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
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