Course 2: Construction of robot model overview;

Projects specification (application);

Modeling

Modeling

Modeling

Modeling

• A particular phenomenon is represented through the model. The model is a particular knowledge assembly, obtained by approximation process, that aspire to become operational;

• Scientific knowledge must be validated continuously by the experiment;

• It has as aim the a priori knowledge, more precisely we wish to know how will ensuing the phenomenon before the experimentation (voire pour prevoire).

Modeling• The art of modeling:

– Oaccam (1285–1349) razor:“Entities should not be

multiplied unnecessarily.”

“When you have two competing theories which

make exactly the same predictions, the one that is

simpler is the better”

– KISS: kipped smart and simple

Modeling

SOutput

Output

Input

Perturbation

Modeling: NMCa

uses

Effec

ts

Black Box

NM: Case study j=0

j=1 j=2

j=m-1

q0

q1

q2

qm-1

1000

1

1

1000

1

1

,2,1,

,22,21,2

,12,11,1

10210

110

120

21

20

11

20

110

21

10

11

10

),(.),(),(....),(.),(),(),(.),(),(

),(.),(),(....

),(.),(),(),(.),(),(

nnnn

n

n

nnnn

n

n

yxyxyx

yxyxyxyxyxyx

qqqqqq

qqqqqqqqqqqq

Diii zyxzyxd

m),,(,),,(

120 ,...,

(x,y,z)D

(x,y,z)i1…im

(x,y,z)D

(x,y,z)i1…im

NM: Case study

)|()()|()()|(

...1k

nkk

iii hdphp

hdphpdhp

)|()()|( ,,, iii hophpohp

)),,(,),,((1)|(

120 ,...,

,

Diiii zyxzyxd

hopm

NM: Case study

ModelingDesires and results…an all time story

u y

y= effects y= DESIRE

u= cause

)()(

1 yfuufy

What are the causes which can produce my desire?

Modeling: The feedback

y

Perturb

Controler Plant

Feedback

e

Senzor

++

+-

r

The control system

r y

e 0

Modeling: J. Watt governor

Desire: constant angular speed for the shaft

Modeling: The robot

r

yy

link i-1

link i

C

link i-1

-+

u

Modeling: the robot

Ac Tr MSt TkV(t) T(t) (t) q(t) x(t)

Modeling: the robot

C E SMR

Pr

qdP

q

e v qo

qpq q+

- ++

q1

q2

1

2

3

Conclusions