# Tag Info

### 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 ...
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 ...

### 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 ...
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. ...

### 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 ...

### 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 ...
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 ...

### 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 $R^B_A$ ...
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 ...
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 ...

### 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 $\mathbf{a} \in \mathbb{R}^{3}$, ...

### 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:...

### 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 ...

### 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 ...

### 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 ...

### 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 ...
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 ...