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 e v i n D e Ma r c o 09/27/12 demarco@gatech.edu 1

Motivation 09/27/12 demarco@gatech.edu 2

Unit Step Input 09/27/12 demarco@gatech.edu 3

Feedback Control 09/27/12 demarco@gatech.edu 4

Coordinate Frame (1) 09/27/12 demarco@gatech.edu 5

Coordinate Frame (2) 09/27/12 demarco@gatech.edu 6

Rotation Matrices ● 2 D R o t a t i o n Ma t r i x ● 3 D R o t a t i o n Ma t r i x 09/27/12 demarco@gatech.edu 7

Rigid Body Dynamics (1) 09/27/12 demarco@gatech.edu 8

Rigid Body Dynamics (2) A n g u l a r a c c e l e r a t i o 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 o a n g u l a r a c c e l e r a t i o n i n b o d y - fj x e d f r a m e . 09/27/12 demarco@gatech.edu 9

Translational Motion (1) 09/27/12 demarco@gatech.edu 10

Translational Motion (2) 09/27/12 demarco@gatech.edu 11

Rotational Motion 09/27/12 demarco@gatech.edu 12

Six DOF Equations of Motion 09/27/12 demarco@gatech.edu 13

Vectorial Representation 09/27/12 demarco@gatech.edu 14

Hydrodynamic Forces & Moments ● R a d i a t i o n I n d u c e d F o r c e s – A d d e d m a s s d u e t o i n e r t i a o f s u r r o u n d i n g fm u i d – R a d i a t i o n - i n d u c e d p o t e n t i a l d a m p i n g d u e t o 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 o r i n g f o r c e s d u e t o w e i g h t a n d b u o y a n c y – S k i n f r i c t i o 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 o v o r t e x s h e d d i n g 09/27/12 demarco@gatech.edu 15

Hydrodynamic Forces & Moments ● E n v i r o n m e n t a l F o 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 o p u l s i o n F o r c e s : – Tir u s t / p r o p e l l e r f o r c e s – C o n t r o l s u r f a c e s / r u d d e r f o r c e s 09/27/12 demarco@gatech.edu 16

Added Mass for AUV V a l u e s c a n b e f o u n d t h r o u g h s t r i p t h e o r y , b u t m o s t o 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 o w t a n k . 09/27/12 demarco@gatech.edu 17

Strip Theory 09/27/12 demarco@gatech.edu 18

Restoring Forces and Moments 09/27/12 demarco@gatech.edu 19

Simulations ● I n o r d e r t o s i m u l a t e o u r A U V w e n e e d : – Mo d e l o f o 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 o r ( r e f e r e n c e s i g n a l ) – C o n t r o l l e r ( o p t i o 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 o n ( O D E ) S o l v e r ● E u l e r ' s Me t h o d ● I m p r o v e d E u l e r ' s Me t h o d ● Tie R u n g e - K u t t a Me t h o d 09/27/12 demarco@gatech.edu 20

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 o n ( O D E ) S o l v e r s – U s u a l l y u s e O D E s o l v e r o p t i o n s t o s e t ● O D E s o l v e r t y p e ● Ma x / m i n s t e p s i z e s ● N o t i f y s o l v e r o f s t i fg n e s s o f A m a t r i x . – I m p l e m e n t a t i o n s : ● Ma t l a b – o d e 4 5 ● O c t a v e – l s o d e ● S c i l a b – o d e 09/27/12 demarco@gatech.edu 21

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 o d e l i s a f u n c t i o n w i t h p r o t o 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 09/27/12 demarco@gatech.edu 22

Control of AUV ● T y p e s o f c o n t r o l n e e d e d : – S p e e d c o n t r o l – H e a d i n g c o n t r o l – D e p t h c o n t r o l 09/27/12 demarco@gatech.edu 23

Affjne Thruster Model 09/27/12 demarco@gatech.edu 24

Stability ● C o n t r o l s - fj x e d s t a b i l i t y – F i x e d c o n t r o l s u r f a c e s a n d c o n s t a n t t h r u s t ● C o n t r o l s - f r e e s t a b i l i t y – C o n t r o l s u r f a c e s a n d t h r u s t a l l o w e d t o v a r y ● L y a p u n o v m e t h o d s ( n o n l i n e a r ) c a n b e u s e d t o d e t e r m i n e s t a b i l i t y o f s y s t e m ● O p e n - l o o p s t a b i l i t y ● C l o s e d - l o o p s t a b i l i t y 09/27/12 demarco@gatech.edu 25

AUV Control Examples 09/27/12 demarco@gatech.edu 26

AUV Control Examples 09/27/12 demarco@gatech.edu 27

Speed Control 09/27/12 demarco@gatech.edu 28

Heading Control ● C o m i n g s o o n . . . 09/27/12 demarco@gatech.edu 29

Decoupled Pitch & Depth Control ● C o m i n g s o o n . . . 09/27/12 demarco@gatech.edu 30

Questions? K e v i n D e Ma r c o d e m a r c o @ g a t e c h . e d u 09/27/12 demarco@gatech.edu 31