Question, for objects in a gravitational field but following a circular path, what is the plane of the 'horizontal'?

[Yorkshire_Pud]

Maybe I am over thinking this and confusing myself but I think it is NOT the gravitational horizontal.
I have it in my mind that the 'horizontal' should be perpendicular to the resultant of the vector sum of gravity and the centripetal acceleration but something seems wrong with that idea.
However if I am in someway correct, how do drones seemingly keep the 'horizon' of the camera parallel to the gravitational horizontal. It is my recollection that in the few flights where I have flown a curved path I never noticed a tilt in the gimbals horizon.
I can not at the moment fly such a path with the drone to check how the gimbal behaves in a sustained circular path with a significant centripetal acceleration as I am temporarily restricted to an area where I can not fly such flights.

Perhaps this is one for the likes of @sar104 etc.

 

[Kilrah]

Basically by relying on multiple types of sensors. If a change in acceleration vector was due to gravity then the object would have rotated, but a gyro would have sensed that rotation so if it didn't then it was dynamic acceleration, ignore it for your horizon calculation. Then measure the earth's magnetic field which is mostly locally constant which gives you an absolute frame of reference, and blend all of that together cleverly.

Overly simplified obviously.

 

[Yorkshire_Pud]

Thanks.
It is a long time since I studied this stuff but from memory gyro's try to maintain a dot or cross product vector perpendicular to the plane of rotation of the mass and the direction of this vector works out to be parallel to the axis of the mass's rotation.
A change in the direction of the vector is an acceleration even if there is no change in the magnitude of the vector.
If correct then I think I can see that a gyro might be unaffected by centripetal acceleration and thus if a drone relies on true gyros it might be unaffected.
But from somewhere I have obtained the impression that drones do not use true gyros, is that wrong?

So are you saying/suggesting that it takes the direction of the magnetic field into consideration as well? If so, clever people these engineers.

 

[Kilrah]

An electronic gyro sensor just measures angular velocity around its axis of sensitivity, unaffected by other movements.

 

[Yorkshire_Pud]

An electronic gyro sensor just measures angular velocity around its axis of sensitivity, unaffected by other movements.

So, are they real gyros?

 

[Kilrah]

Yes of course. They're ubiquitous at this point, you'll find a full 9DOF IMU in every phone nowadays.

 

[Yorkshire_Pud]

Blimey, thanks for this.

 

[Gagey52]

You guys got me, I’m going back to bed.
Regards

 

[Lets Fly]

So, are they real gyros?

Just tilt your phone, how do you think the image flipped?

 

[Yorkshire_Pud]

Just tilt your phone, how do you think the image flipped?

Thanks but just tilting the phone etc. is a different scenario, there are only two forces acting on the phone in that case, gravity and the 'upthrust' from your hand.
When 'rounding a bend' there is a third force to be considered, centripetal acceleration in towards the centre of the curve.

 

[Kilrah]

Just tilt your phone, how do you think the image flipped?

Only an accelerometer is needed for this. But as mentioned since phones have full IMUs it's still likely calculating a full orientation anyway nowadays.

 

[Lets Fly]

Thanks but just tilting the phone etc. is a different scenario, there are only two forces acting on the phone in that case, gravity and the 'upthrust' from your hand.
When 'rounding a bend' there is a third force to be considered, centripetal acceleration in towards the centre of the curve.

Thats true, but a gyro acts on any angle in any direction, what would make a difference about a third direction?

 

[retiredNH]

Maybe I am over thinking this and confusing myself

Yes, you're over-thinking it. Why not view it as a black box, and marvel at it's effectiveness.
The only reason I can think of that you might want to understand it further is if you wanted to hack it, but DJI makes it pretty difficult for us mere mortals to do so.

 

[sar104]

Maybe I am over thinking this and confusing myself but I think it is NOT the gravitational horizontal.
I have it in my mind that the 'horizontal' should be perpendicular to the resultant of the vector sum of gravity and the centripetal acceleration but something seems wrong with that idea.
However if I am in someway correct, how do drones seemingly keep the 'horizon' of the camera parallel to the gravitational horizontal. It is my recollection that in the few flights where I have flown a curved path I never noticed a tilt in the gimbals horizon.
I can not at the moment fly such a path with the drone to check how the gimbal behaves in a sustained circular path with a significant centripetal acceleration as I am temporarily restricted to an area where I can not fly such flights.

Perhaps this is one for the likes of @sar104 etc.

A bit late seeing your question, but since it hasn't actually been answered I'll jump in.

Horizontal is defined relative to a frame of reference, in this case the earth's local gravitational field, and so it is independent of motion or orientation in that frame. In other words it's not the plane perpendicular to the resultant acceleration vector acting on an object unless the object is at rest or in uniform motion.

So the question is how does the FC, or gimbal, keep track of horizontal. That's done via the fusion of differential inertial data from the accelerometers and rate gyros with the absolute data from GNSS, compass and barometer added at low gain via a Kalman-type algorithm.

It's actually simplest to ignore the role of the absolute data to understand how it works. Once the IMU orientation is initialized by the compass and accelerometers, it is a relatively simple mathematical problem to use just the rate gyro and accelerometer data to compute subsequent orientation and velocity. That's ignoring drift and bias in those sensors of course, which is why the solution will deviate from reality over time and why the absolute values from GNSS, compass and barometer are needed to correct the solution.

If you are interested in the detailed solution then this paper describes the fully inertial solution. The use case is different, but the mathematics are the same:

The Application of Quaternions to Strap-Down MEMS Sensor Data

We describe the mathematical transformations required to convert the data recorded using typical 6-axis microelectromechanical systems (MEMS) sensor packages (3-axis rate gyroscopes and 3-axis accelerometers) when attached to an object undergoing a short duration loading event, such as blast...

www.mdpi.com