My Math Forum Reverse Quaternion Kinematics equations. BVP?

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 December 19th, 2012, 02:41 AM #1 Newbie   Joined: Dec 2012 Posts: 4 Thanks: 0 Reverse Quaternion Kinematics equations. BVP? Hi all! I'm programming an attitude estimation and control algorithm for a satellite. So I need a reference "trayectory" for my control system to try to follow. The generation of that attitude profile is tricky: point to the sun, if sat has access to a certain city, point to it, the point again to the sun... and so on. So I've managed to make a q(t) to make all that possible, but I need the angular velocities that yield that reference attitude quaternion as a function of time. While I have already figured out a way to get them, they are not perfectly mathematically calculated, showing some nasty discontinuities at certain times, where transition maneuvers between an initial and final attitude quaternions take place. So, the problem is, given the quaternion kinematic equations: $\begin{equation} \dot q =\frac{1}{2} \left[ \begin{array}{cccc} q_4 & -q_3 & q_2 & q_1 \\ q_3 & q_4 & -q_1 & q_2 \\ -q_2 & q_1 & q_4 & q_3 \\ -q_1 & -q_2 & -q_3 & q_4 \end{array}\right] \left[ \begin{array}{c} \omega_1 \\ \omega_2 \\ \omega_3 \\ 0 \end{array}\right]\end{equation}$ and the initial and final quaternion $q_1\, ,q_2 ,$what is $\vec \omega(t)$? I think the problem would be a boundary value problem, but I don't really know. Does anyone can point me in the right direction?? maybe a matlab supereasy command ? On a sidenote: since we are dealing with attitude quaternions, they are constrained to be $||q(t)||=1$ (which doesn't apply to $\dot q$ BTW), just in case it helps... Thanks in advance!! PS: This is a duplicate thread, because I posted this in the wrong forum in the first place...
 December 19th, 2012, 02:58 AM #2 Newbie   Joined: Dec 2012 Posts: 4 Thanks: 0 Re: Reverse Quaternion Kinematics equations. BVP? Sorry I forgot, I also have initial and final conditions for $\omega$ !!!

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