chapter 3author.uthm.edu.my/uthm/www/content/lessons/4952/chapter 3... · 11 position and...

1

CHAPTER 3

MEASUREMENT SYSTEMS

APPLICATION

Content

bull Position and displacement measurement

bull Acceleration measurement

bull Velocity measurement

bull Force measurement

2

Position and displacement

bull Sensing methods

bull Potentiometers

bull Linear Variable Differential Transformer

(LVDT)

bull Synchro systems

bull Resolvers

bull Optical encoder

bull Proximity sensor

bull Photoelectric sensors

bull Additional Accelerometer and Gyroscope

3


Linear Rotary

Potentiometer Potentiometer

Capacitive Capacitive

Inductive Inductive

Linear Variable-Differential

Transformer (LVDT)

Rotary Variable-Differential

Transformer (RVDT)

Synchro systems

Resolvers

Optical encoder

Photoelectric sensors

Proximity sensor

Accelerometers Gyroscope

4

Already covered in

previous slides

Add in


Synchro and Resolver

5


Synchro

6

bull Synchro act as a ldquotransmitterrdquo and ldquoreceiverrdquo

bull ldquotransmitterrdquo to control the rotary position of ldquoreceiver

Source Lessons In Electric Circuits Volume II ndash AC By Tony R Kuphaldt in

openbookprojectnetelectricCircuits


Synchro

7

bull AC voltmeter registers voltage if the ldquoreceiverrdquo rotor is not

rotated exactly 90 or 270 degrees from the ldquotransmitterrdquo

rotor



8


Resolver

bull two stator winding placed at 90deg to each other and a

single rotor winding driven by alternating current

bull polar to rectangular conversion

bull angle (rotor) co-ordinates sin and cosine (stator)

bull proportional voltages on the stator windings



9


Resolver

bull The coordinates (X Y) are available on the resolver stator

coils

bull 119883 = 119881 cos ang119887119890119886119903119894119899119892

bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892



10


Applying Synhros as Resolver



11





bull A TDX torque differential transmitter sums an electrical

angle input with a shaft angle

bull input producing an electrical angle output

bull A TDR torque differential receiver sums two electrical

angle inputs producing a shaft

bull angle output

bull A CT control transformer detects a null when the rotor

is positioned at a right angle to the stator angle input A

CT is typically a component of a servondash feedback

system

12





bull A Resolver outputs a quadrature sin and cosine(theta)

representation of the shaft angle

bull input instead of a three-phase output

bull The three-phase output of a TX is converted to a

resolver style output by a Scott-T transformer



13

Both act as rotary position sensor



Stator winding fixed

at 120deg to each

other


at 90deg to each

other


Synchro in linear displacement

14

bull Modify synchro to resolver to measure linear

displacement

bull Inductsyn product brand Also known as linear encoder




Optical encoder

15

16

Concepts related to encoders

bull What is an encoder

A rotary encoder is a sensor for

converting rotary motion or position to

a series of electronic pulses

17

Basic architectures of

encoders

bull Linear architecture

Linear encoders which consist of a long linear read

track (analogous to the code disk of a rotary

encoder) together with a compact read head

address these concerns We offer three grades of

linear encoders to suit a variety of application

requirements

Introduction

bull Encoders and sensors allow control and feedback loops to be established

bull Without the knowledge of position andor speed it is impossible to maintain accuracy and control

bull Information provided by encoders and sensors is limited by various things including data transmission frequency and also by the physical limits of the system being controlled

Encoders - Introduction

bull Incremental encoders emit pulses which

determine how far the device has rotated (if a

rotary encoder) or moved (if a linear encoder)

bull Incremental encoders may be rotary or linear

The first key specification is the number of

pulses per revolution (PPR) or pulses per inch

(or centimeter) PPR of 250 512 1000 1024 or

even up to 100000 pulses per revolution are

available


bull Absolute encoders are used to determine the absolute or actual rotary or linear position of part of a machine

bull Absolute encoders have multiple slit photo-transistor LED sets -- most commonly 10 or 12

bull Resolutions of up to 1 part in 23 bits (000034 degrees) are available in some rotary encoders Other rotary encoders offer multiple turn capability with the ability to determine 1 part in 4096 per revolution over a total of 4096 revolutions

bull Some linear encoders can measure movements as small as 10microm to 10nm

21

bull rotary motion

bull linear motion used in conjunction with mechanical measuring standards such as lead screws and convert rotary motion (incremental or absolute) into electrical signals

bull ef fec t ive and low cost feedback dev ices

bull In high-accuracy applications

bull error sources (lead screw cumulative and periodic error thermal expansion and nut backlash for example)

Incremental Rotary Encoders

22

Absolute Rotary Encoders

bull Absolute encoders have a unique code that can be detected for each angular position

bull Absolute encoders are much more complex and

expensive than incremental encoders

23

Incremental encoders bull Pulses from LEDS are counted to provide rotary position

bull Two detectors are used to determine direction

(quadrature)

bull Index pulse used to denote start point

24

The applications

bull Positioning

bull a lead screw or rack-and-pinion converts rotary motion to linear

motion

bull an encoder converts the same motion into electronic pulses

The pulses typically are used as input signals for counters

PLCs or numerical-control equipment

25

The applications

bull Length measurement

bull Roll or sheet materials

bull cut-to-length machinery

bull An encoder + a measuring wheel or coupled to a roller

bull electronic pulses == units of length

bull very precise operation is possible

26

Encoders are wildly used in industry

bull machine tools

bull textile machinery

bull printing presses

bull wood working machines

bull handling technology

bull conveying and storage technology

bull robotics

The applications

27

Anatomy of Rotary Optical

Absolute Encoder

trelectroniccom

Encoders ndash Types (Rotary)

bull Absolute optical

ndash robots

bull Incremental Hollow shaft

bull Modular

bull Panel mount optical

ndash medical devices audio equipment

bull Magnetoresistive

ndash cranes dirty environments

Application of Rotary

Encoders

bull Painting Robots (automotive)

bull CAT Scan machines

bull Precision machining equipment

bull Microscopes

bull Aerospace

Applications Continued

Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs

Key Encoder Specs You must know the following information to specify an

encoder

bull Absolute or Incremental Encoder

bull Rotary or Linear Encoder

bull Resolution required

bull Uni-directional or Bi-directional motion

bull Operating voltage very commonly 5 volts also 12 and 24 volts available

bull Mechanical requirements ndash Shaft diameter and length

ndash Mounting holes and spacing

ndash Overall length and diameter

bull Environmental considerations ndash Dust moisture etc

ndash Shock Vibration etc

ndash Operating temperature

ndash RPM duty cycle

35

How to integrate

36

Application examples

Model 716 (Cube Encoder) made by ECP were

equipped on the lumber devices to produce up to

15 more lumber from each log

37


The Company of Ground Force mounts EPC

encoder on the trucks used at mining operations to

measure the rotation of pump shafts and of augers

The pumps deliver wet ingredients while the

augers deliver the dry ingredients

38

Example

Given an incremental encoder of 50 pulsesrev

determine

a) The resolution

b) What is the rotational angle if 15 pulses are

recorded

c) 500 pulses are recorded in 4 seconds What is the

rotational speed (rpm)

Example

An automatic cutting machine is designed to cut a

continuous plastic strip into blocks of specific length It is

fed continuously to a cutter via a pair of feeder discs whose

diameter is 200mm An incremental encoder of 100

pulsesrev is coupled to the disc Determine the number of

encoder output pulses if the block length is

(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40

Example An numerical control (NC) worktable operates by

closed-loop positioning The system is shown below

The lead screw has a pitch of 6mm and is coupled to

the motor shaft with a gear ratio of 51 (five turns of

drive motor for each turn of the screw) The optical

encoder generates 48 pulsesrev of its output shaft

The table is programmed to move a distance of

250mm at a feed speed rate = 500mmmin

Determine

Continued next page

41

Example continued a) How many pulses should be received by the

control system to verify that the table has moved

exactly 250mm (Ans 2000 pulses)

b) The pulse rate of the encoder (Ans 66667Hz)

c) The drive motor speed that correspond to the

specified feed rate (Ans 416667 revmin)

MP Groove (2008) Automation Production Systems and

Computer-Integrated Manufacturing Ed 3 pg184

Rotary Encoder Online ref

bull httpwwwomron-

apcommyapplication_solutionsmainasp

bull httpwwwiaomroncomproductscategorysensorsrota

ry-encodersincrementalindexhtml

bull httpabrockwellautomationcomMotion-Control

bull httpwwwfestocomcmsnl-be_be9733htm

bull Morehellip

42

Mechatronics - Foundations and Applications

Position Measurement in Inertial Systems

Adopted from

Title Lecture Position Measurement in Inertial Systems

DescriptionSpace Shuttle Lecture Position Measurement in Inertial Systems Christian Wimmer of surface sensor on

launch platform (complementary error characteristics) ndash PowerPoint PPT presentation

httppowershowcomview1210df9-NmE1YLecture_Position_Measurement_in_Inertial_Systems_powerpoint_ppt_presentation

Accelerometer

Gyroscope



1 Motivation applications

2 Basic principles of position measurement

3 Sensor technology

Motivation

Johnnie A biped walking machine

Orientation

Stabilization

Navigation

Motivation

Automotive Applications

Drive dynamics Analysis

Analysis of test route topology

Driver assistance systems

Motivation

Aeronautics and Space Industry

Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation

Military Applications

ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems

Helicopter Platforms

Naval Navigation

Submarines

Motivation

Industrial robotic Systems

Maintenance

Production

Basic Principles

Measurement by inertia and integration

Acceleration

Velocity

Position

Newtonlsquos 2 Axiom

F = m x a

BASIC PRINCIPLE OF DYNAMICS

Measurement system

with 3 sensitive axes

3 Accelerometers

3 Gyroscope

Basic Principles Gimballed Platform Technology

3 accelerometers

3 gyroscopes

cardanic Platform

ISOLATED FROM ROTATIONAL MOTION

TORQUE MOTORS TO MAINTAINE DIRECTION

ROLL PITCH AND YAW DEDUCED FROM

RELATIVE GIMBAL POSITION

GEOMETRIC SYSTEM

Basic Principles

Strapdown Technology

Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles


The measurement principle

SENSORS FASTENED DIRECTLY ON THE VEHICLE

BODY FIXED COORDINATE SYSTEM

ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h

Vehiclelsquos acceleration in inertial axes (1Newton)

Problem All quantities are obtained in vehiclersquos frame (local)

Euler Derivatives

Basic Principles

2

2( )i p i OP i i ie e e

d dv r f g A f g

dt dt

Interlude relative kinematics

Differentiation

2 2

2 22i p i OP ie e OP ie e OP e ie e OP e ie e ie e OPe

d d d dv r A r r r r

dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P

Frame Mechanisation I i-Frame

Vehiclelsquos velocity (ground speed) and Coriolis Equation

abbreviated

Differentiation Applying Coriolis Equation (earthlsquos turn rate is constant)

subscipt with respect to superscript denotes the axis set slash resolved in axis set

Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt

Frame Mechanisation II i-Frame

Newtonrsquos 2nd axiom

abbreviated

Recombination i-frame axes Substitution


Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i

e ie e lv f v g i b i i i

e ib ie e lv A f v g

Basic Principles

Basic Principles

Strapdown Attitude Representation

Direction cosine matrix

Quaternions

Euler angles

No singularities perfect for internal

computations

singularities good physical appreciation

Basic Principles

Strapdown Attitude Representation Direction Cosine Matrix

11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance

Simple Derivative Axis projection

b

nb nb nbA A

0

0

0

z y

b

nb z x

y x

With skew symmetric matrix

Basic Principles

Strapdown Attitude Representation Quaternions

Idea Transformation is single rotation about one axis

cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z

Components of angle Vector

defined with respect to reference frame

Magnitude of rotation

Operations analogous to 2 Parameter Complex number

p a ib jc kd

Basic Principles

Strapdown Attitude Representation Euler Angles

Rotation about reference z axis through angle

Rotation about new y axis through angle

Rotation about new z axis through angle

cos cos cos sin sin sin cos sin sin cos sin cos

cos sin cos sin sin sin sin sin cos cos sin sin

sin sin cos cos cos

nbA

1 T

nb bn bnA A A 90 Singularity

Gimbal angle pick-off

Sensor Technology

Accelerometers

Physical principles

Potentiometric

LVDT (linear voltage differential transformer)

Piezoelectric

F ma mg Newtonrsquos 2nd axiom

gravitational part Compensation

Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers

Servo principle (Force Feedback)

Intern closed loop feedback

Better linearity

Null seeking instead of displacement measurement

1 - seismic mass

2 - position sensing device

3 - servo mechanism

4 - damper

5 - case

Many more different construction of a accelerometer For more detail refer to D H

Titterton J L Weston Strapdown Inertial Navigation Technology

Sensor Technology

Gyroscopes

Vibratory Gyroscopes

Optical Gyroscopes

Historical definition

Sensor Technology

Gyroscopes Vibratory Gyroscopes

Coriolis principle 1 axis velocity caused by harmonic oscillation (piezoelectric)

2 axis rotation

3 axis acceleration measurement

Problems High noise

Temperature drifts

Translational acceleration

vibration

Sensor Technology


Many more different construction of a gyroscope For more detail refer to D H Titterton J L

Weston Strapdown Inertial Navigation Technology

Content

bull Position and displacement measurement

bull Acceleration measurement

bull Velocity measurement

bull Force measurement

2



bull Potentiometers


(LVDT)


bull Resolvers





3


Linear Rotary



Inductive Inductive


Transformer (LVDT)


Transformer (RVDT)

Synchro systems

Resolvers

Optical encoder


Proximity sensor


4

Already covered in

previous slides

Add in



5


Synchro

6






Synchro

7



rotor



8


Resolver








9


Resolver


coils

bull 119883 = 119881 cos ang119887119890119886119903119894119899119892

bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892



10





11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology






bull Potentiometers


(LVDT)


bull Resolvers





3


Linear Rotary



Inductive Inductive


Transformer (LVDT)


Transformer (RVDT)

Synchro systems

Resolvers

Optical encoder


Proximity sensor


4

Already covered in

previous slides

Add in



5


Synchro

6






Synchro

7



rotor



8


Resolver








9


Resolver


coils

bull 119883 = 119881 cos ang119887119890119886119903119894119899119892

bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892



10





11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





Linear Rotary



Inductive Inductive


Transformer (LVDT)


Transformer (RVDT)

Synchro systems

Resolvers

Optical encoder


Proximity sensor


4

Already covered in

previous slides

Add in



5


Synchro

6






Synchro

7



rotor



8


Resolver








9


Resolver


coils

bull 119883 = 119881 cos ang119887119890119886119903119894119899119892

bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892



10





11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology






5


Synchro

6






Synchro

7



rotor



8


Resolver








9


Resolver


coils

bull 119883 = 119881 cos ang119887119890119886119903119894119899119892

bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892



10





11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





Synchro

6






Synchro

7



rotor



8


Resolver








9


Resolver


coils

bull 119883 = 119881 cos ang119887119890119886119903119894119899119892

bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892



10





11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





Synchro

7



rotor



8


Resolver








9


Resolver


coils

bull 119883 = 119881 cos ang119887119890119886119903119894119899119892

bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892



10





11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




8


Resolver








9


Resolver


coils

bull 119883 = 119881 cos ang119887119890119886119903119894119899119892

bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892



10





11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




9


Resolver


coils

bull 119883 = 119881 cos ang119887119890119886119903119894119899119892

bull 119884 = 119881 119904119894119899 ang119887119890119886119903119894119899119892



10





11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




10





11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




11










bull angle output




system

12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




12












13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology






13





at 120deg to each

other


at 90deg to each

other



14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology






14


displacement





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





Optical encoder

15

16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




16






17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




17


encoders







requirements

Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Introduction













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology













available






21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology









21

bull rotary motion






22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




22





23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




23



(quadrature)


24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




24

The applications

bull Positioning


motion




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




25

The applications







26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




26


bull machine tools






bull robotics

The applications

27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




27


Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





Absolute Encoder

trelectroniccom



ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology






ndash robots


bull Modular






Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





Encoders




bull Microscopes

bull Aerospace


Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





Vtech

Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Vendors

bull Omega

bull Renishaw

bull TRElectronic

bull RENCO

bull ServoTek

bull AMCI

bull DuraCoder

33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




33

Vendors

bull Heidenhain

bull Renco

bull Renishaw

bull autonics

bull Stegmann

bull Pepperl+Fuchs


encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





encoder













35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




35

How to integrate

36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




36





37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




37







38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




38

Example


determine

a) The resolution


recorded



Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Example







(a) 30mm

(b) 1000mm 39

Feeder disc

Cut blocks

40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




40









Determine

Continued next page

41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




41










bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





bull httpwwwomron-






bull Morehellip

42



Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology






Adopted from





Accelerometer

Gyroscope





3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology







3 Sensor technology

Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Motivation


Orientation

Stabilization

Navigation

Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Motivation





Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Motivation


Autopilot systems

Helicopters

Airplane

Space Shuttle

Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Motivation


ICBM CM

Drones (UAV)

Torpedoes

Jets

Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Motivation

Maritime Systems


Naval Navigation

Submarines

Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Motivation


Maintenance

Production

Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Basic Principles


Acceleration

Velocity

Position


F = m x a


Measurement system


3 Accelerometers

3 Gyroscope


3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology





3 accelerometers

3 gyroscopes

cardanic Platform





GEOMETRIC SYSTEM

Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Basic Principles


Body fixed

3 Accelerometers

3 Gyroscopes

Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Basic Principles





ANALYTIC SYSTEM

Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Basic Principles

Reference Frames

i-frame

e-frame

n-frame

b-frame

Also normed WGS 84

15041 e

ie h



Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology






Euler Derivatives

Basic Principles

2


d dv r f g A f g

dt dt


Differentiation

2 2



dt dt dt dt

trans cor rot cent

Inertial system i

Moving system e

P = CoM

O

P



abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology






abbreviated



Basic Principles

( ) ( )

ie

i e

d dr r r

dt dt

( )

e

e

dr v

dt

2

2

( ) ( )( )

e ie

i ii

d d dr v r

dt dt dt

2

2

( )( )

e ie e ie ie

ii

d dr v v r

dt dt



abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology






abbreviated



Basic Principles

2

2

( )

e ie e ie ie

i

dv f v r g

dt l ie ieg g r

2

2

( )

e ie e l

i

dv f v g

dt

i i i i i



Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Basic Principles

Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Basic Principles



Quaternions

Euler angles


computations


Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Basic Principles


11 12 13

21 22 23

31 32 33

nb

c c c

A c c c

c c c

1 313 cos n b

c n n

For Instance


b

nb nb nbA A

0

0

0

z y

b

nb z x

y x


Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Basic Principles



cos 2

( )sin 2

( )sin 2

( )sin 2

x

y

z

a

bp

c

d

x y z





p a ib jc kd

Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Basic Principles







sin sin cos cos cos

nbA

1 T



Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Sensor Technology

Accelerometers

Physical principles

Potentiometric


Piezoelectric



Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Sensor Technology

Accelerometers

Potentiometric

+

-

Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Sensor Technology

Accelerometers


Uses Induction

Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Sensor Technology

Accelerometers

Piezoelectric

Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Sensor Technology

Accelerometers



Better linearity


1 - seismic mass


3 - servo mechanism

4 - damper

5 - case



Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Sensor Technology

Gyroscopes


Optical Gyroscopes


Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Sensor Technology



2 axis rotation


Problems High noise

Temperature drifts


vibration

Sensor Technology




Sensor Technology




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