How Do You Convert Drone Position Errors into Roll and Pitch Angles?

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Young_kids
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TL;DR
computing remaining 3D angles from x, y and the angle in between them
Hi guys
We have a problem we we are building a flight controller for a drone, but fail to understand how to construct the position controller.
It takes the x, y positions and the angle in between them which we call yaw. How to compute the angles roll and pitch for the desired x and y positions. We have an idea of the following
1580113421740.png

Can someone explain what formula that converts the x error and y error as well as the angle yaw to the desired roll and pitch angles.

We found a formula

1580113599756.png

and
1580113623166.png

But we don't understand why, hope you can help
 

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Young_kids said:
It takes the x, y positions and the angle in between them which we call yaw. How to compute the angles roll and pitch for the desired x and y positions.
If the direction is just horizontal (x & y), why do you need the other angles?
 
A.T. said:
If the direction is just horizontal (x & y), why do you need the other angles?

Because we are making a cascaded control setup, the inner loop controls, pitch, roll, yaw, z. As this is an underactuated system, the desired pitch and roll angles are obtained by cascaded controllers, which make up the outer loop. This outer loop takes the x_error, y_error and measured yaw, and should compute the desired pitch and roll angles in order to achieve the desired position. We are unsure how to compute these desired desired pitch and roll angles, can you give us a hint please
 
anorlunda said:
Before looking at specific equations, the overall plan for cascaded loops must make sense. Can you post a block diagram of the entire control scheme from sensors to actuators?

Hi anorlunda
Thanks for replying. Our block diagram is as follows overall
1580131382071.png

We are unsure of how do the world to body conversion, where the x_error, y_error and yaw are used to compute the desired roll and pitch angle