0
$\begingroup$

I have been looking into non-linear control algorithms for controlling a quadcopter. I know that we have total 6 DOF for a quad (3 translation and 3 rotation) and our input belongs to $\mathbb{R}^4$, i.e. the 4 motor inputs. So if I look at a quad following a specified trajectory $x(t)$, where $x\in \mathbb{R}^3 $. Then I am actually controlling only the desired position coordinates. Angles and angular velocity vary such that position is attained, but we don't actually command the angles.

So, my doubt is we have 4-degree input but only 3-degree controlled output. Is it possible to have position tracking along with a particular angle, such as yaw tracking? Controlling 4 states using 4 commands? Am I fundamentally wrong in my reasoning?

Alternatively, in terms of movements being directly actuated, we do have 3-moment torques and a thrust as an input. Would we consider this as 4 DOF command instead?

Any reference or paper would be welcome too.

$\endgroup$

1 Answer 1

1
$\begingroup$

You are fundamentally right in your description of the quadrotor system.

One thing that you oversaw a bit is how your four inputs are mapping to the system dynamics, indeed here 4 motors leads to 4 controllable quantities but it's not always the case. Think for example of an octorotor, with quadrotor configuration, ie, 2 motors per corner of the frame.

Is it possible to have position tracking along with a particular angle, such as yaw tracking?

This is typically what is done in linear control of quadrotor, by relying on the near-hovering approximation. An outer control loop generates the orientation, and its derivative, to be tracked to follow a position trajectory, when an inner loop tracks the orientation and its derivative, the yaw can be chosen arbitrarily at this stage (or set to follow a trajectory). Note that from the quadrotor design this is only possible for yaw, as yaw orientation doesn't influence the total thrust orientation. A complete introduction paper on quadrotor is DOI: 10.1109/MRA.2012.2206474

As for more complex control in SE(3) you can look for DOI: 0.1109/CDC.2010.5717652

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.