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The orientation error vector is defined as \mathbf{e}_o(t) = \mathbf{r}(t)\sin\phi(t)

OrientationError

Illustration of the orientation error vector

Reference: Luh, J.Y.S. et al, “Resolved-acceleration control of mechanical manipulators,” IEEE Trans. Automat. Contr., vol.25, no.3, pp.468-474, 1980.