CMSC828T Vision, Planning And Control In Aerial Robotics QUADROTOR - - PowerPoint PPT Presentation

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CMSC828T Vision, Planning And Control In Aerial Robotics

QUADROTOR DYNAMICS

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Why is Dynamics Important?

Point A to Point B

Most of these slides are inspired by MEAM620 Slides at UPenn

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Forces and Moments

𝑐1

𝑐2 𝑐3

𝑠

4

𝑠3 𝑁1 𝑁2 𝑁3 𝑁4 𝐺

4

𝐺3 𝐺2 𝐺

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𝑏2 𝑏3 𝑏1 𝑃 𝑠𝐶

𝐵

𝑐1 𝑐2 𝑐3

World/Inertial Frame

Body Frame 𝜕4 𝜕3 𝜕2 𝜕1

𝑁1 𝑁3 𝑁4 𝑁2

𝑀

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Forces and Moments

Recall fluid dynamics,

𝐺𝑗 ∝ 𝜕𝑗

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𝐺𝑗 = kF𝜕𝑗

2

𝑁𝑗= kM𝜕𝑗

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Net Force:

𝐺 = ∑𝐺𝑗 − mg𝑐3 𝑗 ∈ {1,2,3,4} kF and kM depends on propellers: # blades, diameter, pitch, material, air viscosity etc.

𝐺

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𝐺3 𝐺2 𝐺

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𝑏2 𝑏3 𝑏1 𝑃 𝑠𝐶

𝐵

𝑐1 𝑐2 𝑐3

World/Inertial Frame

Body Frame 𝜕4 𝜕3 𝜕2 𝜕1

𝑁1 𝑁3 𝑁4 𝑁2

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𝐵𝜕𝐶 = 𝑞𝑐1 + 𝑟𝑐2 + 𝑠𝑐3

In Inertial frame: 𝑛 ሷ 𝑠 = −𝑛𝑕 + 𝑆𝐶

𝐵

𝐺

1 + 𝐺2 + 𝐺3 + 𝐺 4

Recall, Euler’s rotation equation: 𝑁 = 𝐽 ሶ 𝜕 + 𝜕 × (𝐽𝜕) Now, in body frame: 𝐽 ሶ 𝑞 ሶ 𝑟 ሶ 𝑠 = 𝑀 𝐺2 − 𝐺

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𝑀 𝐺3 − 𝐺

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𝑁1 − 𝑁2 + 𝑁3 − 𝑁4 − 𝑞 𝑟 𝑠 × 𝐽 𝑞 𝑟 𝑠

Newton-Euler Equation for a Quadrotor

𝑣1 𝑣2

𝑐1 𝑐2 𝑐3 𝑀

Angular velocities in body frame

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Newton-Euler Equation for a Quadrotor

Remember: 𝐺𝑗 = 𝑙𝐺𝜕𝑗

2 and 𝑁𝑗 = 𝑙𝑁𝜕𝑗 2

Let 𝛿 =

𝑙𝑁 𝑙𝐺 = 𝑁𝑗 𝐺𝑗

𝐽 ሶ 𝑞 ሶ 𝑟 ሶ 𝑠 = 𝑀 𝐺2 − 𝐺

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𝑀 𝐺3 − 𝐺

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𝑁1 − 𝑁2 + 𝑁3 − 𝑁4 − 𝑞 𝑟 𝑠 × 𝐽 𝑞 𝑟 𝑠 𝐽 ሶ 𝑞 ሶ 𝑟 ሶ 𝑠 = 𝑀 −𝑀 −𝑀 𝛿 −𝛿 𝑀 𝛿 −𝛿 𝐺

1

𝐺2 𝐺3 𝐺

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− 𝑞 𝑟 𝑠 × 𝐽 𝑞 𝑟 𝑠

𝑐1 𝑐2 𝑐3 𝑀

𝑣2

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Controller Inputs

𝑣 = 𝑣1 𝑣2 = 1 1 𝑀 1 1 −𝑀 −𝑀 𝛿 −𝛿 𝑀 𝛿 −𝛿 𝐺

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𝐺2 𝐺3 𝐺

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= thrust momentx momenty momentz Everything is in the body frame!

𝐺

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𝐺3 𝐺2 𝐺

1

𝑐1 𝑐2 𝑐3 Body Frame 𝜕4 𝜕3 𝜕2 𝜕1 9/7/2017 7