Orientation questions

[doug1880]

Hi. I have a few questions about tool orientation.

Q1. In jog mode using the Teach Pendant to reorienting a tool, if I choose something other than Tool (the default) for the Coord system (like World, Base, or WObj), does manually reorienting about X or Y or Z refer to the chosen Coord system axes or some other?

Q2. How does the choice of work object (WObj) affect Manually reorienting the tool?

Q3. The orient portion of a robtarget specifies angular displacement relative to what reference Coord system? WObj?  

Q4. When I convert a robtarget's quaternion to Roll-Pitch-Yaw, is Roll the rotation about X, Pitch about Y, and Yaw about Z (in the coordinate system that is the answer to Q3)?

Q5. Are Roll-Pitch-Yaw angles relative to stationary axes (i.e. does the order of applying the R-P-Y angles affect the final orientation - unlike Euler angles)?

Thanks much!

[Robotter]

Hello Doug:
I am trying to answer your queries, hope it is satisfactory.

1) The X,Y,Z and the reorienting will be wrt to the coord system you have selected. but it will be about the default TCP that you have setup

2) The X,Y,Z and the reorienting will be wrt to the coord system you have selected. but it will be about the default TCP that you have setup

3) Yes. usually Wobj. it will be Wobj0 if you haven't set any user frame

4)  usually J4,J5 & J6 motions are termed as the pitch, roll and yaw. The definitions from the web are pasted below for your understanding.
Roll: Rotation of the robot end-effector in a plane perpendicular to the end of the manipulator arm.
Pitch: Rotation of the end-effector in a vertical plane around the end of the robot manipulator arm
Yaw: Rotation of the end-effector in a horizontal plane around the end of the manipulator arm. Side to side motion at an axis

5) I'm not sure if I understood your question correctly? can you rephrase it? what is a stationary axis?

[doug1880]

Hello Doug:
...snipped...
:
4)  usually J4,J5 & J6 motions are termed as the pitch, roll and yaw. The definitions from the web are pasted below for your understanding.
Roll: Rotation of the robot end-effector in a plane perpendicular to the end of the manipulator arm.
Pitch: Rotation of the end-effector in a vertical plane around the end of the robot manipulator arm
Yaw: Rotation of the end-effector in a horizontal plane around the end of the manipulator arm. Side to side motion at an axis

5) I'm not sure if I understood your question correctly? can you rephrase it? what is a stationary axis?

Thank you for your response. In regards to the last two questions, Q4 & Q5:

Q4.
Your answer for R-P-Y makes sense however, the R-P-Y angle values are in reference to a set of X, Y, and Z axes for what coordinate system?

I have an ABB utility program that converts back and forth various rotation conventions. I would like to convert back and forth between quaternion (q1 - q4) and R-P-Y. I'm just not really 100% sure what reference coordinate system the angular displacements given as Roll, Pitch, and Yaw refer to. I want to test it out on some of our robots but I'm having trouble getting enough time to "play" with them and then put them back in service without causing lost production.

Q5.
There are many ways to specify orientation. Orientation given by three angles can be in reference to a fixed or stationary coordinate system. In that case the three angles are relative to 3 distinct rotations about the fixed coordinate system's X, Y, and Z axes. In this case, you could sequentially rotate about each of the three axes in any order you wish and you will end up in exactly the same final orientation.

The alternative is the three angles are "Euler angles". There are many different Euler angle conventions for specifying orientation. As an example, the EulerZYX convention specifies three sequential rotations (and the order matters): first we rotate the X-Y axes about the Z axes by the Z angular displacement number. Note that both the X and Y axes have rotated around Z (are non-stationary) and are in a new orientation (assuming the Z number is non-zero). Call the rotated axes X' and Y'. Next we must rotate the NEW X' and original Z axes around the NEW Y' axis. Now the original X axis has been rotated twice (call it X'') and the Z axis once (call it Z') - assuming a non-zero Y number. The third and final rotation in the sequence is to rotate the Y'-Z' axes around the X'' axes. In this type of orientation convention, we must follow the rotation sequence around Z, then around Y', then around X''.  If you try a different sequence, say Y-Z'-X'', using the EulerZYX numbers, you will almost certainly (depending on the Z, Y, X angle values) end up in a completely different final orientation then the rotation sequence around Z, then Y', then X''.

My question is, does ABB define Roll-Pitch-Yaw angles relative to a fixed coordinate system or are they like the EulerZYX convention (or EulerXYZ?) where each successive rotation is about a previously rotated axis? If it's a fixed coordinate system then which one is it? [Sorry for the length of this question!]     
 

[doug1880]

I was able to experiment on one of our robots. For anyone interested, this is what I've concluded.

1.   Reorienting the tool in Manual Jog mode on the Teach Pendent uses the coordinate system selected in "Coord" for the X, Y, and Z axes directions. Reorienting always keeps the TCP at the same location in space and rotates the tool about the selected axis, regardless of choice of Coord. So, if you select WObj for Coords and some particular work object and tool, it's as if the origin of that work object's X, Y, and Z axes is translated (but not rotated) so that it coincides with the TCP for the selected tool. Reorienting about X would, in that case, rotate the tool about a line that's parallel with the work object's X axis and passes through the TCP. The same should hold for any other choice of Coord. 

If "Tool" is selected for the Coord choice, reorienting around Z would rotate the tool about its own Z axis. In this case, the rotation would also rotate the tool's X and Y axes directions about the Z axis in space. Therefore, a subsequent reorientation about X or Y would be dependent on the initial rotation about Z. It apparently works as if the "Tool" coordinate axes were firmly attached to the tool itself with the origin located at the TCP. Rotating the tool about one of its axes rotates the other two axes about that axis.

2.   When converting from an orientation given as a quaternion to that of Roll-Pitch-Yaw angles in the ABB orientation converter utility, Roll, Pitch, and Yaw are the angular displacements about the Z, Y, and X axes respectively. These axes directions depend upon the particular work object and tool definitions used when the quaternion (orientation) was originally defined. A quaternion by itself merely specifies three angular displacements. Those displacements could refer to any coordinate system. They remain unattached to any particular coordinate system until they are used as part of a robtarget in a motion instruction. A motion instruction then furnishes the tool and work object, which in turn furnishes the specific coordinate system (X, Y, Z directions) to which the orientation is referenced. Displacement frames and any other type of coordinate transformations should also come into play in determining the specific axes directions to which a particular orientation is referenced, whether using quaternion (q1-q4) or its Roll-Pitch-Yaw angular equivalent.

If anyone has any additions or corrections please feel free.