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Meaning of a negative step response with quaternion
It's not technically robotics but:
I've been trying to reproduce in Simulink a spacecraft attitude simulation using quaternions, and the kinematics and dynamics seem to work fine, however I'm having a bit of trouble with the controller.
I followed the model give in the 7th chapter which seems to be some sort of a PD controller. The control equation I used is:
$q_e$ is the quaternion error,
$\omega_e$ is the rotation speed error
But my results seems to be off.
With : Initial quaternion and rotation speed are $q_i = [0;0;0;1]$ and $ \omega_i = [0;0;0]$
I give a desired reference of $q = [0;1;0;1]$ and $ \omega = [0;0;0]$.
I get the following response:
$q(1)$ and $q(3)$ are staying at zero as expected.
$q(2)$ is going towards -1 instead of 1 (As far as I understand the sign ambiguity does not explain this since q(4) is staying around 1)
$q(4)$ is not maintaining at 1. (I am not sure if this is related to the fact that the controller is only a PD)
It looks like you are negating your reference inputs in the summing junctions.2018-08-15 03:32:23