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Investigation on numerical solution for a robot arm problem

Ponalagusamy R., Senthilkumar S.

Journal of Automation Mobile Robotics and Intelligent Systems

2009

Vol. 3, No. 3

34-40

The aim of this article is focused on providing numerical solutions for a Robot arm problem using the Runge-Kutta sixth-order algorithm. The parameters involved in problem of a Robot control have also been discussed through RKsixth-order algorithm. The précised 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. Experimental 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 ( is a complex Number) using RK-Butcher algorithm obtained by Murugesan et. al. [Murugesan K., Sekar S., Murugesh V., Park J.Y., "Numerical solution of an Industrial Robot arm Control Problem using the RK-Butcher Algorithm", International Journal of Computer Applications in Technology, vol.19, no. 2, 2004, pp. 132-138] is not correct and the stability regions for RK-fourth order (RKAM) and RK-Butcher methods have been presented incorrectly. They have made a mistake in determining the range for real parts of (h is a step size) involved in the test equation for RKAM and RK-Butcher algorithms. 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 and to present graphically the stability regions of the RKAM and the RK-Butcher methods. The stability polynomial and stability region of RK-Sixth order are also reported. Based on the numerical results it is observed that the error involved in the numerical solution obtained by RK-Sixth order is less in comparison with that obtained by the RK-Fifth order and RK-Fourth order respectively.