I have a problem with the coordinate system change between two 3D rotation sensors A and B. The coordinate systems have the same origin and are (mostly) perpendicular. I tested a somewhat pure rotation around each axis, while measuring for both sensors at the same time.
These are the angle axis rotations over time (x = red, y = green, z = blue), A on the left chart and B on the right chart:
I have now two questions:
- Does it make sense to compare two angle axis representations or is it completely nuts? Is there a better way of comparing rotations?
- What is the transformation between the two coordinate systems?
Looking at the chart I came up with this:
$z_{A} = -x_{B}$
$x_{A} = y_{B}$
$y_{A} = z_{B}$
Hence the rotation matrix (coordinate system change) from B to A is:
$R_{BA} = \begin{bmatrix} 0 & 0 & -1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ \end{bmatrix}$
Supposedly by then doing $R_{BA} * R_{B}$ I should get $R_A$, but it's not what happens, I get completely different values.
It was the right reasoning, the only problem was that the rotation between the sensors was not a simple 90/180 deg around some axis.