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

INTERFACE

MAPLE

MATLAB

• How the idea was born

• Maple and Matlab

• Characteristics of Maple and Matlab, as well as the description of some interfaces

•Introduction

•Introduction

•General description of the interface Maple

Matlab and how to use it

•Examples

•Conclusions

•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

•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

•Current software available

• Maple characteristics

• Matlab characteristics

• Current Interfaces

•Maple characteristics

• Very powerful symbolic language software

• Capacity of inputs and outputs (files)

• User friendly and easy programming

• Graphics capacity

•Advantages

•Maple characteristics

• 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

•Disadvantages

•Matlab characteristics

• Very powerful numerical software

• Capacity of inputs and outputs (files)

•Advantages

•Matlab characteristics

• The numerical methods used are very efficient

• It is a very versatile software due to the

“Toolboxes” that are available for many

applications

•Advantages

•Matlab characteristics

• It is not very user friendly

• Does not handle general symbolic expressions

• Particular manner for user interaction

•Disadvantages

•Current Interfaces

• Matlab Interface Maple (Symbolic Toolbox)

• Mathematica Interface (Symbolic Numeric)

• Mathematica Interface Fortran or C

AN INTERFACE

MAPLE

MATLAB

•General Description

• Platform: Unix

• Programming: Language C1. Initial problem in Maple

2. Program mm.map (it translates the output from Maple as input to Matlab)

•General Description

3. Matlab execution (Optimization Toolbox with the selected subroutine)

• Results in a Matlab.res file

•Interface Maple-Matlab

Program in C

MAPLE MATLAB

mm.map

1 3

2

•Optimization Toolbox

• Constr• Minimax• fmin, fminu, fmins• attgoal• leastsq

ConstraintMinimaxMinimizationGoal AttainmentLeast Squares

•Flow chart START

Define Optimization Subroutine

Input.map

Constraints?

mm.map

func.m

Result.map

my.con

OptimizationConditions(Optim.m)

(Maple)

(Maple)

(Matlab)

(Matlab)

yes

no

Kinematic Design Optimization of Robot Manipulators

•Examples

Kinematics Design Optimization of Planar Robot Manipulators

• Manipulability

• Isotropy condition criterion (2 cases)

• Upper bound on Condition number

• Upper bound on Rank Preservation

Kinematics Design Optimization Kinematics Design Optimization

of Robot Manipulatorsof Robot Manipulators

Using Upper bound on Using Upper bound on Rank Preservation: Rank Preservation: - 7 DOF Anthropomorphic - 7 DOF Anthropomorphic Manipulator; - 7 DOF Space Manipulator; - 7 DOF Space Station Robot ManipulatorStation Robot Manipulator

•Flow chart START

Optimization subroutine: constr

Input.map

Constraints?

mm.map

func.m

Result.map

g[1]=3.0-(11+12+13)

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)

(Maple)

(Maple)

(Matlab)

(Matlab)

yes

no

(Case A: Manipulability)

constraint

Optim.m

•Conclusions

• Detailed study of software for mathematical (Symbolic and Numeric) computation

• Interface Maple Matlab

•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

Thanks !Thanks !