Improving the Precision and Speed of Euler Angles Computation from Low-Cost Rotation Sensor Data [PDF]
Sensors, 2015 This article compares three different algorithms used to compute Euler angles from data obtained by the angular rate sensor (e.g., MEMS gyroscope)—the algorithms based on a rotational matrix, on transforming angular velocity to time derivations of the ...
Aleš Janota +3 more
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Compact Lie Groups, Generalised Euler Angles, and Applications
Universe, 2022 This is mainly a review of an intense 15-year long collaboration between the authors on explicit realisations of compact Lie groups and their applications.
Sergio Luigi Cacciatori, Antonio Scotti
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Variations on the theme Euler angles [PDF]
Surveys in Mathematics and its Applications, 2019 We discuss different parameterizations of the Lie group SO(3). The well-known Rodrigues formula describes the three dimensional orthogonal matrices in terms of their axes and angles of rotation.
Clementina D. Mladenova +1 more
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Fused Angles and the Deficiencies of Euler Angles [PDF]
2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2018 Just like the well-established Euler angles representation, fused angles are a convenient parameterisation for rotations in three-dimensional Euclidean space. They were developed in the context of balancing bodies, most specifically walking bipedal robots, but have since found wider application due to their useful properties.
Philipp Allgeuer, Sven Behnke
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On the Euler angles for SU(N) [PDF]
Journal of Mathematical Physics, 2006 In this paper we reconsider the problem of the Euler parametrization for the unitary groups. After constructing the generic group element in terms of generalized angles, we compute the invariant measure on SU(N) and then we determine the full range of the parameters, using both topological and geometrical methods.
Sérgio L Cacciatori, Bianca L Cerchiai
exaly +3 more sources
Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra
ISPRS International Journal of Geo-Information, 2020 The three-dimensional coordinate’s transformation from one system to another, and more specifically, the Helmert transformation problem, is one of the most well-known transformations in the field of engineering.
Stefania Ioannidou, George Pantazis
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An Enhanced Dynamic Model of a Spatial Parallel Mechanism Receiving Direct Constraints from the Base at Two Point-Contact Higher Kinematic Pairs [PDF]
BiomimeticsIn this paper, a biologically congruent parallel mechanism (PM) inspired by the masticatory system of human beings has been proposed to recreate complete chewing behaviours in three-dimensional space.
Chen Cheng, Xiaojing Yuan, Yenan Li
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Application of Krylov–Bogoliubov–Mitropolski method to asymmetric gyrostatic 3D motion in multi-fields [PDF]
Scientific ReportsThe 3D rotary movement of an asymmetric rigid body (RB) in space around a fixed point is investigated. A gyrostatic torque (GT), a magnetic field (MF), and a Newtonian force field (NFF) all have an impact on the RB’s ability to rotate.
T. S. Amer +2 more
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Analytical Formulation of Relationship Between Sensors and Euler Angle Errors for Arbitrary Stationary Alignment Based on Accelerometer and Magnetometer [PDF]
SensorsAn attitude and heading reference system (AHRS) based on the inertial measurement unit is crucial for various applications. In an AHRS, stationary alignments are performed to determine the initial orientation of the sensor frame with respect to the ...
Chang June Lee, Jung Keun Lee
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A New Analytical Method to Improve Attitude Correction in Inertial Navigation Systems [PDF]
AUT Journal of Modeling and Simulation, 2022 Inertial Navigation Systems suffer from accumulative errors due to their dead reckoning structure. Consequently, the navigation reset or realigning process of such systems is unavoidable.
Hamed Mohammadkarimi +3 more
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