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I completed the course of Aerial Robotics in Coursera and I want to implement what I learned in a real quadrotor. The thing is that when I see the equations given like this: enter image description here For the sake of the argument let's assume I have implemented the PD Controllers and every moment I find u1 (the sum of the forces applied to the quadrotor) and u2 (the sum of the moments applied to the quadrotor). I then ask myself: How can I find what force and moment should specifically each one of the motors produce? And here I am stuck as I can't find an answer.Could anyone help?

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closed as unclear what you're asking by Bence Kaulics, Mark Booth Nov 29 '16 at 11:45

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ are you planning on having a physical quadrotor which you are controlling? $\endgroup$ – holmeski Nov 24 '16 at 14:33
  • $\begingroup$ yeap, I do have one and I'm controling it with Arduino for now $\endgroup$ – M.Karam Nov 24 '16 at 14:54
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    $\begingroup$ i recommend getting a purpose built autopilot. it'll save a lot of headaches $\endgroup$ – holmeski Nov 24 '16 at 15:01
  • $\begingroup$ Yeah but the thing is that the purpose of the drone is not to control it with PID $\endgroup$ – M.Karam Nov 24 '16 at 15:16
  • $\begingroup$ But to experiment on nonlinear control $\endgroup$ – M.Karam Nov 24 '16 at 15:17
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If i've understood your question correctly, you are trying to convert the desired set of moments and total force which you calculated from a hypothetical pd controller into a set of forces. This is the relation that needs to be solved

\begin{equation} \begin{bmatrix} u_1\\ \mathbf{u}_2 \end{bmatrix} = \begin{bmatrix} 1&1&1&1\\ 0&L&0&-L\\ -L&0&L&0\\ \gamma&-\gamma&\gamma&-\gamma \end{bmatrix} \begin{bmatrix} F_1\\ F_2\\ F_3\\ F_4\\ \end{bmatrix} \end{equation}

where $u_1$ is the total force of all motors and $\mathbf{u}_2$ is the vector of moments acting on the system. This can simply be solved for by inverting this matrix. So \begin{equation} \begin{bmatrix} 1&1&1&1\\ 0&L&0&-L\\ -L&0&L&0\\ \gamma&-\gamma&\gamma&-\gamma \end{bmatrix}^{-1} \begin{bmatrix} u_1\\ \mathbf{u}_2 \end{bmatrix} = \begin{bmatrix} F_1\\ F_2\\ F_3\\ F_4\\ \end{bmatrix} \end{equation}

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