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A MAPLE-MATLAB INTERFACE

A MAPLE-MATLAB INTERFACE. A CASE FOR THE OPTIMIZATION TOOLBOX. Enrique Díaz de León * - René V. Mayorga ** - Graciano Dieck*** * ITESM - Guadalajara Campus, Mexico ** University of Regina, Canada *** ITESM - Monterrey Campus, Mexico. MAPLE. MATLAB. INTERFACE. Introduction.

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A MAPLE-MATLAB INTERFACE

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  1. A MAPLE-MATLAB INTERFACE A CASE FOR THE OPTIMIZATION TOOLBOX Enrique Díaz de León * - René V. Mayorga ** - Graciano Dieck*** * ITESM - Guadalajara Campus, Mexico ** University of Regina, Canada *** ITESM - Monterrey Campus, Mexico

  2. MAPLE MATLAB INTERFACE

  3. Introduction • How the idea was born • Maple and Matlab • Characteristics of Maple and Matlab, • as well as the description of some • interfaces

  4. General description of the interface Maple • Matlab • and how to use it • Examples • Conclusions • Introduction

  5. How was the idea born? • Kinematic Design Optimization of Manipulators • Initial problem in symbolic form using Maple • Find a numerical solution with the use of the • Optimization ToolBox in Matlab

  6. How was the idea born? • A “manual” step by step process • The need of an option to manipulate • the inputs to obtain different outputs • efficiently

  7. Current software available • Maple characteristics • Matlab characteristics • Current Interfaces

  8. Maple characteristics • Advantages • Verypowerful symbolic language software • Capacity of inputs and outputs (files) • User friendly and easy programming • Graphics capacity

  9. Maple characteristics • Disadvantages • Some numerical methods used are not very • efficient • There are certain type of procedures that • can not be realized completely • Does not have routines for Optimization

  10. Matlab characteristics • Advantages • Verypowerful numerical software • Capacity of inputs and outputs (files)

  11. Matlab characteristics • Advantages • The numerical methods used are very efficient • It is a very versatile software due to the • “Toolboxes” that are available for many • applications

  12. Matlab characteristics • Disadvantages • It is not very user friendly • Does not handle general symbolic expressions • Particular manner for user interaction

  13. Current Interfaces • Matlab Interface Maple • (Symbolic Toolbox) • Mathematica Interface • (Symbolic Numeric) • Mathematica Interface Fortran or C

  14. MAPLE MATLAB AN INTERFACE

  15. General Description • Platform: Unix • Programming: Language C • 1. Initial problem in Maple • 2. Program mm.map (it translates the output from Maple as input to Matlab)

  16. General Description • 3. Matlab execution • (Optimization Toolbox with the • selected subroutine) • Results in a Matlab.res file

  17. Program in C 1 3 MATLAB MAPLE 2 mm.map • Interface Maple-Matlab

  18. Optimization Toolbox • Constr • Minimax • fmin, fminu, fmins • attgoal • leastsq Constraint Minimax Minimization Goal Attainment Least Squares

  19. START Define Optimization Subroutine Input.map (Maple) yes my.con no Constraints? mm.map (Maple) Optimization Conditions (Optim.m) (Matlab) func.m (Matlab) Result.map • Flow chart

  20. Examples Kinematic Design Optimization of Robot Manipulators

  21. Kinematics Design Optimization of Planar Robot Manipulators • Manipulability • Isotropy condition criterion (2 cases) • Upper bound on Condition number • Upper bound on Rank Preservation

  22. Kinematics Design Optimization of Robot Manipulators • Using Upper bound on Rank Preservation: - 7 DOF Anthropomorphic Manipulator; - 7 DOF Space Station Robot Manipulator

  23. START Optimization subroutine: constr (Case A: Manipulability) Input.map (Maple) constraint yes g[1]=3.0-(11+12+13) no Constraints? Optim.m mm.map (Maple) x0=(1.7,1.7,1.7,1,1,1) vl b=( , ,  ,.5,.5,.5) vu b =(-  ,- ,-  ,.95,.95,.95) options(13)=1 constr(func,x0,options) (Matlab) func.m (Matlab) Result.map • Flow chart

  24. Detailed study of software for • mathematical (Symbolic and • Numeric) computation • Interface Maple Matlab • Conclusions

  25. Conclusions • Useful Software Tool for the solution of • problems formulated in Symbolic Form • requiring for their solution very efficient • numerical methods such as those • provided by Matlab • Application: • Kinematic Design Analysis/Optimization • of Robot Manipulators

  26. Thanks !

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