11
votes
Rotation matrix sign convention confusion.
I think that the main issue is that you're trying to read your rotation matrices from left to right. The sign changes seem random, but actually cycle in an ordinary way. Below follows a more elaborate ...
- 562
6
votes
Accepted
How to avoid gimbal with Quaternions
Quaternions are a more efficient way of storing the orientation matrix of a frame.
I use the vector-scalar convention for quaternions (3+1 = 4 quantities) and have defined the following utility ...
- 383
5
votes
Generate transformation matrices for rotating around a object?
Remember that the columns of a rotation matrix are simply unit vectors indicating where each axis points. Lets say your end-effector is at $p_e = (x_e, y_e, z_e)$, and the center of the circle is at $...
Ben♦
- 5,825
5
votes
Why Euler Angle is set to be in ZYZ order?
Euler angles are not always consistently defined as ZYZ. But this convention is common in robotics because many six-axis robotic manipulators have their fourth axis as a rotation about the forearm, ...
- 4,386
5
votes
Accepted
Using pre multiply or post multipy for rotational matrix to get a new homogenous transformation matrix?
When working with rigid-body transformations, it is crucial to understand which coordinate frame the transformation is defined in. Further, there are different notations for this, so it is important ...
- 340
5
votes
Accepted
How to compute the orientation error between two 3D coordinate frames?
The rotation error between two frames can be viewed in two ways:
The orientation of one frame as seen from the other, calculated by multiplying the inverse of the observing frame by the observed ...
- 618
4
votes
What is the torque/force required to rotate the base of a robot arm?
You need enough torque to overcome friction, and to accelerate the load.
If you know the friction torque ($\tau_f$), and the mass moment of inertia along the motor axis ($I$), then the minimum motor ...
- 385
4
votes
Explanation for exponential coordinate of rotation
The author expects a background that includes a course in physics or mechanics where this equation is taught. When that is the case, this equation gives you instantaneous velocity of a particle (point)...
- 4,355
4
votes
Accepted
Adjusting the PWM frequency and duty cycle to achieve the desired angular velocity in differential drive robots
At first, I did not go trough your code to check for errors in the formulas but from a high level perspective this seems ok. Therefore, your position controller is fine.
What you lack is a lowlevel ...
4
votes
Accepted
How can I draw a line using rotation of two circles?
Made a quick diagram and a couple of calculations in matlab, let me know if it works for you.
First of all, I am assuming you are considering your piece of paper as your reference coordinate system (...
- 214
4
votes
Accepted
What is the consquence of Gimbal lock?
I made a clip for you (https://i.stack.imgur.com/Z0q5Y.jpg) using Unity, which internally represents rotations as quaternions, but uses Euler angles for display and positioning.
You can see that, at ...
- 15.9k
3
votes
Accepted
Solving Inverse Kinematics with unknown orientation
There is no way that you can solve for an IK solution without you -- either explicitly or implicitly -- specifying a criterion for choosing one solution among many others. But that does not mean that ...
- 1,829
3
votes
Accepted
How to rotate a rotation quaternion in the body frame to a rotation quaternion in the world frame?
As pointed out in my earlier comment, this is actually simpler than you may think. Remember, $qs$ and $qr$ are fundamentally different, where the former represents orientation (in reference to the ...
- 217
3
votes
Accepted
Convert Twist from frame B to frame A
Hint: First, write the transformation matrix as
$$
T = \begin{bmatrix}
R &p\\0_{1\times3} &1
\end{bmatrix}.
$$
Now we use the relations $\omega_a = R\omega_b$ and $q_a = Rq_b + p$. Then since $...
- 1,829
3
votes
Rotation matrix sign convention confusion.
The real dig to the sign convention is direction and the way humans like to perceive things orderly or at least using a reference. clockwise and anti-clockwise directions only exist with ...
- 131
3
votes
Accepted
Dealing with fixed transformations while solving inverse kinematics
Hopefully you still have only 4 rows in your DH matrix, not 8 as you said. I think you mean that your Jacobian matrix has 8 $\require{enclose} \enclose{horizontalstrike}{\text{rows}}$ columns.
...
- 4,386
3
votes
Shield IMU from magnetic interferences
Nope. Magnetometers measure the magnetic field. The field it's measuring is going to be the sum of fields from a variety of sources. The field you're interested in is the earth's. But it is not ...
- 1,843
3
votes
Most accurate rotation representation for small angles
@jpro, I think you are not understanding something about kinematics. Whether you use Euler angles, or homogeneous transforms, or rotation matrices, or quaternians, or any other kinematic ...
- 4,386
3
votes
Accepted
A closed-form solution of $\textbf{R}\textbf{R}_1=\textbf{R}_2\textbf{R}$ w.r.t $\textbf{R}$
I believe you can solve this using a least squares approach since all the math in equation is linear. Rearrange the equation so
\begin{equation}
\bf RR_1 -R_2R = 0
\end{equation}
Set up the relation
...
- 1,843
3
votes
How to compute the orientation error between two 3D coordinate frames?
A rotation matrix represents the rotation between two frames. Therefore, it does not make sense to talk about in which "one" frame the error rotation is expressed. Namely, the rotation matrix $R^B_A$ ...
- 941
3
votes
Accepted
Does every rotation vector has an one-to-one corresponding rotation matrix?
Mathematically a rotation vector(or axis angle) representation will always convert to the same rotation matrix.
However, multiple different rotation vectors can lead to the same rotation matrix.
A ...
- 1,811
3
votes
Accepted
Calculating rotation matrix efficiently
The accelerometer measures the gravity vector in the body frame, call it $a$. If you normalize that, say $\hat a$, it's the third row of the rotation matrix $R$ that represents the rotation of the ...
- 449
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
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
2
votes
Mechanical odometer with digital output
The automotive industry frequently uses Hall effect sensors to measure shaft and gear rotation. The Hall effect has some beneficial properties: it operates over a wide range of temperatures, is more ...
- 4,386
2
votes
Most accurate rotation representation for small angles
It sounds to me like you want something where you can (exaggerating) express 30 degrees as thirty 1 degree transforms, such that you can then do something where $\sin{(1)} \approx 1$ and "cheat" that ...
- 15.9k
2
votes
Dealing with fixed transformations while solving inverse kinematics
Having 8 rows in the DH parameters table is completely ok. However, this does not lead to 8 rows in your jacobi matrix. The size of the jacobi matrix is always given by number of degrees of freedom in ...
- 6,632
2
votes
forward and inverse kinematics of arm
From now, I will solely answer your second question about forward kinematics, which is usually easier to solve than inverse kinematics.
First you should sketch your robot in a plan using textbook ...
- 1,402
2
votes
Accepted
Orocos KDL issue with Rotation (matrix) - Inverse Kinematics
The vector and rotation together define the pose of the end-effector, which means its position and orientation. There are 6 degrees of freedom here (presumably), so you can think of the position as a ...
- 3,230
2
votes
Accepted
Explanation for exponential coordinate of rotation
First note that
$p(0)$ travels along an arc of the circle of radius $r = \Vert p \Vert \sin(\phi)$ centered at a point on the axis of $\omega$; and
the velocity $\dot{p}$ is perpendicular to the arc ...
- 1,829
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