Quadrotor dynamical equations on center of propeller

Question

I work on a quadrotor project. It is commonly wide dynamical model according to the center of quadrotor. However, I need quadrotor dynamic equations on center of one of the propellers. It seems very complexity and hard.

Can anyone help me about that equations or suggest some sources? tips etc..

Can you provide a reference for the equations at the center? — John Alexiou, Jan 24 '14 at 18:39
Equations are shown here at the center. Desired equations are summarized in part 4.1 control modelling. http://www.control.lth.se/documents/2008/5823.pdf — user38138, Jan 26 '14 at 09:06

score 0 · Accepted Answer · edited Apr 13 '17 at 12:39

I can only help with the equations of motion. The controls part you have to develop on your own.

Here are the transformation rules between two coordinate systems, in order to transform your equations of motion. See answer https://physics.stackexchange.com/a/80449/392 for details on how to transform from the center of mass C to another arbitrary point A.

$$ \begin{aligned} \sum \vec{F} &= m \vec{a}_A - m \vec{c}\times \vec{\alpha} + m \vec{\omega}\times\vec{\omega}\times\vec{c} \\ \sum \vec{M}_A &= I_C \vec{\alpha} + m \vec{c} \times \vec{a}_A - m \vec{c} \times \vec{c} \times \vec{\alpha} +\vec{\omega} I_C \vec{\omega} + m \vec{c} \times \left( \vec{\omega} \times \vec{\omega} \times \vec{c} \right) \end{aligned} $$

Quadrotor dynamical equations on center of propeller

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