[已解决]数学:欧拉角+机器人:如何计算? [英] [SOLVED] Maths: Euler angles + robots: how to calculate?

问题描述

大家好，

我的数学技能不是世界上最好的...:〜

这里的问题是我有一个机器人，我需要用数学方法计算出不同的点.

这里的主要思想是我在空间中有两个方向不同的点:

XYZ是空间中的位置.
ABC是欧拉角.

P1 = {XYZABC}
P2 = {X''Y''Z''A''B''C''}

这里的问题是，如果我将机器人从P1发送到P2，则机器人会自动进行移动，而不会出现任何问题.

但是我需要的是将运动分成几部分以产生振动.这意味着我不仅需要能够计算XYZ位置(我们很快就会知道)，还需要计算每个点的方向...

获取方向是我们遇到问题的地方...

有人给你的小费吗?

预先谢谢您.

Hello all,

My math skills are not the best in the world... :~

The problem here is that I have a robot and I need to calculate different points mathematically.

The main idea here is that I have two points in the space with different orientations:

XYZ is the position in the space.
ABC is the euler angle.

P1 = {XYZABC}
P2 = {X''Y''Z''A''B''C''}

The problem here is that if I send the robot from P1 to P2 the robot makes the movement automatically without any problem.

But what I de need is to divide the movement in segments in order to make an oscillation. This means that I need to be able to calculate not only the XYZ position here (something that we got soon) but the orientation in each of the points...

Getting the orientation is where we are having problems...

Any tip from someone?

Thank you in advance.

推荐答案

ABC角必须考虑为(请注意大写字母):
XYZ =基本坐标
xyz =工具坐标

如果得到Z并扭曲XY平面，则得到X''Y''，其中A是X和X之间的角度"

如果现在获得新的Y''并扭曲X''Z平面，则将获得X''''z平面，其中B是Z和z之间的角度

如果现在获得新的z轴并扭曲X''''Y''平面，则得到xy，其中C是X''''和x
之间的角度


但是当您说P1和P2之间的振荡"时，我不太了解您，是否有碰撞的危险?还是什么意思?

无论如何... ABC是考虑机器人起点的工具相对位置的角度.因此，这非常取决于场景如何从P1安全地移到P2.
我建议您从P1到原点，再从原点到P2，在您这种情况下可以吗?还是必须直接从P1转到P2?

如果是最后一个选择...，我将尝试找到中间点，以便从一个位置移动到下一个位置，您只能移动一个相对刀具轴.然后配置机器人以进行插补，以使运动保持恒定，甚至在结束实际运动之前开始移动到下一个位置.

The ABC angles have to be considered as (note the capital letters):
XYZ = base coordinates
xyz = tool coordinates

If you get Z and twist the XY-Plane, you get X''Y'' where A is the angle between X and X''

If you now get the new Y'' and twist the X''Z plane, you will get X''''z-Plane where B is the angle between Z and z

If you now get the new z axis and twist the X''''Y'' plane, then you get xy, where C is the angle between X'''' and x



But I don''t really understand you when you say "oscilations" between P1 and P2, is there any risk of collision? or what do you mean?

Anyways... the ABC are angles of the relative position of the tool considering the start point at the basis of the robot. So it is very, very, very dependant on how the scenario looks like to move safely from P1 to P2.
I would recommend you to go from P1 to the origin and from origin to P2, is that possible in you case? or do you MUST go directly from P1 to P2?

If the last option... I would try to find the middle points so that from one position to the next one you move ONLY one of the tool-relative axis. And then configure the robot to interpolate the ways in order to make the movement constant and even starting to move to the next position before getting the actual movement ended.

解决:首先，我需要从EULER到QUATERNIONS，然后计算插值.之后，我将结果(以四元数表示)传递回了EULER角.

Solved: First I have needed to go from EULER to QUATERNIONS and then calculate the interpolations. After that I''ve passed the results (in quaternions) back to EULER angles.

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