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

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

AUV Dynamics A u t o n o m o 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 o r g i a T e c h V I P Ma r i t i m e R o b o t i c s F a l l 2 0 1 2 K


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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

  • @

g a t e c h . e d u