Haptics ME7960, Sect. 007 Td ’ ClToday’s Class...Potentiometer (not common in haptics – noisy Tachometer (pulse or generator)Tachometer (pulse or generator) Optical gray-scale

HapticsME7960, Sect. 007

Lect. 3: Physical HapticLect. 3: Physical Haptic Systems

Spring 2011Prof William ProvancherProf. William Provancher

University of UtahSalt Lake City, UT USA

We would like to acknowledge the many colleagues whose course materials were borrowed and adapted in putting together this course, namely: Drs. Allison Okamura (JHU), Katherine Kuchenbecker (U Penn), Francois Conti, Federico Barbagli, and Kenneth Salisbury (Stanford), Ed Colgate (Northwestern), Hong Tan (Purdue), Blake Hannaford and Ganesh Sankaranarayanan (U. Washington), and Karon MacLean (UBC).

T d ’ ClToday’s Class Physical Haptic Systems Physical Haptic Systems

Actuators for haptic/tactile systems Actuator types Actuator examples

Sensors Amplifier Control Card

O i f C t l A hit t Overview of Control Architecture Overall system view Admittance/Impedance type devices KinematicsKinematics

Readings Diego Ruspini and Oussama Khatib, “Haptic Display for Human

Interaction with Virtual Dynamic Environments,” Journal of R b ti S t 18(12) 769 783 (2001)

2

Robotic Systems 18(12),769–783 (2001) read through p. 774

Ph i l H ti S tPhysical Haptic Systems Basic Elements of a haptic system Basic Elements of a haptic system

Physical device (the plant of a control system) Actuators and transmission

S

Discussed today

Sensors High power (current) amplifier + power supply

(what magnitude of currents?) Controller Computer Controller Control (DAQ) Card( ) Servo control loop (typically

at 1kHz) Why??? Analog Controller (quite rare)

3

Analog Controller (quite rare)

Illustration from K. J. Kuchenbecker and G. Niemeyer, “Induced Master Motion in Force-Reflecting Teleoperation.” ASME Journal of Dynamic Systems, Measurement, and Control. Volume 128(4):800-810, December 2006.

© W. Provancher 2009

Physical Haptic SystemsPhysical Haptic Systems

Actuators and transmissionActuators and transmission

4



H ti /T til A t t T Electromagnetic Actuators

Haptic/Tactile Actuator Types Not typically used in haptic Electromagnetic Actuators

Electric motors DC Brushed PM Motors

(most commonly used in haptics)DC B hl

systems. Why??

DC Brushless Stepper Motors

Voice coils and linear motors Lawrence force W

/Kg)

Lawrence force Pneumatic Actuators Hydraulic

SMA r Den

sity

(W

SMA Piezoelectric Electro-rheological

Pow

erWeight (Kg)

5

Magneto-rheological (and magnetic particle brakes) … An interesting exception can be found in

Lawrence, D. A., Pao, L. Y., and Aphanuphong, S. 2006. Unwarping Encoder Ripple in Low Cost Haptic Interfaces. In Proceedings of Haptics Symposium (March 25 - 29, 2006), Washington, DC, 12.

© A. Okamura 2006 + W. Provancher 2009

Brushed DC (direct current) PM ( t t) t(permanent magnet) motors Most commonly used

BrushRotor(armature) Most commonly used

actuator in haptic devices How do they work? Brush

Commutator( )

Rotating armature with coil windings is caused to rotate relative to a permanent magnet

current is transmitted through brushes to armature, Stator

(Permanent

Housing

and is constantly switched so that the armature magnetic field remains fixed

(Permanent Magnets)

6© A. Okamura 2006 + W. Provancher 2009

DC Motors: Two-pole ExamplePermanent

3-pole most common (Maxon motors have more)

PermanentMagnet

( )

Power supplied through brushes generates a magnetic field around the armaturearmature.

The north pole of the armature is pushed away from the north magnet andfrom the north magnet and pulled toward the south, causing rotation.

When the armaturecommutator

When the armature becomes horizontal, the connections between the commutator and the brushes reverse, and the process repeats

PermanentMagnetBrush

7

process repeats.Source: wikipedia.org

[Slide courtesy of S. Bamberg, Univ. of Utah]

DC t tDC motor terms Cogging / Torque Ripple Cogging / Torque Ripple

Tendency for torque output to ripple as the brushes transfer power (on bad motors this can be felt)

Friction/damping Caused by bearings and eddy currents (mostly, it’s

coulomb friction that you feel but at high speedscoulomb friction that you feel, but at high speeds, especially through a geared transmission, viscous friction can begin to dominate)

St ll t Stall torque Max torque delivered by motor when operated continuously

without cooling (In most applications, you design

8

g ( pp , y gmotors to stay away from stall for efficiency. However, haptic devices are mostly standing still)


M t E tiMotor Equations

Torque constant K Torque constant, KT

Kt = Ke (for Kt ≡ N*m/A, Ke ≡ V/(Rad/s))Kt = 9 55 x 10-3 Ke N*m/A (for Kt ≡ N*m/A Ke ≡ V/KRPM)

Dynamic equation

Kt = 9.55 x 10 Ke N m/A (for Kt ≡ N m/A, Ke ≡ V/KRPM)Kt = 1.3524 Ke oz*in/A (for Kt ≡ oz*in/A, Ke ≡ V/KRPM)

Dynamic equation

9

Back EMFArmatureResistance

ArmatureInductance


B h d DC tBrushed DC motors Pros BrushRotor

(armature) Pros High bandwidth linear

actuator Easy to obtain with a wide

Brush

Commutator( )

Easy to obtain with a wide variety of sizes

Easy to control Cons Cons To get large torques, the

armature inertia gets too high to make a good Stator

(Permanent

Housing

impedance device Generates lots of heat Relatively expensive for

d lit t (

(Permanent Magnets)

10

good quality motors (e.g., Maxon motors)


DC Motors with leadscrews or b ll f li tiballscrews for linear motion Pros Pros High mechanical advantage

and high forcesg Can render stiff interactions

Cons

Haptic Master

Most not backdrivable Requires (expensive) force

sensor Haptic Master (Moog Inc.)

sensor Difficult controller design Possible eccentric vibration

11© W. Provancher 2009

http://www.engineersedge.com/hydraulic/images/linear-actuator-animation.gif

Possible eccentric vibration

DC Motors with capstan drives for rotary motionfor rotary motion

MotorCapstanPulley

Pros Cog-less “gear-

ratio” transmission

SensAble (Premium) Phantom

MotorEduHaptics.org

ratio” transmission Cons Issues with friction

TMotor

Capstan Pulley

Cable Issues with friction

transmission of cable on capstan pulley Sector

P lle

Cable


High cable tension high drag Possibly high reflected N2 inertia

Pulley

DC Motors with capstan drives for linear motion

Pros Cog-less linear

transmission

Clark, J. E., Provancher, W. R., Mitiguy, P. “Theory, Simulation, And Hardware: Lab Design For An Integrated System Dynamics Education,” In Proc. of ASME IMECE, Orlando, FL, Nov. 5–11, 2005, p 147–153.

Cons Relatively low forces

TCable Issues with friction

transmission of cable on t ll

TMotorCable


capstan pulleyMotor

Capstan Pulley Cable

V i C il A t tVoice Coil Actuators

Pros Pros Very high bandwidth linear

actuatoractuator Relatively high forces

Cons Cons Large relative size Short stroke Short stroke Generates lots of heat

Illustrations from Dimitrios A. Kontarinis and Robert D. Howe, “Tactile Display of Vibratory Information in


, p y yTeleoperation and Virtual Environments.” PRESENCE, 4(4):387-402, 1995Murray, A.M. and Klatzky, R.L. and Khosla, P.K, Psychophysical Characterization and Testbed Validation of a Wearable Vibrotactile Glove for Telemanipulation, Presence: Teleoperators & Virtual Environments, MIT Press 12:2, pp. 156-182, 2003

Lawrentz force magnetic l it ti d ilevitation devices

Pros Pros 6-DOF force feedback

ConsC l it Complexity hardware design Controller Controller

Limited workspace

15

Illustrations from butterflyhaptics.com/ andBerkelman, P. “A Novel Coil Configuration to Extend the Motion Range of Lorentz Force Magnetic Levitation Devices for Haptic Interaction”, Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems San Diego, CA, USA, Oct 29 - Nov 2, 2007 © W. Provancher 2009

P ti t tPneumatic actuators How do they work? How do they work?

Compressed air pressure is used to transfer energy from the power source to haptic interface. p p

Many different types (piston, McKibben, …) Concerns are friction and bandwidth Concerns are friction and bandwidth

16

Festo.comwww.pneumaticsfirst.org


Pneumatic actuators,cont. McKibben Artificial Muscle McKibben Artificial Muscle,

pneumatically actuated with similar properties to biological musclesmuscles Spring-like, flexible, for use within

robotic arms and for prosthesis Shadowrobot hand High force to weight ratio Constructed from internal air

bladder and outer braided weave Shadowrobot McKibben Actuatorshell

As bladder inflates, shell allows for expansion while maintaining cylindrical shape causing the

Shadowrobot. McKibben Actuator

17

cylindrical shape, causing the muscle to shorten http://www.shadowrobot.com/airmuscles/

© R. Wood (Harvard ES159/259) 2008 + W. Provancher 2009

Inflated – contractedDeflated – extended

Examples of pneumatic actuators f t til di lfor tactile displays

4x6 Pneumatic Array4x6 Pneumatic Array

M.B. Cohn, M. Lam, and R.S. Fearing, ``Tactile Feedback for Teleoperation'' SPIE Conf. 1833, Telemanipulator Technology, Boston, MA, Nov. 15-16, 1992.

G. Moy, C. Wagner, and R.S. Fearing, A Compliant Tactile Display for Teletaction IEEE Int Conf on Robotics and Automation April 2000

18

Teletaction, IEEE Int. Conf. on Robotics and Automation, April 2000.


H d li t tHydraulic actuators Pros Pros High forces Small actuator size on arm

d ff tor end effector Cons Dangerous: Can kill you!!g y Need big hydraulic pump Hydraulic seals need

maintenancemaintenance

19

Sarcos Dexterous Master & ArmSame basic actuator designs as pneumatics (with modifications)

www.pneumaticsfirst.org © W. Provancher 2009

Shape Memory Alloy (SMA)(Li A t t )(Linear Actuators) Most commonly in wire form: contracts when heated Most commonly in wire form: contracts when heated Repeated strains can be up to 3%

Based upon a solid state phase change (molecular realignment) Two phases: Martensite and Austenite At low temperatures the material is Martensite At low temperatures, the material is Martensite If the Martensite material is loaded, this creates a

deformation (typically seen as a shortening wire) ‘Shape memory’ occurs when heated: the material will Shape memory occurs when heated: the material will

‘remember’ its undeformed shape by heating to the Austenite phase Since the Austenite and undeformed Martensite phases have

20

Since the Austenite and undeformed Martensite phases have the same shape


Sh M All (SMA)Shape Memory Alloy (SMA)

Pros Pros Relatively robust

High force / High power density High force / High power density Small size Inexpensive and readily available (especially in Inexpensive and readily available (especially in

wire form) Cons Cons Low efficiency (bad for portable applications) Gets hot (bad for direct contact with skin typically… however, see

21

( yp y ,[Scheibe et al. 2007] on next slide).


Examples of SMA T til Di lSMA Tactile Displays

[Fisher 1996]

[Kontarinis et al 1995] [Wellman et al 1997]

22

[Kontarinis, et al. 1995] [Wellman, et al. 1997]

Scheibe, R. and Moehring, M. and Froehlich, B., Tactile Feedback at the Finger Tips for Improved Direct Interaction in Immersive Environments, Proc. IEEE Symposium on 3D User Interfaces 2007 pp. 10-14, 2007 © W. Provancher 2009

Pi l t i A t tPiezoelectric Actuators Piezoelectric crystal strains when voltage is applied Piezoelectric crystal strains when voltage is applied Strains can be up to 0.1%

Details Direct piezoelectric effect: a piezoelectric material will

generate charges (electric field) upon the application of stress along a properly poled direction

Converse piezoelectric effect: a piezoelectric material will change its shape upon the application of an electric field (along a poled direction)

charge separation

23

after poling: createsa dipole


Examples of Pi l t i T til Di lPiezoelectric Tactile Displays

Glassmire thesis (2006)

TPaD: Tactile Pattern Display.

Piezoelectric tactile pin array

TPaD: Tactile Pattern Display.

24

Piezoelectric tactile pin array[Summers & Chanter 2002]


[Homma, et al. 2004]Winfield & Colgate (2007)http://lims.mech.northwestern.edu/projects/TPaD/index.htm


SensorsSensorsPositionSensor

ForceSensor

25



S i h ti tSensors in haptic systems Motion sensors

Rotary motion Incremental and absolute Encoders (also resolvers, but less common) Hall effect sensor Potentiometer (not common in haptics – noisy Tachometer (pulse or generator)Tachometer (pulse or generator) Optical gray-scale analog sensors

Linear (translational) motion (less common) Encoders, potentiometer, optical emitter-detector,

Acceleration MEMS (most common now) MEMS (most common now) Piezoelectric and others

3D, 6-DOF motion Vision based (Vicon), ultrasonic (Logitech), magnetic (Polhemus, Ascension Flock of Birds),

others( ) ( ) Pressure (Tactile) (Also shape, but less common)

Capacitive, piezoelectric… Force sensors

Load cells (flexure + strain/displacement sensor)FSRs

26

FSRs Others…

We’ll discuss the most common of these © W. Provancher 2009

Force Sensors6-Axis JR3 ForceTorque Load Cell

How do they work? Typically a flexure + a strain

gage (sometimes alsogage (sometimes also piezoelectric sensors, but these tend to drift) Good quality 6-axis force-torque JR3 com Good quality 6 axis force torque

sensor is ~$6-7K Force Sensing Resistor

(FSR)

JR3.com

ATI Nano17 Transducer

(FSR) Piezoresistive ink Tons of sensor drift

Ch $10

Interlink FSR

Cheap ~$10

www.ati-ia.comTekscan Flexiforce FSR

27© W. Provancher 2009www.tekscan.com/flexiforce

www.interlinkelectronics.com

T ki S A li tiTracking Sensor Applications

Eye tracking Eye tracking Head tracking Body tracking Hand tracking Most important for typical haptic interfaces

28© A. Okamura 2006

D f F dDegrees of Freedom

Number of independent position variables Number of independent position variables needed to in order to locate all parts of a mechanismmechanism

DOF of motion DOF f i DOF of sensing

DOF of actuation DOF does not always correspond to number

of joints!


S tSensor types

Magnetic Magnetic Optical Acoustic Inertial Mechanical Most important for typical haptic interfaces


M h i l T kMechanical Trackers

Ground based linkages most commonly used Ground-based linkages most commonly used Position Sensors

Di i l d ( i l MR) Digital: encoders (optical or MR) Analog: Hall-effect (magnetic)


O ti l E dOptical Encoders How do they work? EmitterDetector How do they work? Focused beam of light aimed at a

paired photodetector is interrupted by a coded patterned disk

Incremental Encoder

a coded patterned disk Produces a number of pulses per

revolution ( pulses = cost) Quantization problems at low Quantization problems at low

speeds Absolute vs. differential encoders

Wikipedia.org

Absolute Encoder

Why choose one vs. other? Extra considerations if choosing

incremental?


saba.kntu.ac.irAbsolute Encoder Disk

Wikipedia.org

O ti l E dOptical Encoders Phase-quadrature encoder Phase quadrature encoder

2 channels, 90° out of phase allows sensing of direction of rotation g 4-fold increase in resolution

Schmitt trigger electronics create square waveform from analog detector signal

MR d k i il l b t ith ti d

33

MR encoders work similarly, but with magnetic sensors and metal disk


Quadrature Encoder States & DecodingDisk rotation CCW

1 1

00

Ch. 1 Encoder Signal

1

00

1

00

Ch. 2 Encoder Signal

Encoder States

00

A B C DSimplified Encoder Disk

EmitterDetectorEncoder States

A B C D

Disk rotation CCW

Simplified Encoder Disk(4 CPR, 16 PPR) (shown in state A)

Ch. 1 Encoder SensorBlockstransmission

Ch. 1

Ch. 2 0

0

0

1

1

1

1

0 45 deg.

CC

W D

Rotatio

of light

2

1

34

A B C D

Disk rotation CW

Ch. 2 Encoder Sensor

iskon

Allowstransmission of light (hole)© W. Provancher 2009

H ll Eff t SHall-Effect Sensors

How do they work? How do they work? A small transverse voltage is generated across a

current-carrying conductor in the presence of acurrent-carrying conductor in the presence of a magnetic field

(Discovery made in 1879, but not useful until the advent ofuntil the advent of semiconductor technology)


H ll Eff t SHall-Effect Sensors

Amount of voltage output related to the strength of magnetic field passing through.

Linear over small range of motion Need to be calibrated

Affected by temperature, other magnetic objects in the environments


H ll Eff t SHall-Effect SensorsFrom StanfordH ti P ddl

Haptic Paddle

magnet

Hall-effectHall effectSensor with

3 leads

The voltage varies sinusoidally with rotation

37

angle© A. Okamura + W. Provancher 2009

M i V l itMeasuring Velocity

Differentiate position Differentiate position advantage: use same sensor as position sensor

disadvantage: get noise signal disadvantage: get noise signal Alternative

f d ti b t ti k for encoders, measure time between ticks


Digital differentiationDigital differentiation Many different methods y Simple Example: Position reading at time 1 = P1

V = P2 – P1t

Position reading at time 2 = P2 t is the period of the servo loop (in sec. or counts)

Th iti i t i ll l d fi d i t l The position is typically sampled on a fixed interval Differentiation increases noise -

39© A. Okamura + W. Provancher 2009

Noisy Velocity readings

Noise on velocity signal can create jitter, especially at high K gains (many haptic controllers don’t even includeat high Kv gains (many haptic controllers don t even include damping)

Common solutions Tach/Generator

Voltage a speed (same source as back EMF) Resolution only as great as your A/D converter Not great at low speeds

Integrate the signal from an accelerometer Integrate the signal from an accelerometer Time per tick rather than ticks per time

use a special chip that measures time between ticks Especially good to do at slow speedsp y g p Fares poorly at high velocities

Filtering (conventional to smooth or Kalman filtering to combine sensor signals)

40

Almost always FILTER your velocity signal!!© W. Provancher 2009

Digital differentiationD li ith i b filt iDealing with noise by filtering How do you deal with noise How do you deal with noise Filtering

Example 1: Pre-filter positionsV = P2 – P1

t Average 20 readings = P1 Average next 20 readings = P2

Example 2: Post-filter Velocities (more common) Example 2: Post filter Velocities (more common) Position reading at time 1 = P1 Position reading at time 2 = P2

C l l t i t t l it Calculate instantaneous velocity Set velocity equal to filtered version of instantaneous

velocity

41

Filtered velocity = Filtered instantaneous velocity used in controller © A. Okamura + W. Provancher 2009

Digital Filtering Common filter types

FIR filters Median (with defined sample window) Moving average (with defined sample window)

IIR filters Fading memory filterg y Filtered value = old_value * filter_ratio

+ current value * (1 – filter_ratio) Typical filter ratio 0.8 to 0.9yp Can simulate in Matlab with a step input to figure out equivalent

cutoff frequency (function of filter_ratio and sample frequency) Filter output = 0.667 at sec and 10%-90% rise time ~2.2

Time constant RC 1/ Corner freq enc f 1/(2 ) Time constant RC = 1/, Corner frequency fc = 1/(2 ) E.g., 90:10 fading memory filter (i.e., filter ratio = 0.9) has

fc = 15.2 Hz when running a 1 KHz servo loop. Set fc near (typically above) the mechanical time constant

42

Set fc near (typically above) the mechanical time constant of your system

Why not just set filter_ratio = .999 ???© W. Provancher 2009


Power AmplifierPower AmplifierPower

Amplifier

43



Power (Current) AmplifiersLMD18200 H-Bridge PWM Amp

Courtesy of Stanford SPDL

PWM (Pulse Width Modulation) More efficient Copley, AMC, etc. make p y

PWM amps with closed-loop current control capability (~$350) Voltage in proportional current out

Other low end H-Bridge PWM amps l il bl ( LMD18200 $10)

AMC PWM Amplifier

also available (e.g., LMD18200, ~$10) Linear

Higher bandwidth than PWM, but not typically neededyp y

Haptic paddle uses a LM675 high current op. amp

Many commercial linear amps also available

44

available


Stanford haptic paddle Linear Amp

Example of PWM Control SignalExample of PWM Control Signal Varying the duty cycle of the PWM

signal is analogous to changing the voltage Equivalent

Voltage

50%C

Voltage

Duty Cycle

~90%Duty Cycle


Duty Cycle

Physical Haptic Systems Computer Controller Control (DAQ) Card( )

ControlCard

46



DAQ/Controller Computer CardUsually a PCI bus card

Common control cards Common control cards Sensoray 626 (~$700)

Four 14-bit D/A outputs, up to 6 encoder inputs,… Four 14 bit D/A outputs, up to 6 encoder inputs,… dSpace 1104 (ACE1104CLP, ~$5K) Quanser Q4 and Q8 ( $4K) IOTech (e.g., DaqBoard/3001 ~$1K)) Servo2go (ISA bus only, but 8 ch. for ~$1K)

Sensoray 626

Computer Boards DAC and Encoder inputs on separate cards

National Instruments

47

National Instruments DAC and Encoder inputs on separate cards


S TSome Terms

AD/DA AD/DA analog to digital

digital to analog digital to analog Interrupt service routine

S L Servo Loop Servo rate Usually needs to be >500 Hz, and most often is

1,000 Hz


D/A d A/DD/A and A/D

Converts between He adecimaBinarDecimal Converts between voltages and counts C t t

Hexadecimal

Binary Decimal

0 0000 0

1 0001 1

2 0010 2

Computer stores information digitally, and communicates with the

3 0011 3

4 0100 4

5 0101 5

6 0110 6 communicates with the outside world using +/-10V signals

7 0111 7

8 1000 8

9 1001 9

A10101010V signals E.g., for 8-bit 0-5V ADC

2.5V = 10000000

A 1010 10

B 1011 11

C 1100 12

D 1101 13

49MSB

E 1110 14

F 1111 15 LSB© A. Okamura 2006

D/A d A/DD/A and A/D

Converts voltages to counts and vice versa Converts voltages to counts and vice versa A 12-bit card:

212 d i l b (4096) 212 decimal numbers (4096)

Decimal (base 10): 2994

Binary (base 2):

1 1 0 0 1 0 0 1 0 1

Hexadecimal (base 16): 1 1 0 0 1 0 0 1 0 1

50

B B 2 = BB2

© A. Okamura 2006

Physical Haptic Systems Computer Controller Admittance/Impedance

ControllerProgramp

Controller code/software

51



The Prototypical Closed Loop C t l S tControl System

Error

Command ControlL

Driver Plant+ Output

Law-

Feedback

• Typical Control Input Terms: Proportional, Derivative, Integral • Combinations: PD PI PID depending on


• Combinations: PD, PI, PID depending on response required

I d d Ad ittImpedance and Admittance

• Impedance Control An impedance (Z) determines the force: p ( )f = func(x) => Z = F(s)/X(s)

• Admittance Control An admittance (Y) determines position: x = func(f) => Y = X(s)/F(s)

• Can’t do both at the same time

53

• A robot or a person can do either © A. Okamura 2009

I d d Ad itt• Most haptic displays use impedance control

Impedance and Admittance Most haptic displays use impedance control

– Allows “transparency” at lower cost

• Robots are both • Examples of admittance control devices:

Steady-Hand Robot and HapticMaster


I d C t l• Robot in force control = impedance

Impedance Control • Robot in force control = impedance • This is the most common haptic display

control modecontrol mode • Virtual environments are expressed more

naturally: Fmotor= kx + bv + manaturally: Fmotor kx bv ma • Typically uses current-control amplifiers

with a DC motor (why??)


Ad itt C t l• Robot in position/velocity control =

Admittance Control Robot in position/velocity control

admittance • Still have to generate a desired force Still have to generate a desired force

(because of current control amp) • Example 1: typical linear admittance control law• Example 1: typical linear admittance control law

vdes= K * FmeasFmotor= Kp*(xdes- xmeas)Fmotor Kp (xdes xmeas)

• Example 2: xdes= func(Fmeas, xmeas)

56

des ( meas, meas)Fmotor= Kp*(xdes- xmeas)


The Prototypical Closed Loop C t l S tControl System

Error

Command ControlL

Driver Plant+ Output

Law-

Feedback

• Typical Control Input Terms: Proportional, Derivative, Integral • Combinations: PD PI PID depending on


• Combinations: PD, PI, PID depending on response required

Example controllerExample controllerImplementing the simplestpossible PID Controllerpossible PID Controller

Control Effort = K * e + K * e K * vControl Effort = KP e + KI e – KD v

KP = Proportional GainP

KI = Integral Gain

KD = Derivative Gain

58

e = Error = Desired Position – Actual Positionv = Velocity


P ti lProportionalKP * e

• Effect: big signal for large error, small signal for small error

P

• Results in some steady-state error Needs a nonzero error to generate a control actionaction

• Essentially a spring at the desired position (F = k x) ( )– High gain makes a stiffer spring and increases

tendency to oscillate


D i tiDerivative– KD * v

• Effect: slows control action and damps oscillations; increases system stability ; y y

• Can also make response more sluggish • Based on first derivative: either noise or Based on first derivative: either noise or

filtering lag (for velocity estimate from position) can actually introduce instability again


I t lIntegralKI * e

• Effect: integrates error over time – Control signal builds up and eventually brings

I

error to zero

• Reduces steady-state error and improves system responsivenesssystem responsiveness

• Unpleasant side effects: – Integrator wind-up – Decreased stability


T i PID t llTuning a PID controller

• Iterate! – Start with P: increase until unstable – Add D until stable – If SS error is a problem, add I – (add D until stable) ( )– Add more P, adjust D, etc.

• Compromise between responsiveness and t bilitstability

• In haptics, the setpoint depends on the context: how stable does it need to be?

62

context: how stable does it need to be?

© A. Okamura 2009

Di ti tiDiscretization

• Sampling introduces “steps” in the signal (“sample and hold”) ( p )

• Transition between stepped and continuous signal can cause problems in feedback control

• Vast topic beyond the scope of this lecture… For now, just remember: – Sample 2 to 10 times (or faster) the fastest frequency in the system – A sufficiently stiff model or controller will eventually

63

y ymake any system unstable

© A. Okamura 2009

Other things your controller ill dwill need

Need Kinematics Need Kinematics Determine endpoint position

Calculate velocities Calculate velocities Calculate force-torque relationships Sometimes need Dynamics Sometimes need Dynamics

If you are weak on these topics, you may t t h k t I t d ti t b tiwant to check out Introduction to robotics:

mechanics and control by Craig (1989) or notes from your robotics course

64

notes from your robotics course.

© A. Okamura 2006

Ki tiKinematics

Think of a Think of a manipulator/ interface as a set of bodiesas a set of bodies connected by a chain of jointsof joints

Revolute most common for hapticcommon for haptic interfaces

65

From Craig, p. 69

© A. Okamura 2006

Ki tiKinematics

Moving between Joint Space and Moving between Joint Space and Cartesian Space

Forward kinematics: based on joint angles, calculate end-effector position

66

calculate end-effector position

© A. Okamura 2006

J i t i blJoint variables

Be careful how you define joint positions Be careful how you define joint positions

Ab l R l i

67

Absolute Relative

© A. Okamura 2006

Ab l t f d ki tiAbsolute forward kinematics

x = L1cos(1) + L2cos(2) y L sin( ) + L sin( )y = L1sin(1) + L2sin(2)

Sometimes done this way with haptic devices (e g can be usedhaptic devices (e.g., can be used when controlling elbow and shoulder joints of a Phantom Premium since its joint motions cause motion

68

joint motions cause motion independently at the end effector)

© A. Okamura 2006

R l ti f d ki tiRelative forward kinematics

x = L1cos(1) + L2cos(1+2)y = L sin( ) + L sin( + )y = L1sin(1) + L2sin(1+ 2)

Usually done this way with robots, sometimes with hapticrobots, sometimes with haptic devices

Typically used if you have actuators t j i t (i l ti t ti )

69

at joints (i.e., relative actuation)

© A. Okamura 2006

V l itVelocity

Recall that the forward kinematics tells us the Recall that the forward kinematics tells us the end-effector position based on joint positions H d l l t l it ? How do we calculate velocity?

Use a matrix called the Jacobian


F l ti j i t tFormulating joint torques

The Jacobian can be used to relate joint The Jacobian can be used to relate joint torques to end-effector forces:

TT

Why is this important for haptic displays?


R di f t tiReading for next time

Diego Ruspini and Oussama Khatib “Haptic Diego Ruspini and Oussama Khatib, HapticDisplay for Human Interaction with Virtual Dynamic Environments ” Journal of RoboticDynamic Environments, Journal of Robotic Systems 18(12),769–783 (2001) read through p 774 read through p. 774

N t l t ill b “H ti R d i ” Next lecture will be on “Haptic Rendering”

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Supplemental Information on Ki ti d J biKinematics and Jacobians

Although “Introduction to Robotics” is a Although Introduction to Robotics is a prerequisite for this class, we recognize that some of you may be a little rusty withsome of you may be a little rusty with kinematics, hence the pages that follow will provide a refresher as a reference to look atprovide a refresher as a reference to look at on your own


J i t i blJoint variables

Be careful how you define joint positions Be careful how you define joint positions

Ab l R l i

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Absolute Relative

© A. Okamura 2006

Ab l t f d ki tiAbsolute forward kinematics

x = L1cos(1) + L2cos(2) y L sin( ) + L sin( )y = L1sin(1) + L2sin(2)

Sometimes done this way with haptic devices (e g can be usedhaptic devices (e.g., can be used when controlling elbow and shoulder joints of a Phantom Premium since its joint motions cause motion

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joint motions cause motion independently at the end effector)

© A. Okamura 2006

R l ti f d ki tiRelative forward kinematics

x = L1cos(1) + L2cos(1+2)y = L sin( ) + L sin( + )y = L1sin(1) + L2sin(1+ 2)

Usually done this way with robots, sometimes with hapticrobots, sometimes with haptic devices

Typically used if you have actuators t j i t (i l ti t ti )

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at joints (i.e., relative actuation)

© A. Okamura 2006

I Ki tiInverse Kinematics

Using the end effector position calculate the Using the end-effector position, calculate the joint angles N t d ft i h ti Not used often in haptics But useful for calibration Th b There can be: No solution (workspace issue)

1 l i 1 solution More than 1 solution


E lExample

Two possible solutions Two possible solutions Two approaches:

algebraic method

geometric method


V l itVelocity

Recall that the forward kinematics tells us the Recall that the forward kinematics tells us the end-effector position based on joint positions H d l l t l it ? How do we calculate velocity?

Use a matrix called the Jacobian


F l ti th J biFormulating the Jacobian Use the chain Use the chain

rule:

Substitute in Substitute in expressions for x & y from ybefore and take partial derivatives

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derivatives:

© A. Okamura 2006

A bl i M t iAssemble in a Matrix


Si l itiSingularities

Most devices will have values for which the Most devices will have values for which the Jacobian is singular Thi th t th d i h l t This means that the device has lost one or more degrees of freedom in Cartesian Space T ki d Two kinds: Workspace boundary

W k i t i Workspace interior


Si l it M thSingularity Math If the matrix is invertible then it is non If the matrix is invertible, then it is non-

singular

Can check invertibility if J by taking the Can check invertibility if J by taking the determinant of J . If it is equal to 0, then it is singular g

Can use this method to check which values of will cause singularities


C l l ti Si l itiCalculating Singularities

Simplify nomenclature: i ( Simplify nomenclature: sin(=s12

For what values of and does this equal zero?

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equal zero?

© A. Okamura 2006

E f lEven more useful….

The Jacobian can be used to relate joint The Jacobian can be used to relate joint torques to end-effector forces:

T Why is this important for haptic displays?


H d t thi ti ?How do you get this equation?

P i i l f i t l k Principle of virtual work States that changing the

coordinate frame does not change the total work of a systemsystem


Documents

Haptics ME7960, Sect. 007 Td ’ ClToday’s Class...Potentiometer (not common in haptics – noisy Tachometer (pulse or generator)Tachometer (pulse or generator) Optical gray-scale