[PPT] - AUV Dynamics A u t o n o m o u s U n d e r w a t e PowerPoint Presentation

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09/27/12 demarco@gatech.edu 1

AUV Dynamics

A u t

n
m
u

s U n d e r w a t e r V e h i c l e ( A U V ) D y n a m i c s

G e

r

g i a T e c h V I P Ma r i t i m e R

b
t

i c s F a l l 2 1 2

K e v i n D e Ma r c

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Motivation

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Unit Step Input

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Feedback Control

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Coordinate Frame (1)

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Coordinate Frame (2)

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Rotation Matrices

2

D R

t

a t i

n

Ma t r i x

3

D R

t

a t i

n

Ma t r i x

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Rigid Body Dynamics (1)

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Rigid Body Dynamics (2)

A n g u l a r a c c e l e r a t i

n

i n e a r t h

fj

x e d f r a m e i s e q u a l t

a

n g u l a r a c c e l e r a t i

n

i n b

d

y

fj

x e d f r a m e .

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Translational Motion (1)

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Translational Motion (2)

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Rotational Motion

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Six DOF Equations of Motion

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Vectorial Representation

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Hydrodynamic Forces & Moments

R

a d i a t i

n

I n d u c e d F

r

c e s

– A

d d e d m a s s d u e t

i

n e r t i a

f

s u r r

u

n d i n g fm u i d

– R

a d i a t i

n
i

n d u c e d p

t

e n t i a l d a m p i n g d u e t

e

n e r g y c a r r i e d a w a y b y g e n e r a t e d s u r f a c e w a v e s .

– R

e s t

r

i n g f

r

c e s d u e t

w

e i g h t a n d b u

y

a n c y

– S

k i n f r i c t i

n

– Wa

v e d r i fu d a m p i n g

– D

a m p i n g d u e t

v
r

t e x s h e d d i n g

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Hydrodynamic Forces & Moments

E

n v i r

n

m e n t a l F

r

c e s :

– O

c e a n c u r r e n t s

– Wa

v e s

– Wi

n d

P

r

p

u l s i

n

F

r

c e s :

– Tir

u s t / p r

p

e l l e r f

r

c e s

– C

n

t r

l

s u r f a c e s / r u d d e r f

r

c e s

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Added Mass for AUV

V a l u e s c a n b e f

u

n d t h r

u

g h s t r i p t h e

r

y , b u t m

s

t

fu

e n a r e d e t e r m i n e d e m p i r i c a l l y i n a t

w

t a n k .

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Strip Theory

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Restoring Forces and Moments

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Simulations

I

n

r

d e r t

s

i m u l a t e

u

r A U V w e n e e d :

– Mo

d e l

f
u

r v e h i c l e

– I

n i t i a l s t a t e

– I

n p u t v e c t

r

( r e f e r e n c e s i g n a l )

– C

n

t r

l

l e r (

p

t i

n

a l ? ! )

– O

r d i n a r y D i fg e r e n t i a l E q u a t i

n

( O D E ) S

l

v e r

E

u l e r ' s Me t h

d
I

m p r

v

e d E u l e r ' s Me t h

d
Tie

R u n g e

K

u t t a Me t h

d

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ODE Solvers

O

r d i n a r y D i fg e r e n t i a l E q u a t i

n

( O D E ) S

l

v e r s

– U

s u a l l y u s e O D E s

l

v e r

p

t i

n

s t

s

e t

O

D E s

l

v e r t y p e

Ma

x / m i n s t e p s i z e s

N
t

i f y s

l

v e r

f

s t i fg n e s s

f

A m a t r i x .

– I

m p l e m e n t a t i

n

s :

Ma

t l a b

– o

d e 4 5

O

c t a v e

– l

s

d

e

S

c i l a b

– o

d e

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Simulating Vehicle Dynamics

t_init = 0; t_step = 0.1; t_final = 5000; tt = t_init:t_step:t_final; x0 = [0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0 ; 0]; yy = ode(x0, t_init, tt, auv_model);

Wh e r e a u v _ m

d

e l i s a f u n c t i

n

w i t h p r

t
t

y p e :

function [xdot] = auv_model(t,x) // // States: // 1: u : surge velocity // 2: v : sway velocity // 3: w : heave velocity // 4: p : roll rate // 5: q : pitch rate // 6: r : yaw rate // 7: xpos : earth x-pos // 8: ypos : earth y-pos // 9: zpos : earth z-pos // 10: phi : roll angle // 11: theta : pitch angle // 12: psi : yaw angle

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Control of AUV

T

y p e s

f

c

n

t r

l

n e e d e d :

– S

p e e d c

n

t r

l

– H

e a d i n g c

n

t r

l

– D

e p t h c

n

t r

l

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Affjne Thruster Model

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Stability

C
n

t r

l

s

fj

x e d s t a b i l i t y

– F

i x e d c

n

t r

l

s u r f a c e s a n d c

n

s t a n t t h r u s t

C
n

t r

l

s

f

r e e s t a b i l i t y

– C

n

t r

l

s u r f a c e s a n d t h r u s t a l l

w

e d t

v

a r y

L

y a p u n

v

m e t h

d

s ( n

n

l i n e a r ) c a n b e u s e d t

d

e t e r m i n e s t a b i l i t y

f

s y s t e m

O

p e n

l
p

s t a b i l i t y

C

l

s

e d

l
p

s t a b i l i t y

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AUV Control Examples

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AUV Control Examples

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Speed Control

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Heading Control

C
m

i n g s

n

. . .

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Decoupled Pitch & Depth Control

C
m

i n g s

n

. . .

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Questions?

K e v i n D e Ma r c

d

e m a r c

@