what's the quickest way to calculate a relative coordinate of a frame, as shown in the code below. The Kuka robot language this ":" is referred to as the geometric operator. I would like to perform this calculation in matlab, scilab, smathstudio or java, could you please advise on which library to use and/or how to proceed?

Frame TableTop=[x1 y1 z1 a1 b1 c1]
Frame RelCoord=[x2 y2 z2 a2 b2 c2]

Frame AbsCoord= TableTop:RelCoord

1 Answer 1


The operation you mentioned can be mathematically formulated as a matrix multiplication.

You build your homogeneous transformation matrices (4x4) for both frames and multiply them.

After than you can extract the 6 coordinates from the resulting matrix. Extracting position is easy, take the first three rows of the last column. Extracting rotations can be done in Matlab easily by using the dcm2angles() function.

Please not that quaterions might be a better alternative to transformation matrices, but are more complicated to implement.


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