Title :
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
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;
Conference_Titel :
Systems Engineering, 1989., IEEE International Conference on
Conference_Location :
Fairborn, OH, USA
DOI :
10.1109/ICSYSE.1989.48736
