Today I will try to explain the strange (to some of you out there it might like look intimidating at first even like it did to us at first) mathematical model to which I gave a link yesterday. I am trying to explain everything from ground up, so some people who are familiar with these facts might have to wait some days before the interesting stuff like complimentary filter and sensor interfacing begins. I will also be mentioning which sensors we are using and why. Plus the all important motor drives and motors. But you will have to be patient for that. Not a lot just a lil.
Coming to today's topic of mathematical model, we have a total of 6 equations. All of these are second order differential equations. In the three differential equations governing the position of the system there are sine cosine terms of roll, pitch and yaw. These sine cosine terms come from the rotation matrix. To explain this we will have to consider two frames of reference i.e. the Earth frame of reference in which we eventually want to control the system while the other one being the quad rotor frame of reference. Now we know that the thrust forces are acting in downward direction in the quad rotor frame of reference. But these thrust forces might not be acting exactly downward when we are considering the Earth frame of reference. So in order to transform the forces from the quad rotor frame of reference to the Earth frame of reference, we use the z column (3rd column) entries of the rotation matrix.
BTW the rotation matrix changes form depending upon the type of Euler angles you are using. But there are many properties that hold for all rotation matrices that are available in the literature. That's all the explaining I am going to do for today. Tomorrow I will moving onto simulations in PRO Engineer or Solid Works and the reason to do it.
Due to the interest that everybody has shown in ICRA2002 research paper, I am going to be uploading a research paper, project report or some other helpful material every day. These papers and reports were a great source of information for us when we started. You need not read each and every bit but at least it will give you an idea on how to proceed and how other people have gone about the task.
And for those of you out there wondering what was our inspiration..... The answer to that is STARMAC (http://hybrid.eecs.berkeley.edu/starmac/).
That's all I have to say for today. Hopefully see you tomorrow. Chao
Today's research paper : http://www.megaupload.com/?d=TGI49014
Feel free to ask me any questions at : wahabengineer@gmail.com
Coming to today's topic of mathematical model, we have a total of 6 equations. All of these are second order differential equations. In the three differential equations governing the position of the system there are sine cosine terms of roll, pitch and yaw. These sine cosine terms come from the rotation matrix. To explain this we will have to consider two frames of reference i.e. the Earth frame of reference in which we eventually want to control the system while the other one being the quad rotor frame of reference. Now we know that the thrust forces are acting in downward direction in the quad rotor frame of reference. But these thrust forces might not be acting exactly downward when we are considering the Earth frame of reference. So in order to transform the forces from the quad rotor frame of reference to the Earth frame of reference, we use the z column (3rd column) entries of the rotation matrix.
BTW the rotation matrix changes form depending upon the type of Euler angles you are using. But there are many properties that hold for all rotation matrices that are available in the literature. That's all the explaining I am going to do for today. Tomorrow I will moving onto simulations in PRO Engineer or Solid Works and the reason to do it.
Due to the interest that everybody has shown in ICRA2002 research paper, I am going to be uploading a research paper, project report or some other helpful material every day. These papers and reports were a great source of information for us when we started. You need not read each and every bit but at least it will give you an idea on how to proceed and how other people have gone about the task.
And for those of you out there wondering what was our inspiration..... The answer to that is STARMAC (http://hybrid.eecs.berkeley.edu/starmac/).
That's all I have to say for today. Hopefully see you tomorrow. Chao
Today's research paper : http://www.megaupload.com/?d=TGI49014
Feel free to ask me any questions at : wahabengineer@gmail.com
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