Rie 28 Presentation

8/13/2019 Rie 28 Presentation

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The Competition

Every two years SENAI promotes the KnowledgeOlympiad;

Industrial Robotics is an occupation where a teamof three students need to develop a mobile robot;

2012 regional competition demanded a robot able

to identify and extinguish fire focuses.

paper 28 p. 2


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The Robot

Pneumatic components (1)

Transmission components(2)

Batteries (3)

Flame detector sensor

board (4)

Step motors (5) Robot chassis (6)

Robot controller (7)

Drives (8)

paper 28 p. 3


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Mathematical model

x

=f

(x, u

) =

cosx3 0

sinx3

00 1

u (1)

paper 28 p. 4


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Mathematical model

paper 28 p. 6


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Mathematical model

e= x21+ x

22 (4)

= atan2(x2, x1) (5)

= x3 . (6)

e=u1cos

=u1sin

e

= u1sin

e +u2.

(7)

paper 28 p. 7


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Mathematical model

r

=

u1+u2b

2

rr (8)

l =u1 u2

b

2

rl(9)

nr =r

2NrT (10)

nl = l

2NlT (11)

paper 28 p. 8


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System Stability

Lyapunov candidate function:

V =12e2 +12(

2 +h2), (12)

Input signal u(k)that makes the system stable:

u1= 1e cos (13)

u2=

2

1cos

sin

(

h), (14)

paper 28 p. 9


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Pose Estimation

xc[k+ 1] = xc[k] + D[k]cosc[k] +[k]

2 (15)

yc[k+ 1] = yc[k] + D[k]sin

c[k] +

[k]

2

(16)

c[k+ 1] = c[k] + [k] (17)

D[k] = nprNpr 2rr+

npl

Npl 2rl

2 (18)

[k] = npr

Npr2rr

npl

Npl2rl

b (19)

paper 28 p. 10


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Simulation Results

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

time(s)

xc(t)

Point Stabilization: xc x time

paper 28 p. 11


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Simulation Results

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

time(s)

yc(t)

Point Stabilization: yc x time

paper 28 p. 12


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Simulation Results

0 2 4 6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

4

4.5

time(s)

thetac(t),rad

Point Stabilization: thetac x time

paper 28 p. 13


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Simulation Results

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

xc(t)

yc(t)

Point Stabilization: xc x yc

paper 28 p. 14


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Simulation Results

0 2 4 6 8 10 12 14 16 18 202

1

0

1

2

3

4

5

time(s)

v(t),m

/s,omega(t),rad/s

Point Stabilization: (v, omega) x time

paper 28 p. 15


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Simulation Results

0 2 4 6 8 10 12 14 16 18 20400

200

0

200

400

600

800

time(s)

npr(t),npl(t)

Point Stabilization: (npr, npl) x time

paper 28 p. 16


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Simulation Results

0 2 4 6 8 10 12 14 16 18 202

1.5

1

0.5

0

0.5

1

1.5

2

2.5

time(s)

xc(t)

Path Tracking: xc x time

paper 28 p. 17


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Simulation Results

0 2 4 6 8 10 12 14 16 18 204

3

2

1

0

1

2

3

4

time(s)

yc(t)

Path Tracking: yc x time

paper 28 p. 18


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Simulation Results

0 2 4 6 8 10 12 14 16 18 201

0

1

2

3

4

5

6

7

time(s)

thetac(t),rad

Path Tracking: thetac x time

paper 28 p. 19


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Simulation Results

2 1.5 1 0.5 0 0.5 1 1.5 2 2.54

3

2

1

0

1

2

3

4

xc(t)

yc(t)

Path Tracking: xc x yc

paper 28 p. 20


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Simulation Results

0 2 4 6 8 10 12 14 16 18 205

0

5

10

15

20

25

30

35

time(s)

v(t),m/s,omega(t),rad/s

Path Tracking: (v, omega) x time

paper 28 p. 21


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Simulation Results

0 2 4 6 8 10 12 14 16 18 2080

60

40

20

0

20

40

60

80

time(s)

npr(t),npl(t)

Path Tracking: (npr, npl) x time

paper 28 p. 22


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Simulation Results

0 2 4 6 8 10 12 14 16 18 205000

0

5000

10000

15000

20000

time(s)

nr,nl

Path Tracking: (nr, nl) x time

paper 28 p. 23

A k l d t


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Acknowledgment

Authors would like to thank Fundao de Apoio Pesquisa do Estado do Rio Grande do Sul

(FAPERGS) and Servio Nacional de AprendizagemIndustrial (SENAI) for the financial support.

paper 28 p. 24

Th k Y !


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Thank You!

QUESTIONS?

paper 28 p. 25

Documents

Rie 28 Presentation