Mismatch between DH matrix computation and visualization of robot on webots

[alecive]

Hello, I'm a relatively new user of Webots and I trying to create a simple exercise in which students can understand Denavit Hartenberg. I'm using UR5e, and a modified version of the UR demo in ENU coordinates (I used the scripts in here to modify the default world file to use ENU).

What I am doing is the following:

1. I imported DH parameters of the UR5e from here
2. I created my DH chain, computed the forward kinematics of the robot and checked that it matches with the excel file available from the link above and also here
3. I computed the end-effector pose by pre-multiplying the forward kinematics above with the base of the robot
4. I visualized the pose with a Transform object

Unfortunately, as you can see here the computed pose does not match with the end-effector pose. It seems to be an issue with rotations, however I do not understand how to debug this (primarily because I'm a new user):

• How can I get the position of the end-effector from within webots?
• Where can I see how webots rotates bodies and reference frames?
• Do you think there may be a hidden bug (for example, emerging from this PR Allow Z vertical axis #1643)?
• Is there a way to create a DH matrix from the proto file? I see there is a URDF-to-PROTO converter, but not the other way around.

Also, I'm trying not to share my code given that this is an assignment (but I can share bits of it if needed). Here is my world file: ure.zip

Thanks for the help!