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

Murugesan, K.; Sekar, S.; Murugesh, V.; Park, J. Y.

doi:10.1504/ijcat.2004.003639

Cited by 16 publications

(5 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The dynamics of a robot arm can be represented by [1,5,13] : For a robot with two degrees of freedom, under the assumption of lumped equivalent masses and mass lesslinks, the dynamics are represented in terms of systems of non-linear equations and by applying the method of reduction, it has been represented in terms of the following system of linear equation of time invariant case. The behavior of the robot arm model has been completely described by state equations and the state equations provides perfect controls [14,15] …”

Section: Robot Arm Modelmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Investigation of an Industrial Robot Arm Control ProblemUsing Haar Wavelet Series

Nandhakumar¹,

Selladurai²,

Sekar³

2009

American J. of Engineering and Applied Sciences

Self Cite

View full text Add to dashboard Cite

Problem statement: An error minimization in robot arm dynamics improves operations and performance of production systems. Many contributions have been made in area of robot dynamics since the earliest study more than two decades, but, a number of researchers are still contributing various principles and new techniques for the best use of robots in reality, especially in the field of industry, as this field of study is inexhaustible. This study attempted to analyze the performance of an industrial robot by comparing solutions obtained using RK method and Single-Term Haar Wavelet Series (STHWS) method. Exact solution of system of equations representing arm model of a robot had been compared with corresponding discrete solution at different time intervals. Absolute error between exact and discrete solutions had also been determined to suggest the method of improving performance of a robot. Approach: Haar wavelet had been applied extensively for signal processing in communications and proved to be a useful mathematical tool for dynamical systems. In this study, STWHS method had been used for solving differential equations. Result had been obtained and compared with exact solutions. Results: Error had been compared by exact solutions, RK and STHWS solutions were reported for non-singular systems and estimated as almost zero. The validation had been carried out with reference to earlier research output appeared in this field of study. Conclusion/Recommendations: For robot arm model selected for study, solution obtained by STHWS was found to be accurate from results.

show abstract

Section: Robot Arm Modelmentioning

confidence: 99%

“…An attempt has been made in this study to analyze an industrial robot and its control problem while minimizing the error of solutions to position the robot accurately by using STWHS for non-singular system robot arm model. The obtained solution have been compared with stated solutions [12,13] and is tabulated.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of an Industrial Robot Arm Control ProblemUsing Haar Wavelet Series

Nandhakumar¹,

Selladurai²,

Sekar³

2009

American J. of Engineering and Applied Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Three of the most widely used Numerical Integration Algorithms are used in Time-Multiplexing Simulation described here. They are the Euler's Algorithm; RK-Gill Algorithm discussed by Oliveira [9] and the RK-Butcher Algorithm discussed by Murugesan et al [5], [6] and Murugesh and Murugesan [7], [8].…”

Section: Numerical Integration Algorithmsmentioning

confidence: 99%

Simulation of Time-Multiplexing Cellular Neural Networks with Numerical Integration Algorithms

Murugesh

Murugesan

2006

Computational Science – ICCS 2006

Self Cite

View full text Add to dashboard Cite

A novel approach to simulate Cellular Neural Networks (CNN) is presented in this paper. The approach, time-multiplexing simulation, is prompted by the need to simulate hardware models and test hardware implementations of CNN. For practical applications, due to hardware limitations, it is impossible to have a one-to-one mapping between the CNN hardware processors and all the pixels of the image. This simulator provides a solution by processing the input image block by block, with the number of pixels in a block being the same as the number of CNN processors in the hardware. The algorithm for implementing this simulator is presented along with popular numerical integration algorithms. Some simulation results and comparisons are also presented.

show abstract

“…Murugesan et al [10] and Sekar et al [13] applied the RK-Butcher algorithm to industrial robot arm control problem and second-order IVPs. In this paper, I introduce the RK-Butcher algorithm for finding the numerical solution of linear and nonlinear stiff problems with more accuracy.…”

Section: Stiff Problems-rk-butcher Algorithmmentioning

confidence: 99%

Analysis of linear and nonlinear stiff problems using the RK‐Butcher algorithm

Sekar

2006

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

I present a numerical solution of linear and nonlinear stiff problems using the RK-Butcher algorithm. The obtained discrete solutions using the RK-Butcher algorithm are found to be very accurate and are compared with the exact solutions of the linear and nonlinear stiff problems and also with the Runge-Kutta method based on arithmetic mean (RKAM). A topic of stability for the RK-Butcher algorithm is discussed in detail. Error graphs for discrete and exact solutions are presented in a graphical form to show the efficiency of the RK-Butcher algorithm. The results obtained show that RK-Butcher algorithm is more useful for solving linear and nonlinear stiff problems and the solution can be obtained for any length of time.

show abstract

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

Cited by 16 publications

References 20 publications

Numerical Investigation of an Industrial Robot Arm Control ProblemUsing Haar Wavelet Series

Numerical Investigation of an Industrial Robot Arm Control ProblemUsing Haar Wavelet Series

Simulation of Time-Multiplexing Cellular Neural Networks with Numerical Integration Algorithms

Analysis of linear and nonlinear stiff problems using the RK‐Butcher algorithm

Contact Info

Product

Resources

About