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09/27/12 [email protected] 1 AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech VIP Maritime Robotics Fall 2012 Kevin DeMarco

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Page 1: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

09/27/12 [email protected] 1

AUV Dynamics

Autonomous Underwater Vehicle (AUV)Dynamics

Georgia Tech VIP Maritime RoboticsFall 2012

Kevin DeMarco

Page 2: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Motivation

Page 3: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Unit Step Input

Page 4: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Feedback Control

Page 5: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Coordinate Frame (1)

Page 6: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Coordinate Frame (2)

Page 7: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Rotation Matrices

● 2D Rotation Matrix

● 3D Rotation Matrix

Page 8: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Rigid Body Dynamics (1)

Page 9: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Rigid Body Dynamics (2)

Angular acceleration in earth-fixed frame is equal to

angular acceleration in body-fixed frame.

Page 10: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Translational Motion (1)

Page 11: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Translational Motion (2)

Page 12: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Rotational Motion

Page 13: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Six DOF Equations of Motion

Page 14: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Vectorial Representation

Page 15: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Hydrodynamic Forces & Moments

● Radiation Induced Forces– Added mass due to inertia of surrounding fluid– Radiation-induced potential damping due to energy

carried away by generated surface waves.– Restoring forces due to weight and buoyancy– Skin friction– Wave drift damping– Damping due to vortex shedding

Page 16: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Hydrodynamic Forces & Moments

● Environmental Forces:– Ocean currents– Waves– Wind

● Propulsion Forces:– Thrust / propeller forces– Control surfaces / rudder forces

Page 17: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Added Mass for AUV

Values can be found through strip theory, but most often are determined empirically in a tow tank.

Page 18: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Strip Theory

Page 19: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Restoring Forces and Moments

Page 20: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Simulations

● In order to simulate our AUV we need:– Model of our vehicle– Initial state– Input vector (reference signal)– Controller (optional?!)– Ordinary Differential Equation (ODE) Solver

● Euler's Method● Improved Euler's Method● The Runge-Kutta Method

Page 21: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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ODE Solvers● Ordinary Differential Equation (ODE) Solvers

– Usually use ODE solver options to set● ODE solver type● Max / min step sizes● Notify solver of stiffness of A matrix.

– Implementations:● Matlab

– ode45● Octave

– lsode● Scilab

– ode

Page 22: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Simulating Vehicle Dynamicst_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);

Where auv_model is a function with prototype:

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

Page 23: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Control of AUV

● Types of control needed:– Speed control– Heading control– Depth control

Page 24: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Affine Thruster Model

Page 25: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Stability

● Controls-fixed stability– Fixed control surfaces and constant thrust

● Controls-free stability– Control surfaces and thrust allowed to vary

● Lyapunov methods (nonlinear) can be used to determine stability of system

● Open-loop stability● Closed-loop stability

Page 26: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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AUV Control Examples

Page 27: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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AUV Control Examples

Page 28: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Speed Control

Page 29: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Heading Control

● Coming soon...

Page 30: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Decoupled Pitch & Depth Control

● Coming soon...

Page 31: Autonomous Underwater Vehicle (AUV) Dynamicsvip.gatech.edu/wiki/images/3/30/Auv-dynamics-presentation.pdf · AUV Dynamics Autonomous Underwater Vehicle (AUV) Dynamics Georgia Tech

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Questions?

Kevin [email protected]