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Enormous amount of real time robot arm research work is still being carried out in different aspects, especially on dynamics of robotic motion and their governing equations. Taha [5] discussed the dynamics of robot arm problems. Research in this field is still on-going and its applications are massive. This is due to its nature of extending accuracy in order to determine approximate solutions and its flexibility. Many studies [4-8] have reported different aspects of linear and non-linear systems. Robust control of a general class of uncertian non-linear systems are investigated by zhihua [10]. Most of the initial value problems (lVPs) are solved using Runge-Kutta (RK) methods which in turn are employed in order to calculate numerical solutions for different problems, which are modelled in terms of differential equations, as in Alexander and Coyle [11], Evans [12 ], Shampine and Watts [14], Shampine and Gordan [18] codes for the Runge-Kutta fourth order method. Runge-Kutta formula of fifth order has been developed by Butcher [15-17]. Numerical solution of robot arm control problem has been described in detail by Gopal et al.[19]. The applications of non-linear differential–algebraic control systems to constrained robot systems have been discussed by Krishnan and Mcclamroch [22]. Asymptotic observer design for constrained robot systems have been analyzed by Huang and Tseng [21]. Using fourth order Runge-Kutta method based on Heronian mean (RKHeM) an attempt has been made to study the parameters concerning the control of a robot arm modelled along with the single term Walsh series (STWS) method [24]. Hung [23] discussed on the dissipitivity of Runge-Kutta methods for dynamical systems with delays. Ponalagusamy and Senthilkumar [25,26] discussed on the implementations and investigations of higher order techniques and algorithms for the robot arm problem. Evans and Sanugi [9] developed parallel integration techniques of Runge-Kutta form for the step by step solution of ordinary differential equations. This paper is organized as follows. Section 2 describes the basics of robot arm model problem with variable structure control and controller design. A brief outline on parallel Runge-Kutta integration techniques is given in section 3. Finally, the results and conclusion on the overall notion of parallel 2-stage 3-order arithmetic mean Runge-Kutta algorithm and obtains almost accurate solution for a given robot arm problem are given in section 4.

Solution to a System of Second Order Robot Arm by Parallel Runge-Kutta Arithmetic Mean Algorithm