# What is the mathematical relationship between parent and child frame in tf?

I am very confused by the coordinate frame in this tutorial.

In this command line syntax

rosrun tf static_transform_publisher x y z yaw pitch roll frame_id child_frame_id period_in_ms

1. Does the value x y z yaw pitch roll represents the transform from child_frame_id to frame_id? Or the other way around?
2. And what is the relationship between frame_id and child_frame_id? What is the order of the yaw pitch row in the transformation? Which one is the correct relationship?

• Extrinsic rotation (occurs about the axes of the fixed coordinate system):

• child_frame_id = R(yaw) * R(pitch) * R(roll) * frame_id + [x,y,z]
• child_frame_id = R(roll) * R(pitch) * R(yaw) * frame_id + [x,y,z]
• Intrinsic rotation (occurs about the axes of a coordinate system XYZ attached to a moving body):

• child_frame_id = frame_id * R(yaw) * R(pitch) * R(roll) + [x,y,z]
• child_frame_id = frame_id * R(roll) * R(pitch) * R(yaw) + [x,y,z]
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Sort by » oldest newest most voted I think the documentation makes this pretty clear, see below.

http://wiki.ros.org/tf/Overview/Trans...

http://wiki.ros.org/Papers/TePRA2013_...

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Thanks for pointing to the document. But could you please (in question 2) let me know which one is the correct mathematical formula? I don't think the document is very clear on what is child. I mean, the tf is the transform from child_frame_id to frame_if? Or the other way around?

Also, is the roll, pitch, yaw in this syntax intrinsic rotation or extrinsic rotation?

I believe you can do the leg work yourself to find out :-) its all there for you

1

@stevemacenski I am trying to do it myself right now. But I was just hoping that someone who is an expert like you can point it out; that is the reason I ask to ROS community here. Also, I don't think the document is very clear, especially about rotation (Euler & quaternion) conventions. (I'm quite sure I will ramp up once I'm familar with ROS convention.) But to newcomers like me, perhaps, in my humble opinion, it would be much easier if we write down the mathematical equations in the document; because the math would say it all.