Logarithm-Based Methods for Interpolating Quaternion Time Series

Author:

Parker Joshua1,Ibarra Dionne2ORCID,Ober David13

Affiliation:

1. Geospatial Research Lab, US Army Corps of Engineers, 7701 Telegraph Rd, Alexandria, VA 22307, USA

2. School of Mathematics, Clayton Campus, Monash University, Melbourne, VIC 3800, Australia

3. Department of Civil Engineering, Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA

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 C2 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.

Funder

Engineer Research Development Center, US Army Corps of Engineers

NSF Division of Mathematical Sciences

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Quaternion Interpolation Under the Angular Velocity Constraint;2023 10th International Conference on Recent Advances in Air and Space Technologies (RAST);2023-06-07

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