Modelling and Simulation of Marine Craft OVERVIEW...Thor I. Fossen. Handbook of Marine Craft Hydrodynamics and Motion Control. ISBN 978-1-119-99149-6, John Wiley & Sons, 2011. Navigation:

Modelling and Simulation of Marine Craft

OVERVIEWEdin OmerdicSenior Research FellowMobile & Marine Robotics Research CentreUniversity of Limerick

Outline

OverviewAgenda

Principles of Guidance, Navigation & Control

GNC Signal Flow Overview

GNC Signal Flow ↔ Lectures

Day 1: Modelling & Simulation of Marine CraftKinematics

Dynamics

Nonlinear 6 DoF Models (ROV)

Hands-on: Modelling & Simulation of ROV (MATLAB/Simulink)

Day 2: Control of Marine Craft

Control Allocation

Control System

Hands-on: Modelling & Simulation of ROV (MATLAB - LabVIEW)

Hands-on: Control of ROV/USV (LabVIEW)

Day 3: Brushless DC Motor Control using FPGA

Introduction

Motor Control with PWM Signal

Hands-on: Thruster Control using FPGA (LabVIEW)

Thor I. Fossen. Handbook of Marine Craft Hydrodynamics and Motion Control. ISBN 978-1-119-99149-6, John Wiley & Sons, 2011.

Navigation: subsystem to determine position/attitude, course, travelled distance and (optionally) velocity and acceleration of a marine craft.

Control: subsystem to determine necessary control forces and moments to be provided by the craft in order to satisfy certain control objective (in conjunction with the guidance system).

Guidance: subsystem that continuously computes the reference (desired) position, velocity and acceleration of a marine craft to be used by the motion control system.

GNC Signal Flow

Weather routing

program

Trajectory

Generator

Motion Control

System

Control

Allocation

Fusion Marine Craft INS (GNSS + AHRS)

OA Sensors

(Radar, Cameras, etc.)

Observer

Weather

data

Waypoints

Guidance

System

Control

System

Obstacle

Avoidance

Module

Estimated

positions and

velocities Navigation

System

Waves, wind

and ocean

currents

Principles of Guidance, Navigation & ControlGNC Signal Flow Overview

Principles of Guidance, Navigation & ControlGNC Signal Flow ↔ Lectures

GNC Signal Flow

Weather routing

program

Trajectory

Generator

Motion Control

System

Control

Allocation


OA Sensors


Observer

Weather

data

Waypoints

Guidance

System

Control

System

Obstacle

Avoidance

Module

Estimated

positions and


System

Waves, wind

and ocean

currents

Day 1: Modelling & Simulation of Marine Craft


GNC Signal Flow

Weather routing

program

Trajectory

Generator

Motion Control

System

Control

Allocation


OA Sensors


Observer

Weather

data

Waypoints

Guidance

System

Control

System

Obstacle

Avoidance

Module

Estimated

positions and


System

Waves, wind

and ocean

currents




GNC Signal Flow

Weather routing

program

Trajectory

Generator

Motion Control

System

Control

Allocation


OA Sensors


Observer

Weather

data

Waypoints

Guidance

System

Control

System

Obstacle

Avoidance

Module

Estimated

positions and


System

Waves, wind

and ocean

currents



Day 3: Brushless DC Motor Control using FPGA

Principles of Guidance, Navigation & ControlDay 1: Modelling & Simulation of Marine CraftKinematics

ECEF

Body

NED

UTMLat, Lon

Unity

Reference Frames


Transformations BODY - NED: Euler Angles

6 DOF Kinematic Equations

ሶ𝒑 Τ𝑏 𝑛𝑛

ሶ𝜽𝑛𝑏=

𝑹𝑏𝑛 𝜽𝑛𝑏 𝟎3×3𝟎3×3 𝑻𝜃 𝜽𝒏𝒃

𝒗 Τ𝑏 𝑛𝑏

𝒘 Τ𝑏 𝑛𝑏

ሶ𝜼 = 𝑱𝜣 𝜼 𝝂 Simulation ModelAttitude representation: Euler Angles

r

q

p

w

v

u

b

nb

b

nb

/

/

w

vv

nb

b

nb

θ

pη

/

Y

P

R

z

y

x

n

n

n

nb

b

nb

θ

pη /

Gain Integrator

0

00 /

nb

b

nb

θ

pη

KINEMATICS


Transformations BODY - NED: Quaternions

6 DOF Kinematic Equations


ሶ𝒒=

𝑹𝑏𝑛 𝒒 𝟎3×3𝟎4×3 𝑻𝒒 𝒒



ሶ𝜼 = 𝑱𝒒 𝜼 𝝂 Simulation ModelAttitude representation: Quaternions

r

q

p

w

v

u

b

nb

b

nb

/

/

w

vv

q

pη

b

nb /

3

2

1

0

/

q

q

q

q

z

y

x

n

n

n

b

nb

q

pη

Gain Integrator

0

00 /

q

pη

b

nb

KINEMATICS


Vector Rotation About General Axis:


Vector Rotation About General Axis:

Principles of Guidance, Navigation & ControlDay 1: Modelling & Simulation of Marine CraftDynamics

6 DoF Rigid-Body Simulation ModelAttitude representation: Euler Angles

r

q

p

w

v

u

b

nb

b

nb

/

/

w

vv

nb

b

nb

θ

pη

/

Y

P

R

z

y

x

n

n

n

nb

b

nb

θ

pη /

Gain Integrator

0

00 /

nb

b

nb

θ

pη

0

00

/

/

b

nb

b

nb

w

vv


ሶ𝜽𝑛𝑏=

𝑹𝑏𝑛 𝜽𝑛𝑏 𝟎3×3𝟎3×3 𝑻𝜃 𝜽𝒏𝒃



ሶ𝜼 = 𝑱𝜣 𝜼 𝝂

b

nb

b

nb

/

/

w

vv

𝑴𝑅𝐵 ሶ𝝂 + 𝑪𝑅𝐵𝒗 = 𝝉𝑅𝐵

ሶ𝝂 = 𝑴𝑅𝐵−1 𝝉𝑅𝐵 − 𝑪𝑅𝐵𝒗

Gain

𝑪𝑅𝐵KINEMATICS

DYNAMICS

+

−

𝝉𝑅𝐵𝑴𝑅𝐵

−1

GainIntegrator


6 DoF Rigid-Body Simulation ModelAttitude representation: Quaternions

r

q

p

w

v

u

b

nb

b

nb

/

/

w

vv

Gain Integrator

0

00

/

/

b

nb

b

nb

w

vv

b

nb

b

nb

/

/

w

vv

𝑴𝑅𝐵 ሶ𝝂 + 𝑪𝑅𝐵𝒗 = 𝝉𝑅𝐵

ሶ𝝂 = 𝑴𝑅𝐵−1 𝝉𝑅𝐵 − 𝑪𝑅𝐵𝒗

Gain

𝑪𝑅𝐵KINEMATICS

DYNAMICS

+

−

𝝉𝑅𝐵𝑴𝑅𝐵

−1

GainIntegrator

q

pη

b

nb /

3

2

1

0

/

q

q

q

q

z

y

x

n

n

n

b

nb

q

pη


ሶ𝒒=

𝑹𝑏𝑛 𝒒 𝟎3×3𝟎4×3 𝑻𝒒 𝒒



ሶ𝜼 = 𝑱𝒒 𝜼 𝝂

0

00 /

q

pη

b

nb


6 DoF Equations of Motion including Ocean Currents (ROV)

𝑴𝑅𝐵 ሶ𝝂 + 𝑪𝑅𝐵 𝒗 𝒗 + 𝒈 𝜼 +𝑴𝐴 ሶ𝝂𝒓 + 𝑪𝐴 𝒗𝑟 𝒗𝑟 + 𝑫 𝒗𝑟 𝒗𝑟 = 𝝉𝑤𝑎𝑣𝑒 + 𝝉𝑝𝑟𝑜𝑝𝑢𝑙𝑠𝑖𝑜𝑛

rigid-body and hydrostatic terms hydrodynamic terms

Restoring Forces and Moments





Ocean Current Velocity Vector(Irrotational Fluid)

n

cnb

n

b

n

cnb

b

n

b

c

b

c vθRvθRv0

vv

13

c

1,

Relative Velocity Vector

𝒗𝑟 = 𝒗 − 𝒗𝑐 =𝒗 Τ𝑏 𝑛𝑏

𝒘 Τ𝑏 𝑛𝑏 −

𝒗𝒄𝑏

𝟎3×1=

𝒗 Τ𝑏 𝑛𝑏 − 𝒗𝒄

𝑏






Wave Spectra





Propulsion System


Nonlinear 6DoF ROV model (Euler Angles)

ሶ𝝂 = 𝑴𝑅𝐵 +𝑴𝐴−1 𝝉𝑤𝑎𝑣𝑒 + 𝝉𝑝𝑟𝑜𝑝𝑢𝑙𝑠𝑖𝑜𝑛 − 𝑪𝑅𝐵 𝒗𝑟 + 𝑪𝐴 𝒗𝑟 𝒗𝑟 − 𝑫 𝒗𝑟 𝒗𝑟 − 𝒈 𝜼

v η η

Gain Integrator

0η 0v

v

Gain

KINEMATICSDYNAMICS

+𝝉𝑝𝑟𝑜𝑝

GainIntegrator

n

cnb

n

b

n

cnb

b

n

b

c

b

c vθRvθRv0

vv

13

c

1

v

+

−

𝑴𝑅𝐵 +𝑴𝐴−1

𝝉𝑤𝑎𝑣𝑒

Gaincr vvv

𝑪𝑅𝐵 + 𝑪𝐴

−

𝑫

−−

𝒈

b

nb

b

nb

/

/

w

vv

nb

b

nb

θ

pη /

+


v η η

Gain Integrator

0η 0v

v

Gain

KINEMATICSDYNAMICS

+𝝉𝑝𝑟𝑜𝑝

GainIntegrator

n

c

n

b

n

c

b

n

b

c

b

c vqRvqRv0

vv

13

c

1

v

+

−

𝑴𝑅𝐵 +𝑴𝐴−1

𝝉𝑤𝑎𝑣𝑒

Gaincr vvv

𝑪𝑅𝐵 + 𝑪𝐴

−

𝑫

−−

𝒈

b

nb

b

nb

/

/

w

vv

q

pη

b

nb /

+

Nonlinear 6DoF ROV model (Quaternions)

ሶ𝝂 = 𝑴𝑅𝐵 +𝑴𝐴−1 𝝉𝑤𝑎𝑣𝑒 + 𝝉𝑝𝑟𝑜𝑝𝑢𝑙𝑠𝑖𝑜𝑛 − 𝑪𝑅𝐵 𝒗𝑟 + 𝑪𝐴 𝒗𝑟 𝒗𝑟 − 𝑫 𝒗𝑟 𝒗𝑟 − 𝒈 𝜼

Principles of Guidance, Navigation & ControlDay 1: Modelling & Simulation of Marine CraftHands-on: Modelling & Simulation of ROV (MATLAB/Simulink)

Principles of Guidance, Navigation & ControlDay 2: Control of Marine CraftControl Allocation

SURGE

HEAVE

SWAY

YAW DoF controllable by horizontal thrusters

DoF controllable by vertical thruster

Final CA Problem


• Virtual control input

• True control input dv

v

v

• Control effectiveness matrix

• Actuator position constraint

• Weighted pseudoinverse solution

p


p

v

Weighted pseudoinverse

1 5

37

0

2 6

4

p

v

v


Hybrid Approach for Control Allocation

Weighted

Pseudoinverse

Fixed-Point

Method

Algorithm:

1. Find pseudoinverse solution.

2. If the solution is feasible, go to step 4.

3. Otherwise, use the fixed-point iterations to find feasible solution.

4. Deliver feasible solution as output.



Virtual Control SpaceTrue Control Space

Virtual Control Space



Error

𝒆𝐻𝑇 = 𝝉𝑑𝐻𝑇 − 𝝉𝐻𝑇

𝒇𝐹𝐹𝐻𝑇 = −𝐾𝒆𝐻𝑇

Force Feedback


Cruise: CV11026

Date: Dec 2011

Location: Bantry Bay

ROV: LATIS

SHIP: CELTIC VOYAGER (DP not available)

ROV Health: All Thrusters OK – simulated faults in HT4 & HT2

Principles of Guidance, Navigation & ControlDay 2: Control of Marine CraftControl System

ROV Control Architecture

Control Allocation

Navigation Data

(ROV)

Disturbances

ROV

Rigid-Body

Dynamics

Propulsion

System

Fault

Diagnosis

Fault Accommodation

dτControl Allocation

dn

HT Saturation Bounds VT Saturation Bounds

Low-Level Controllers

Winner Control Cluster

ROV Mode Control Cluster

ROV

AUV

Emergency Control Cluster

Emergency

Standard

Operation

Mode

Switch

Faults

Fusion Obstacle Avoidance Control Cluster

+

+

Standard Control Cluster Coordinator

Exclusive

Mode

Switch

Arbitration

Navigation Data

(Support Vessel)

Pilot Input Interface

Mission Planner

Map

Builder

Way Points

DatabaseMission Builder

Interface & Data Management

Trajectory Planner

Collaborative Behaviours

Exclusive Behaviours

LLCτ

VJτ Synthesis

Fusion


Architecture

AutotuningImplementation

Low Level Controllers


Description

ExamplesImplementation

Middle Level Controllers

Principles of Guidance, Navigation & ControlDay 2: Control of Marine CraftHands-on: Modelling & Simulation of ROV (MATLAB - LabVIEW)

Principles of Guidance, Navigation & ControlDay 2: Control of Marine CraftHands-on: Control of ROV/USV (LabVIEW)

Principles of Guidance, Navigation & ControlDay 3: Brushless DC Motor Control using FPGAIntroduction

myRIO T200 Thruster

Principles of Guidance, Navigation & ControlDay 3: Brushless DC Motor Control using FPGAMotor Control with PWM Signal

TPWM = 2.5 (ms)

Stopped

TS = 1.5 (ms)

TPWM = 2.5 (ms)

Max Forward

TS = 1.9 (ms)

TPWM = 2.5 (ms)

Max Reverse

TS = 1.1 (ms)

Duty Cycle = 0.60

Duty Cycle = 0.76

Duty Cycle = 0.44

Stopped Max Forward

Max Reverse

+1000-100

nd (%)

Duty Cycle

0.44

0.60

0.76

Motor friction (Dead Zone problem) neglected!

Principles of Guidance, Navigation & ControlDay 3: Brushless DC Motor Control using FPGAMotor Control with PWM Signal

nd > 0

nd < 0

nd = 0

Duty Cycle

Stopped Max Forward

Max Reverse

+1000-100

nd (%)

0.44

0.60

0.76

0.62

0.58

A+

B+

A-B-

Taking into account motor friction (Dead Zone)!

Principles of Guidance, Navigation & ControlDay 3: Brushless DC Motor Control using FPGAHands-on: Thruster Control using FPGA (LabVIEW)

Interconnection between myRIO and T200 Thruster

Modelling and Simulation of Marine Craft OVERVIEW...Thor I. Fossen. Handbook of Marine Craft Hydrodynamics and Motion Control. ISBN 978-1-119-99149-6, John Wiley & Sons, 2011. Navigation:

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