telegraph Rd, Alexandria, VA 22307, USA
    Department of Civil Engineering, Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA
    These authors contributed equally to this work.)

Abstract

In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C 2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive interpolation, i.e., interpolating an arbitrary quaternion time series. To accomplish this, we provide a robust method of taking the logarithm of a quaternion time series such that the variables θ and n ^ have a consistent and continuous axis-angle representation. We then demonstrate how logarithmic quaternion interpolation out-performs Renormalized Quaternion Bezier interpolation by orders of magnitude.

Suggested Citation

  • Joshua Parker & Dionne Ibarra & David Ober, 2023. "Logarithm-Based Methods for Interpolating Quaternion Time Series," Mathematics, MDPI, vol. 11(5), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1131-:d:1079315
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    References listed on IDEAS

    as
    1. Yasong Pu & Yaoyao Shi & Xiaojun Lin & Yuan Hu & Zhishan Li, 2020. "C 2 -Continuous Orientation Planning for Robot End-Effector with B-Spline Curve Based on Logarithmic Quaternion," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-16, July.
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