A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

Author

Tzes, Anthony P. ; Yurkovich, Stephen ; Langer, F. Dieter

Author_Institution

Dept. of Electr. Eng., Ohio State Univ., Columbus, OH, USA

fYear

1989

fDate

0-0 1989

Firstpage

557

Lastpage

560

Abstract

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to: (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.<>

Keywords

approximation theory; difference equations; partial differential equations; robots; Euler-Bernoulli beam equation; Macsyma symbolic language; PDE; algorithm; beam displacement; boundary conditions; discretization; distributed actuation term; distributed sensing; expert program; finite-difference approximations; finite-dimensional model; flexible manipulator control dynamics; flexible-link robotic systems; mass; multiprocessor environment; numerical method; partial differential equation; space coordinates; time coordinates; Approximation methods; Difference equations; Partial differential equations; Robots;

fLanguage

English

Publisher

ieee

Conference_Titel

Systems Engineering, 1989., IEEE International Conference on

Conference_Location

Fairborn, OH, USA

Type

conf

DOI

10.1109/ICSYSE.1989.48736

Filename

48736