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 ...
JJM Driessen's user avatar
6 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 ...
Parker Lusk's user avatar
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 ...
John Alexiou's user avatar
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's user avatar
  • 5,855
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, ...
SteveO's user avatar
  • 4,386
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 ...
RLH's user avatar
  • 619
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 ...
Christo's user avatar
  • 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)...
hauptmech's user avatar
  • 4,435
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 ...
Marco Sütterlin's user avatar
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 (...
Victor Jaramillo's user avatar
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 ...
Chuck's user avatar
  • 16k
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 ...
Petch Puttichai's user avatar
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 ...
Biscuits's user avatar
  • 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 $...
Petch Puttichai's user avatar
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 ...
linker's user avatar
  • 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. ...
SteveO's user avatar
  • 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 ...
holmeski's user avatar
  • 1,853
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 ...
SteveO's user avatar
  • 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 ...
holmeski's user avatar
  • 1,853
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 $R^B_A$ ...
fibonatic's user avatar
  • 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 ...
edwinem's user avatar
  • 1,861
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 ...
Alex's user avatar
  • 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 $\mathbf{a} \in \mathbb{R}^{3}$, ...
domo_arigato's user avatar
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:...
guero64's user avatar
  • 338
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 ...
SteveO's user avatar
  • 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 ...
Chuck's user avatar
  • 16k
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 ...
50k4's user avatar
  • 6,662
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 ...
N. Staub's user avatar
  • 1,412
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 ...
Shahbaz's user avatar
  • 3,250
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 ...
Petch Puttichai's user avatar

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