Calculation of the distance of rotation matrices and translation of two objects on one plane

Question

I have a question about Rotation (R) and Translation (T) matrices, I hope someone can help me as we use R and T in robotics to find the position of the robot.

I have an R and T frame of an object in relation to a camera frame and an R and T of a second object relative to the same camera. If both objects are on a common surface / plane

Question No. 1: (being on the same surface / plane), this means that R is the same for both objects relative to the camera! is this assumption true?

question # 2: how can I calculate the distance between objects (for example, along the x or y axis) using translation matrices?

I have a 1x3 transformation matrix and a 3x3 rotation matrix => I inferred a 4x4 transformation matrix from R and T

early

Answer 1

Answer to 2): If the translation is a vector that is the result of subtracting the position of point 2 to the position of point 1, then the Euclidean distance follows the formula related here .

Then you just need to calculate sqrt (x ^ 2 + y ^ 2 + z ^ 2) as (x, y, z) translation vectors (between 1 and 2), since this is already the difference between the two coordinate points.

This means that you need to calculate the Euclidean norm of the translation vector.

If you have 2 translation vectors (one for each point), then simply subtract them and calculate the Euclidean distance of the resulting vector.

Answer 2

1) Yes, it is. If 2 objects belong to the same coordinate system, and they have the same plane (the same vector view), then with a force they have the same rotation matrix. You can find out how the rotation matrix is ​​created HERE . This is very convenient if you do not know how to do it. This one has a very good example. 2) You can use the Euclidean distance using the same point (center of links for each object). This is the same as traslation.

Remember: 1º make all turns and then traslation. If you go through 1º, you will do it wrong.

Hope this helps!