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

CMSC828T Vision, Planning And Control In Aerial Robotics QUADROTOR DYNAMICS 9/7/2017 1 z

Why is Dynamics Important? Point A to Point B Most of these slides are inspired by MEAM620 Slides at UPenn 9/7/2017 2 z

Forces and Moments 𝐺 2 𝐺 3 𝑁 2 𝑁 3 𝑁 3 𝑁 2 𝐺 1 𝑐 2 𝜕 2 𝑐 3 𝜕 3 𝐺 𝑁 1 4 𝑠 3 𝑁 4 𝑐 3 𝜕 1 𝜕 4 𝑠 4 𝑐 2 𝑁 1 𝑐 1 𝑁 4 𝑐 1 Body Frame 𝑏 3 𝑀 𝐵 𝑠 𝐶 𝑃 𝑏 2 World/Inertial Frame 𝑏 1 9/7/2017 3 z

Forces and Moments 𝐺 2 𝐺 3 𝑁 2 𝑁 3 𝐺 Recall fluid dynamics, 1 𝜕 2 𝑐 3 𝜕 3 𝐺 2 𝐺 𝑗 ∝ 𝜕 𝑗 𝑁 1 4 𝑁 4 2 𝜕 1 𝐺 𝑗 = k F 𝜕 𝑗 𝜕 4 2 𝑁 𝑗 = k M 𝜕 𝑗 𝑐 2 Net Force: 𝑐 1 𝐺 = ∑𝐺 𝑗 − mg𝑐 3 𝑗 ∈ {1,2,3,4} Body Frame 𝑏 3 𝑀 𝐵 𝑠 𝐶 𝑃 𝑏 2 k F and k M depends on propellers: # blades, World/Inertial Frame diameter, pitch, material, air viscosity etc. 𝑏 1 9/7/2017 4 z

ሶ ሶ ሶ Newton-Euler Equation for a Quadrotor 𝐵 𝜕 𝐶 = 𝑞𝑐 1 + 𝑟𝑐 2 + 𝑠𝑐 3 Angular velocities in body frame 𝑐 3 In Inertial frame: 0 0 𝐵 0 0 𝑛 ሷ 𝑠 = + 𝑆 𝐶 −𝑛𝑕 𝐺 1 + 𝐺 2 + 𝐺 3 + 𝐺 4 𝑣 1 𝑐 2 Recall, Euler’s rotation equation: 𝑐 1 𝑁 = 𝐽 ሶ 𝜕 + 𝜕 × (𝐽𝜕) 𝑀 𝑣 2 Now, in body frame: 𝑀 𝐺 2 − 𝐺 𝑞 𝑞 𝑞 4 𝑟 𝑟 𝐽 = 𝑀 𝐺 3 − 𝐺 − × 𝐽 𝑟 1 𝑠 𝑠 𝑁 1 − 𝑁 2 + 𝑁 3 − 𝑁 4 𝑠 9/7/2017 5 z

ሶ ሶ ሶ ሶ ሶ ሶ Newton-Euler Equation for a Quadrotor 𝑐 3 2 and 𝑁 𝑗 = 𝑙 𝑁 𝜕 𝑗 2 Remember: 𝐺 𝑗 = 𝑙 𝐺 𝜕 𝑗 𝑙 𝑁 𝑁 𝑗 Let 𝛿 = 𝑙 𝐺 = 𝐺 𝑗 𝑀 𝐺 2 − 𝐺 𝑞 𝑞 𝑞 4 𝑐 2 𝑟 𝑟 𝐽 = 𝑀 𝐺 3 − 𝐺 − × 𝐽 𝑟 1 𝑠 𝑠 𝑁 1 − 𝑁 2 + 𝑁 3 − 𝑁 4 𝑐 1 𝑠 𝑣 2 𝑀 𝐺 1 𝑞 𝑞 𝑞 0 𝑀 0 −𝑀 𝐺 2 −𝑀 0 𝑀 0 𝐽 = − 𝑟 × 𝐽 𝑟 𝑟 𝐺 3 𝛿 −𝛿 𝛿 −𝛿 𝑠 𝑠 𝑠 𝐺 4 9/7/2017 6 z

Controller Inputs 𝐺 2 𝐺 1 1 1 1 𝐺 3 1 𝑣 = 𝑣 1 𝐺 2 𝜕 2 0 𝑀 0 −𝑀 𝜕 3 𝑣 2 = −𝑀 𝑀 0 0 𝐺 3 𝐺 1 𝑐 3 𝛿 −𝛿 𝛿 −𝛿 𝐺 𝐺 4 4 𝜕 1 𝜕 4 thrust moment x = moment y moment z 𝑐 2 𝑐 1 Everything is in the body frame! Body Frame 9/7/2017 7 z