Abstract: This paper presents an algorithm of robot CP motion trajectories planning basedupon the work done by J.Y.S.Luh etc.The traveling path is specified by a groupof parameter equations in cartesian coordinate.The time interval〔O,T〕is divided intom segments,and the coefficients of polynomial at each segment are obtained in rec-urrence form.In the final part of the paper,the problem of minimum-time trajectories planning is also considered.Compared with the cubic spline function approach presented by Luh etc.,the proposed algorithm is not only easily converted into computer programs,but also needs less computation amount.