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How to transpose and rotate frames and get new coordinates

Hi everyone,

I am new in the ROS world and still don't get some concepts. Could anyone explain me how to use the transformPose?

Let's assume I have a global frame A and an end-of-efector frame B. Let's assume that in the frame B I have a point P_b. I want to get P_b's coordinates in the frame A (P_b->a). Mathematically speaking, it's really simple. But what are those steps in ROS? I know I can get a translation vector and quaternions using lookupTransform applied to my frames. What comes next? Do I have to calculate P_b->a manually or can call a function to get the new coordinates (transformPose or transformQuaterions?