after having been determined my control loops for my quadcopter project, I'm going to determine the motor commands (PWM duty cycle) from the motor forces/torques. I was following the guidelines of this document but when I was trying to do the inverse of the matrix M (page 17) it has determinant equal to 0. The procedure is correct? Anyone can suggest me some other link for doing this conversion? I have searched in the Internet but I haven't found so much about that. Thanks The part of the document that I'm referring is the following: enter image description here

  • $\begingroup$ As a comment, because I don't have an answer, I verified that M is not invertible. In the section just before where you quote, the author states motor speed is proportional to PWM duration, and lift (vertical force) is proportional to speed squared, so it would seem as though lift (force) were proportional to PWM squared. It's a shame it looks like this paper was authored by a university professor and impossible math is stated like it's a fact. $\endgroup$
    – Chuck
    Jun 2, 2015 at 0:42
  • $\begingroup$ ok thanks @Chuck, I'm trying to do the same thing in another way, if you want give a look to my new question robotics.stackexchange.com/questions/7415/… $\endgroup$
    – Daniel
    Jun 4, 2015 at 8:24

1 Answer 1


Each axis input is a linear combination of the control input and the sensor (gyros and accelerometers) for that axis. Not necessarily answering your question, but add this to your matrix


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.