How a Quadcopter is Controlled

This little quad took a lot of damage, but a final trip into the asphalt finally did it in.

This little quad took a lot of damage, but a final trip into the asphalt finally did it in.

As I write this today, I am finally without a quadcopter that works correctly.*  After another particularly brutal crash into asphalt, one of my motors seems to have seized up.  I’ve ordered repair parts, as well as another little quadcopter, but I’ve started playing with the idea of actually building my own.  Or at least a frame to house the internals from a store-bough model.

As I have a CNC router, I don’t think this would be out of the question, but drawing one up correctly would mean I need to understand how it works.  After a bit of searching, I found this thread on “Aeroquad” which referred to several papers, including this one that seemed to make the most sense without interpreting the massive amount of equations.

I’d like to think I could still work the equations out, but engineering school was quite a few years ago.  In my spare time at least, I prefer to experiment rather than carefully figuring things out.  To this end, the figure found on page 39 on the referenced paper was quite helpful:

quadrotor

The rotational speed is proportional to the width of the arrows.  The figure is from this PDF linked earlier.  The “front” of this quad is set up differently than the Hubsan X4 (available from Amazon), in that the “front” would be rotated 45 degrees so that the two front props form a horizontal line.  Although rotated, this shouldn’t affect the basic control concept.  As I see it, there are 3 aspects to quadcopter control: vertical movement, horizontal movement, and rotational movement.

Vertical Movement:

As seen in the lower-left figure, when all the rotors’ speeds are increased by the same amount, a greater thrust is produced, lifting the craft straight up vertically.

Horizontal Movement:

As seen in the bottom-right figure, when the two rotors on the vertical cross-member are held at a medium thrust, and the other two are offset, the craft will slide to the direction opposite of the high-thrust prop.  In a two-engine forward configuration, the two engines opposite of the direction of travel would increase thrust, allowing for the craft to slide in the opposite direction.

Rotational Movement:

The reason that a quadcopter’s motors are counter-rotating is so that the torque coming from each will be cancelled out and the craft won’t spin uncontrollably.  This is the same reason that a normal helicopter has a tail rotor.  During pure “sliding” motion, the sum of the torque coming from the clockwise rotors has to equal the torque out of the counter-clockwise rotors.  As seen in the lower-right figure above, the counter-clockwise rotors are at a medium speed, where the clockwise rotors are at a fast and slow speed.

If the sum of the torques coming out of the rotors gets off-balance, the quadcopter turns.  If the sum of the torques coming out of the rotors is clockwise, the craft will turn counter-clockwise and vice-versa.

Here’s a video of me flying my little quadcopter around in the garage with the lights dimmed.  The lights on the craft allow it to be seen and controlled.

Putting it all together:

Quadcopters are capable of going up, down, turning, and sliding at the same time, which is just a combination of all these effects.  Controlling one manually isn’t too hard, but there are a lot of factors that have to be balanced.  Although I’ve never tried to write software to control one, I can see how it could be done, and I’m almost tempted to try my hand at it.

Of course there’s the various responsibilities of real life to worry about, so that idea might just stay an idea.  I’ve often thought that if I had enough money I could hire engineers and technicians to put together my wacky ideas all day, sort of like Jay Leno’s garage.  Maybe I need to work on my stand-up routine.

Please keep in mind that I’m not an expert, and I haven’t read everything on this subject.  Even the whole of the linked report wasn’t fully read, so please don’t take what I say here as an absolute fact.

*After writing that I had no quadcopter, I received another Hubsan ‘copter from Amazon.  I’ve been much gentler on it this time, and actually haven’t had to repair it besides a new set of propellers.  Apparently practice makes perfect, or at least slightly better…

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