I'm doing a tool tracking project using ArUco QR code tracking. I'm a bit confused about the order of multiplication of homogeneous matrix when I do frame transformation. I cannot locate where I am making mistakes at, so please try to look for any conceptual mistakes I made as you read through the text.
Please follow the link for the image!
Diagram annotation for frame transformation plan
Picture of QR code attached tool
So basically I have these
- Some QR codes attached to my tool (please see the link).
- A camera that can get the camera pose estimation relative to the QR code. These camera poses are marked as T_21 (2 to 1) on the diagram.
- A floor plane that I can get the camera pose estimation relative to its left bottom corner. I want to make this as the global axis. This is annotated as T_01 (0 to 1).
- I also know the geometric relationship between the QR code centres and the tip of the tool. This is annotated as T_23 (2 to 3).
What I want to calculate is the tooltip's position relative to the global axis, which is T_03 on the diagram. From my understanding of vectors, I think T_03 = T_23 * T_12 * T_01 (Shown on purple colour on the diagram). But since we don't have T_23, we need to invert T_32.
The inverting process is as follows, from my understanding:
If T_32 = [R d ; 0 1], where R is 3x3 rotation matrix and d is 3x1 translation matrix,
then T_23 = [R^T -R^T * d ; 0 1].
I have done these, but I'm getting a massive error in the position of the tooltip relative to the global axis. Please help me find where I made a mistake at. Thanks all!
