System of second order robot arm problem by an efficient numerical integration algorithm

Purpose: The aim of this article is focused on providing numerical solutions for system of second order robot arm problem using the Runge-Kutta Sixth order algorithm. Design/methodology/approach: The parameters governing the arm model of a robot control problem have also been discussed through RK-sixth-order algorithm. The precised solution of the system of equations representing the arm model of a robot has been compared with the corresponding approximate solutions at different time intervals. Findings: Results and comparison show the efficiency of the numerical integration algorithm based on the absolute error between the exact and approximate solutions. The stability polynomial for the test equation ̇γ=λγ (λ is a complex Number) using RK-butcher algorithm obtained by Murugesan et. al. [1] and Park et. al. [2,3] is not correct and the stability regions for RK-Butcher methods have been absurdly presented. They have made a blunder in determining the range for real parts of λh (h is a step size) involved in the test equation for RK-Butcher algorithms. Further, they have abruptly drawn the stability region for STWS method assuming that it is based on the Taylor’s series technique. Research limitations/implications: It is noticed that STWS algorithm is not based on the Taylor’s series method and it is an A-stable method. In the present paper, a corrective measure has been taken to obtain the stability polynomial for the case of RK-Butcher algorithm, the ranges for the real part of λh and to present graphically the stability regions of the RK-Butcher methods. Originality/value: Based on the numerical results and graphs, a thorough comparison is carried out between the numerical algorithms.