Orientation in space
UAV geometry and control

Article REF: S7818 V1

Orientation in space
UAV geometry and control

Author : Luc JAULIN

Publication date: April 10, 2022 | Lire en français

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2. Orientation in space

We're going to remind you of a few fundamental concepts for representing the orientation of objects in space, bearing in mind that this orientation evolves over time.

2.1 Rotation vector

The vector product between two vectors ω and $x \in ℝ^{3}$ is classically defined as follows:

\begin{array}{l} ω \land x = (\begin{matrix} ω_{x} \\ ω_{y} \\ ω_{z} \end{matrix}) \land (\begin{matrix} x_{1} \\ x_{2} \\ x_{3} \end{matrix}) = (\begin{matrix} x_{3} ω_{y} - x_{2} ω_{z} \\ x_{1} ω_{z} - x_{3} ω_{x} \\ x_{2} ω_{x} - x_{1} ω_{y} \end{matrix}) \end{array}

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Bibliography

(1) - DOMBRE (E.), KHALIL (W.) - Robot manipulators : modeling, performance analysis and control. - ISTE Ltd. (2007).
(2) - BEARD (R.), McLAIN (T.) - Small Unmanned Aircraft, Theory and Practice. - Princeton University Press (2012)....

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