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

Abstract

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.