3
votes
How do we derive the loop closure equations?
I think perhaps you can proceed as follows:
First consider the each segment as a vector, $\bar{r}_1$, $\bar{r}_2$, etc.
The vectors each add as you place the tip of each to the tail of the following:...
- 336
3
votes
Get a rotation to align a vector, n with another vector, a and be able to rotate around a
Assuming you are working in 3-dimensions, this is exactly what the cross-product does. To find the vector of rotation that rotates $\mathbf{n} \in \mathbb{R}^{3}$ into $\mathbf{a} \in \mathbb{R}^{3}$, ...
- 884
2
votes
Accepted
geometric meaning of rotation matrices related to different frames
Using the notation you have given, the intuitive geometric meaning of rotation matrix multiplication is most clear when the subscript of the first matrix is equal to the superscript of the second (i.e....
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2
votes
Using an IMU to determine the axis about which it is being rotated
If you look at a Bode plot you can design a simple low pass filter by using something like this:
$v_n = c_1 \:v_{n-1} + c_2 \: v_{n,raw}$. This is called a ``difference equation'' and fairly simple to ...
- 53
1
vote
Calculate target orientation
From what you've said here, the goal pose relative to the robot_base frame has the following properties:
Takes the transform of the ...
- 674
1
vote
From euler angles to rotation matrix and vice versa
Assuming that Rotation is scipy.spatial.transform.Rotation, the seq string specifying the ...
- 191
1
vote
From Euler angles to Rotation matrix Staubli
Consider using elemental rotation matrices as defined on this wikipedia.org page:
... then substituting the angle into the trigonometric functions in the matrix and finally cross multiplying the X, Y ...
- 496
1
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How are these equivalent rotation coordinates related?
They are written in the angle-axis representation. In the angle axis representation, the direction of the 3d vector gives the axis of rotation (rotates counter clockwise around it). These two ...
- 125
1
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Calculation of IMU offset for Placement of Inertial measurement unit away from centre of mass
The second post you link there seems to explain it pretty well:
Starting from the well known acceleration transformation formula between an arbitrary point A and the center of mass C with $\vec{c} = \...
- 15.9k
1
vote
Accepted
Center of gravity offset for accelerometer and gyroscope readings
As mentioned in the comment above, I did work like this professionally for a long time. I'll start by saying that I've tried putting IMUs on cranes in the past, and you're really just better off ...
- 15.9k
1
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Rotate sensor frame to body frame
Yes and no.
If you look carefully the coordinate system in the first picture does not match with the coordinate system in the aircraft picture. Why?
Because the X axis in the first picture is ...
- 584
1
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geometric meaning of rotation matrices related to different frames
I believe your question regarding the geometric meaning of rotation matrices to different frames I explain on Medium
1
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Rotate while strafing with mecanum wheels
Yes. A robot with 4 fixed mecanum wheels is able to translate and rotate simultaneously. There are many links online which provide tutorials on how to do this:
https://www.instructables.com/Mecanum-...
Ben♦
- 5,825
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