Angle estimation of simultaneous orthogonal rotations from 3D gyroscope measurements

Stančin, Sara (author), Tomažič, Sašo (author)

A 3D gyroscope provides measurements of angular velocities around its three intrinsic orthogonal axes, enabling angular orientation estimation. Because the measured angular velocities represent simultaneous rotations, it is not appropriate to consider them sequentially. Rotations in general are not commutative, and each possible rotation sequence has a different resulting angular orientation. None of these angular orientations is the correct simultaneous rotation result. However, every angular orientation can be represented by a single rotation. This paper presents an analytic derivation of the axis and angle of the single rotation equivalent to three simultaneous rotations around orthogonal axes when the measured angular velocities or their proportions are approximately constant. Based on the resulting expressions, a vector called the simultaneous orthogonal rotations angle (SORA) is defined, with components equal to the angles of three simultaneous rotations around coordinate system axes. The orientation and magnitude of this vector are equal to the equivalent single rotation axis and angle, respectively. As long as the orientation of the actual rotation axis is constant, given the SORA, the angular orientation of a rigid body can be calculated in a single step, thus making it possible to avoid computing the iterative infinitesimal rotation approximation. The performed test measurements confirm the validity of the SORA concept. SORA is simple and well-suited for use in the real-time calculation of angular orientation based on angular velocity measurements derived using a gyroscope. Moreover, because of its demonstrated simplicity, SORA can also be used in general angular orientation notation.

• Language: English
• Keywords: gyroscope, angular velocity, angular orientation, simultaneous rotations, rotation axis, rotation angle, spatial angle
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FE - Faculty of Electrical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2011
• Number of pages: Str. 8536-8549
• Numbering: Vol. 11, iss. 9
• PID: 20.500.12556/RUL-129623
• UDC: 62
• ISSN on article: 1424-8220
• DOI: 10.3390/s110908536
• COBISS.SI-ID: 8574804
• Publication date in RUL: 06.09.2021

Record is a part of a journal

• Title: Sensors
• Shortened title: Sensors
• Publisher: MDPI
• ISSN: 1424-8220
• COBISS.SI-ID: 10176278

Licences

• License: CC BY 3.0, Creative Commons Attribution 3.0 Unported
• Link: https://creativecommons.org/licenses/by/3.0/deed.en
• Description: You are free to reproduce and redistribute the material in any medium or format. You are free to remix, transform, and build upon the material for any purpose, even commercially. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
• Licensing start date: 02.09.2011

Secondary language

• Language: Slovenian
• Keywords: žiroskop, kotna hitrost, kotna orientacija, simultane rotacije, os rotacije, kot rotacije, prostorski kot

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P2-0246
• Name: Algoritmi in optimizacijski postopki v telekomunikacijah