This project started out as an experiment. Most multirotors have their rotors in a planar configuration. I noticed this is mostly true even when the props are titled in racing quads. (which is actually unnecessary). The idea is that if the moment arms do not change, standard flight controllers should be able to control non-planar shaped quadrotors as long as the control board is mounted near the center of gravity. I decided to try the idea out and it turns out it is able to fly pretty well.
- Basic Theory
Quadrotors control their attitude using thrust generated from each rotor on the arms. The torque which control the attitude can be calculated as the picture below.
Moving the rotors along the z axis of the quad does not change the moment arm which results in the same amount of torque. The moment of inertia may increase due to the displacement of the motors(further out from the center of gravity) but this can be controlled with a little more of P gain in the controller.
- Build
The configuration and part list is shown below.
– Motors : Turnigy Brushless motor Aerodrive 1200kv
– Props : 10X4.5 SF props
– ESC : Multistar 20A UBEC
– Flight Controller : KK2.1
– Battery : Zippy Flight Max 11.1V 3000mAh
– Frame : Tarrot carbon fiber quadrotor frame v2
Used two tarot quadrotor frames and mounted each frame using pennuts. Below is the picture of initial fitting the parts before wiring.
The battery was mounted just below the flight controller so that the center of graivity should be near the flight controller.
ESCs are mounted on different plates. I tied mounting everything symmetrically to prevent it from messing up the inertial moments.
I am so excited what I can do with this quad!
You can also view the project in the 404warehouse blog:
http://404warehouse.net/2015/09/22/symmetric-non-planar-quadrotor/
Comments
Hi, I'm doing a similar non-planner motor configuration, with a px4 controller. Need help modifying the mixer files etc.
How will the mixer file change for a conifg. like above? thanks.
Hi, I'm doing a similar non-planner motor configuration, with a px4 controller. Need help modifying the mixer files etc.
How will the mixer file change for a conifg. like above? thanks.
@Ryan The project itself was just for fun, but now I am realizing applications (mainly interacting with close objects) that such forms can be advantageous
@Geoff Thanks for pointing out the notion of symmetric / non-symmteric!
and you are right! I should change the name of the project for it!
@Ryan one *slight advantage*, if the z axis spacing will fit the payload, is a camera view without props, legs, etc in the frame. This, of course, assumes the camera field of view is less than the copter stuff that could spoil the image.
Just saying... It is an interesting study in vector analysis.
-=Doug
Probably a stupid question, but what are the benefits of a non-planar copter? Other than just looking awesome in a strange way when its in the air?
I've build a few copters with pixhawk not mounted in the CG. I thought it wouldn't be ideal, but it didn't fit anywhere else. I never noticed any abnormalities in flight stability...
This configuration is not symmetric about all of the body axes. The vertical separation of two neighboring motors introduces cross moments of inertia when expressing the inertia tensor in the body axes. If the x-axis is to the right or left in your diagram, with the y-axis into or out of the page, then this configuration will introduce an Ixz term.
The roll and yaw equations of motion will then become coupled (e.g. see slide 14 here). This isn't by itself a bad thing. The quad controllers will be fighting the motion resulting from these cross moments, so as long as the term doesn't become too large, there shouldn't be major issues.
If instead of putting two neighboring motors in one plane and the other two in the other, you instead put the diagonally opposite motors in the same plane then you'd have no cross moments of inertia and avoid the coupling of the roll and yaw axes. This would likely be better structurally as well since you could have two continuous beams supporting the rotors.
A thought on this: Does this create thrust that is directed into the center of the quad? That is, it seems to me from looking at the diagram that the force vectors from the props would be "compressing" the quadcopter, thus reducing efficiency from a conventionally planar design, I may be wrong
I believe the only downside of the IMU being away from the CG, in any configuration, is that at non-trivial angular rates it'll experience a centrifugal force. The force will always be in the same direction perhaps tricking the ahrs slightly if it's not written to detect centrifugal force. In terms of the AHRS maths it's relatively easy for the software to do online calibration (i.e. transparent to the user) for the centrifugal force and even tell exactly how far the IMU is mounted from the CG. From there it's easy to compensate for any effects. I don't think ArduCopter does this.
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