Reverse Quaternion Kienmatics equations

In summary, the conversation discusses the challenge of generating a reference trajectory for a control system to follow in the context of programming an attitude estimation and control algorithm for a satellite. The suggested solution is to use a numerical integration method, such as the Runge-Kutta method, and the "ode45" function in MATLAB to solve for the angular velocities at each time step. Further clarification and assistance are offered if needed.
  • #1
zuba
1
0
Hi all!, first post!

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.

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 quaternion \begin{equation}q(t),\end{equation} what is \begin{equation}\vec \omega(t)?.\end{equation} 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 :biggrin:?

Thanks in advance!
 
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  • #2


Hello!

I understand your dilemma and it can be quite challenging to generate a reference trajectory for a control system to follow. One approach you could take is to use a numerical integration method, such as the Runge-Kutta method, to solve for the angular velocities at each time step. This will provide a more accurate and continuous solution compared to your current method.

In terms of MATLAB commands, you can use the "ode45" function to numerically integrate the kinematic equations and solve for the angular velocities. You will need to define a function that takes in the quaternion and outputs the angular velocities, and then use that function as an input for "ode45". This will give you a vector of angular velocities at each time step, which you can then use to generate your reference trajectory.

I hope this helps and good luck with your project! Feel free to ask any further questions or clarification.
 

1. What are Reverse Quaternion Kinematics equations?

Reverse Quaternion Kinematics equations are a set of mathematical equations used to calculate the orientation of a moving object in three-dimensional space. They are based on the principles of quaternion algebra and are commonly used in robotics, computer graphics, and animation.

2. How do Reverse Quaternion Kinematics equations work?

Reverse Quaternion Kinematics equations work by using a combination of position and orientation data to calculate the rotational movement of an object. This is done by converting the position and orientation data into quaternion representations and then applying mathematical operations to determine the final orientation of the object.

3. What are the benefits of using Reverse Quaternion Kinematics equations?

Reverse Quaternion Kinematics equations offer several benefits, including improved accuracy and efficiency in calculating object orientation, the ability to handle complex movements and rotations, and compatibility with both linear and rotational movement. They also provide a more intuitive representation of object orientation compared to traditional Euler angles.

4. How are Reverse Quaternion Kinematics equations different from Forward Quaternion Kinematics equations?

The main difference between Reverse Quaternion Kinematics equations and Forward Quaternion Kinematics equations is the direction in which they are applied. While Reverse Quaternion Kinematics equations are used to calculate the orientation of a moving object, Forward Quaternion Kinematics equations are used to determine the rotational movement necessary to achieve a desired orientation.

5. How are Reverse Quaternion Kinematics equations applied in real-world scenarios?

Reverse Quaternion Kinematics equations are widely used in robotics, computer graphics, and animation to accurately represent the movement and orientation of objects. They are also used in motion capture systems to track the movement of human actors and athletes, and in virtual reality applications to create realistic movements and interactions.

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