“…Conflicts of Interest: The authors declare no conflict of interest.Abbreviations The following abbreviations are used in this manuscript: DMP Dynamic Movement Primitive DND Directional Normal Distribution DoF Degree of freedom DS Dynamical System EM Expectation-Maximization where the entries of the matrix R VS (t) are R (0,0)VS (t) = (1 − a 2 x ) cos(t) + a 2 x , R (0,1) VS (t) = −a x a y cos(t) + a z sin(t) + a x a y , R (0,2) VS (t) = −a x a z cos(t) − a y sin(t) + a x a z , R (1,0) VS (t) = −a x a y cos(t) − a z sin(t) + a x a y , R (1,1) VS (t) = (1 − a 2 y ) cos(t) + a2 y , VS (t) = −a y a z cos(t) + a x sin(t) + a y a z , R (2,0) VS (t) = −a x a z cos(t) + a y sin(t) + a x a z , R (2,1) VS (t) = −a y a z cos(t) − a x sin(t) + a y a z , R (2,2)VS (t) = (1 − a 2 z ) cos(t) + a 2 z , with R (i,j)VS (t) being the entry of the ith row and jth column. The matrix can be written in the formR VS (t) = D cos(t) + E sin(t) + F with D = 1 − a 2 x −a x a y −a x a z −a x a y 1 − a 2 y −a y a z −a x a z −a y a z 1 − a 2 VI (t) = R VS (t)R SI = (D cos(t) + E sin(t) + F) = DR SI cos(t) + ER SI sin(t) + FR SI .The values of the constant vectors d, e and f used in(11) can then be found by multiplying the matrices and vectorizing the resulting matrices.R(0,0) FV = R FS (0, 0)(a 2…”