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Representing Rotation in Simulink using Quaternion |
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PP: 267-272 |
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Author(s) |
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Logah Perumal,
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Abstract |
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| Euler angles were commonly used to represent rotation of a body, but it leads to an undesired phenomenon known as gimbal
lock. This undesired phenomenon can be overcome by using quaternion, which was founded by SirWilliam Rowan Hamilton. Since its
introduction, conversion between Euler angles and quaternion became essential; to enable quaternion to be compatible with applications
developed using Euler angles and vice versa. In this work, a Simulink program is developed to demonstrate use of quaternion in
representing rotation of a body in 3-dimensional space. Simulink program developed in this paper utilizes six degree of freedom
animation block (employs Euler rotation sequence of XYZ), which enables users to graphically see and maneuver a missile in random
orientation as it flies in a 3-dimensional Euclidean space. Random quaternion sequence is converted to Euler angles with XYZ sequence
(in accordance to Euler rotation sequence utilized by the animation block) using new method known as sets of regions. Use of sets of
regions enables quaternion to be applied in random sequence and gimbal lock phenomenon is avoided entirely. |
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