The Semi-Analytic and Numerical Solution of an Industrial Robot Arm Control Problem and its Integral Representation

Abstract The corner of stone of this paper is the numerical treatment of the Robot arm control problem and its integral representation. The semi-analytic and numerical solutions are introduced using two impressive techniques. The first is the Chebyshev collocation method and the second is the differential transform method. The comparison from the error point of view between the exact solution and the numerical solution obtained by two techniques used are considered. Also, the integral representation of the Robot arm control system of equations are constructed and gives the same result obtained for the differential form. The advantage of the integral form is the non-locality and globality. The results and comparison between our techniques with other classic techniques which solve the same problem are introduced in the form of tables and figures with the help of Mathematica program to investigate and explain the efficiency and applicability of differential transform and Chebyshev collocation methods.