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 (...
- 114
3
votes
Representation of 2D coordinate space with orientation
You need to resort to the Special Euclidean groups.
In particular, in your planar case, the group is $SE\left(2\right)$ and thus the representation is the following:
$
T=\left(\begin{matrix} R & ...
- 3,875
3
votes
given position and orientation of two coordinate frames, how to transfer a vector from one to another
A homogeneous transform $T$ is 4x4 matrix that looks like:
$$T=\begin{bmatrix}
R & t \\
0_3 & 1
\end{bmatrix}$$
where $R$ is a 3x3 rotation matrix and $t$ is the translation. The rotation ...
- 1,661
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 ...
- 4,366
3
votes
Accepted
Mobile robot algorithm implementation error
So I'll point out what might be some problems, at-a-glance, but wow this is one of the longest questions I've seen here. I'm pretty swamped with real-life stuff at the moment, so I'll just point these ...
- 15.7k
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 ...
- 15.7k
2
votes
Fence avoidance for manually controlled robot
I think that your problem is rather uncommon, so there may be no solutions ready to use without any modifications. However, you may have a look at "The Dynamic Window Approach to Collision Avoidance" ...
- 963
2
votes
Do I need to use Inverse Kinematics if I have the coordinates of all joints?
People use complex inverse kinematics because they do not have the joint positions. In the case of an industrial robto, you know the you want the end effector at a certain position, and you calculate (...
- 6,612
2
votes
Accepted
relationship between geometric twist jacobian and wrench
I'd suggest thinking about the problem this way:
When you construct a Jacobian for an arm, it will typically map your joint velocities to to one of three representations of the end effector velocity:
...
- 619
1
vote
Explanation of the epipolar constraint in stereo imaging
Doesn't it hold for ANY two vectors v and w that v⋅(v×w)=0?
-> Yes
but you should think about the later part of the lecture where this obvious equation is converted into an essential matrix ...
- 1,487
1
vote
given current position and Quaternion and target local rotations (α, β, γ, in radians), how to calculate the new Quaternion
It is often useful to create a 2D example and use rigid-body transforms (i.e., $T\in\text{SE}(2)$, where ${\small T=\begin{bmatrix}R&t\\0&1\end{bmatrix}}$, $R\in\text{SO}(2),t\in\mathbb{R}^2$)....
- 340
1
vote
What is the idea behind calling configuration space a metric space?
I did not read the book. But one of possible thinks that came to my mind is this:
There is big field in mathematica dedicated to preciselly define some terms (set, metric, metric space, ...) and prove ...
- 453
1
vote
Accepted
Bearing landmark localization
So the method to figure of something with only bearing measurements is called triangulation. While I think your method works you can much more easily solve it using sin rule.
Given at least 1 side ...
- 1,661
1
vote
Accepted
Finding orientation angles of end-effector from the DH parameter table and transformation matrices
Your $A_{0.3}$ matrix is a 4x4 transformation matrix. In a general form these 4x4 matrices can be subdivided into a 3x3 rotation and a 3x1 translation part. (The remaining parts can be used for ...
- 6,612
1
vote
Efficient sphere surface area search
I suppose this is a question of what is "most efficient" and what are you actually doing? And how are you going about simulating it?
Are you looking for a mathematical proof of how to find all ...
- 518
1
vote
Vısual sensor.camera lenses with a field of view of more than 180 degree
Simple fisheye lens model will cover angles over 180 degrees. Fisheye lens model maps the incident angles into x,y coordinate on the image using a polynomial function. Thus, whatever the fov is, it ...
- 1,487
1
vote
Vısual sensor.camera lenses with a field of view of more than 180 degree
Consider the alternate approach of using a parabolic mirror. The advantage clearly bing cost and possibly operating under lower light conditions. The disadvantages include more distortion, seeing the ...
- 451
1
vote
Image coordinate to robot coordinate
The standard way to perform projection transforms between camera images and the world outside is through a projection matrix. Look at this presentation starting at page 25 for an introduction to the ...
- 1,296
1
vote
Accepted
Recognizing a line from three r-theta ultrasonic distance readings?
Checking for three is a subset of checking for many; so, I am going to consider the more general solution. I will discuss the three point solution at the end.
First, convert the polar coordinates to ...
- 705
1
vote
6 axis robot arm with non-perpendicular axes?
The sketch seems to represent a Kuka KR60-HA, doesn't it?
First of all, one might ask oneself, why, for instance, the rotation axis of joints 4 and 6 is the same. My ad-hoc answer would be that Kuka ...
- 51
1
vote
Generalized Voronoi Diagram
The project repositories at Florida State should get you what you are looking for: https://people.sc.fsu.edu/~jburkardt/m_src/m_src.html
Look at not only the projects which start with "voronoi_," ...
- 4,366
1
vote
Accepted
Angle to a circle tangent line
First, determine the angle $\phi$ between the robot $<\!a_{x},a_{y},\theta\!>$ and the target $<\!p_{x},p_{y}\!>$ as follows
$$
\phi = \tan^{-1} \left( \frac{ p_{y} - a_{y} }{ p_{x} - a_{...
- 2,429
1
vote
Accepted
Which geo-projection to use for odometry
It probably depends on the size of the area where you want to operate your robot.
For me it was always good enough to use equirectangular projection, because for my assumptions "at most 1km large ...
- 729
1
vote
Accepted
6D localization with 6 lasers
Solution : Is there another solution without prerotating vectors ?
I finally got a solution, and here it is.
Python, ROS geometry library, numpy
My actual code/maths in short :
1) Rotate the ...
- 181
1
vote
Accepted
Relative orientation of two robots
Applying the rotation sequence (x-y-z) that you specify, your first robot tool will have the following rotation matrix:
$R_1 = \begin{bmatrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 &...
- 1,377
Only top scored, non community-wiki answers of a minimum length are eligible