μžμœ λ„ : Degrees of Freedom (DOFs)

\[A=\begin{bmatrix} acos(\theta) \; -asin(\theta) \; c \\ asin(\theta) \; acos(\theta) \; d \\ 0 \; 0 \; 1\\ \end{bmatrix} \rightarrow DoF(A) = 4\]


How to compute Motion

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μ™Όμͺ½ 3κ°œλŠ” body-fixed frame, 였λ₯Έμͺ½ 2κ°œλŠ” global frame μ—μ„œ μ •μ˜λ¨

\[[u,v,w] \; \rightarrow \, [\dot{x} \; \dot{y} \; \dot{z}] \\ [p,q,r] \; \rightarrow \, [\dot{\phi} \; \dot{\theta} \; \dot{\psi}] \\\]

\(\rightarrow \,\) μ™Όμͺ½μ—μ„œ 였λ₯Έμͺ½μœΌλ‘œ κ°€κΈ° μœ„ν•΄μ„œλŠ” Euler Angle Transformation이 ν•„μš”!


Euler Angle Transformation

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Coordinate Transformation

μ’Œν‘œκ³„κ°„ λ³€ν™˜μ„ ν•΄λ³΄μž!
A와 B ν”„λ ˆμž„ μ‚¬μ΄μ˜ Transformation을 ν•΄λ³΄μž

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Yaw angle

roll pitch yaw라고 λΆ€λ₯΄μ§€λ§Œ μ‹€μ œ λ³€ν™˜μ€ yaw pitch roll μˆœμ„œλ‘œ λ³€ν™˜λ¨

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Pitch angle

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Roll angle

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Position Transformation Matrix

보톡은 global frameμ—μ„œ ν‘œν˜„λ˜λŠ” body-fixed frame의 λ³€ν™˜μ„ 많이 씀!
i.e. Odometry
λ”°λΌμ„œ μ•„λž˜μ²˜λŸΌ λ³€ν™˜μ„ 해보면 yaw-pitch-roll μˆœμ„œλ‘œ 행렬이 곱해짐을 확인

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Linear Velocity Transformation

\(\therefore \,\) 선속도와 각속도도 Transformation으둜 ν‘œν˜„ κ°€λŠ₯!

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Angular Velocity Transformation

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Simulation of 6-DoF Motion

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Underactuated Systems

Control input의 κ°œμˆ˜λ³΄λ‹€ Dimension of configuration spaceκ°€ 큰 μ‹œμŠ€ν…œ!!!

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Underactuated Vehicle

Underactuated μ‹œμŠ€ν…œμ€ 우리 주변에 ꡉμž₯히 많이 있음!

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