The (m × 1) vector function k(·) — nonlinear in general — allows computation of the operational space variables from the knowledge of the joint spacevariables.
It is worth noticing that the dependence of the orientation componentsof the function k(q) in (2.82) on the joint variables is not easy to express except for simple cases. In fact, in the most general case of a six-dimensionaloperational space (m = 6), the computation of the three components of thefunction φe(q) cannot be performed in closed form but goes through thecomputation of the elements of the rotation matrix, i.e., ne(q), se(q), ae(q).The equations that allow the determination of the Euler angles from the tripletof unit vectors ne, se, ae were given in Sect. 2.4.
Operational Space control -
End effector description is directly used to control it's position: