Numerical solution of an industrial robot arm control problem using the RK-Butcher algorithm

In this paper, the parameters governing the arm model of a robot control problem have been studied through RK Butcher algorithm. The exact solution of the system of equations representing the arm model of a robot have been compared with the corresponding discrete solutions (approximate solutions) at different time intervals using the above mentioned RK Butcher algorithm and also the absolute error between the exact and discrete solutions have been determined. An elaborate, well composed comparison has been carried out with the aid of the obtained results and graphs.

[1]  Linda R. Petzold,et al.  On order reduction for Runge-Kutta methods applies to differential algebraic systems and to stiff systems of ODEs , 1990 .

[2]  Chengming Huang,et al.  Dissipativity of Runge-Kutta methods for dynamical systems with delays , 2000 .

[3]  L. Shampine,et al.  Some practical Runge-Kutta formulas , 1986 .

[4]  Said Oucheriah,et al.  Robust tracking and model following of uncertain dynamic delay systems by memoryless linear controllers , 1999, IEEE Trans. Autom. Control..

[5]  David J. Evans,et al.  Analysis of different second order systems via runge-kutta method , 1999, Int. J. Comput. Math..

[6]  David J. Evans,et al.  Analysis of non-linear singular system from fluid dynamics using extended runge-kutta methods , 2000, Int. J. Comput. Math..

[7]  R. Alexander,et al.  Runge-Kutta methods and differential-algebraic systems , 1990 .

[8]  Lawrence F. Shampine,et al.  The art of writing a Runge-Kutta code. II. , 1979 .

[9]  Lawrence F. Shampine,et al.  The Art of Writing a Runge-Kutta Code, Part I , 1977 .

[10]  David J. Evans,et al.  A comparison of extended runge-kutta formulae based on variety of means to solve system of ivps , 2001, Int. J. Comput. Math..

[11]  David J. Evans.  A new 4th order runge-kutta method for initial value problems with error control , 1991, Int. J. Comput. Math..

[12]  Hariharan Krishnan,et al.  Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems , 1994, Autom..

[13]  Homayoun Seraji,et al.  Configuration Control of a Mobile Dexterous Robot: Real-Time Implementation and Experimentation , 1997, Int. J. Robotics Res..

[14]  Michael A. Malcolm,et al.  Computer methods for mathematical computations , 1977 .

[15]  J. Butcher.  The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[16]  David J. Evans,et al.  A Fourth Order Embedded Runge-Kutta RKACeM(4,4) Method Based on Arithmetic and Centroidal Means with Error Control , 2002, Int. J. Comput. Math..

[17]  Marios M. Polycarpou,et al.  A Robust Adaptive Nonlinear Control Design , 1993, 1993 American Control Conference.

[18]  L. Shampine,et al.  Computer solution of ordinary differential equations : the initial value problem , 1975 .

[19]  Morris Bader.  A new technique for the early detection of stiffness in coupled differential equations and application to standard Runge-Kutta algorithms , 1998 .

[20]  J. Butcher.  On Runge-Kutta processes of high order , 1964, Journal of the Australian Mathematical Society.

[21]  A. Pugh,et al.  Robot control: theory and applications , 1988 .

[22]  Erwin Fehlberg,et al.  Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme , 1970, Computing.

[23]  Morris Bader.  A comparative study of new truncation error estimates and intrinsic accuracies of some higher order Runge-Kutta algorithms , 1987, Comput. Chem..