Get anim. gifs of motors

http://e-www.motorola.com/collateral/MOTORDCTUT.html

& the other aminated gif I have downloaded

Controlling motors and controlling robots…

PID motor control

The fine art of motor arranging…

getting things done even when you can’t control what you’re doing...

First, to refresh your memory…

Spherical Stepper Motor

complete motor

statorrotor

applications

Nanorover No More…

JPL’s “nanorover” was to be used by ISAS to explore 1989ML

Electroactive Polymer wiper

The solution to many problems!

the MUSES-C project• optical navigation camera• LIDAR

• laser range finder

• completely map the asteroid

g = 0.0001 m/s2

play ball!

feature extraction sample

collection

(Slightly) Tamer Projects

Extinguishers’ Maze

Possible designs

Extinguishers

Include pictures of things NOT working, if you have themThere is a camera in the gray cabinet in B120 andSoftware on the robot croupier’s PCI also have a video camera (as do many of you)

Write-up

“FlameBot”

QuickTime™ and a YUV420 codec decompressor are needed to see this p icture.

Possible architectures

Doing HW

Playing golf ? (Paul P.)

Mazlov’s hierarchy of human needs (Will)

Hockey goalie (Eric)

Shopping at Lowe’s or Home Depot !

Clown balancing on stilts ??

avoid whirlingwork

sleepseek human help

check noteswork

Rodney Brooks: subsumption

Possible architectures

Doing HW

Playing golf ? (Paul P.)

Mazlov’s hierarchy of human needs (Will)

Hockey goalie (Eric)

Shopping at Lowe’s or Home Depot !

Clown balancing on stilts ??

avoid whirlingwork

sleepseek human help

check noteswork

Rodney Brooks: subsumption

Ron Arkin: motor schemas

Trying to get around the Libra complex as a freshman

Driving a car: attracted to green lights & the goal; repelled by cars & red lights

Adjusting the shower water (Paul P) or seasoning spaghetti sauce (Ken)

Finding avalanche survivors (Brie) or Skiing (Eric)

Football players or a soccer player with the ball

Mingling at a party -- drifting toward food; away from certain people

(like a maze, but more embarrassing)

Possible architectures

Doing HW

Playing golf ? (Paul P.)

Mazlov’s hierarchy of human needs (Will)

Hockey goalie (Eric)

Shopping at Lowe’s or Home Depot !

Clown balancing on stilts ??

avoid whirlingwork

sleepseek human help

check noteswork

Rodney Brooks: subsumption

Ron Arkin: motor schemas

Trying to get around the Libra complex as a freshman

Driving a car: attracted to green lights & the goal; repelled by cars & red lights

Adjusting the shower water (Paul P) or seasoning spaghetti sauce (Ken)

Finding avalanche survivors (Brie) or Skiing (Eric)

Football players or a soccer player with the ball

Mingling at a party -- drifting toward food; away from certain people

(like a maze, but more embarrassing)

Erann Gat: 3-layer architectureMudder studying for a test (Paul R)

Low-level control

getting things done even when you can’t control what you’re doing...PID control

Low-level control

getting things done even when you can’t control what you’re doing...PID control

N

S

N S

stator

rotor

commutator on shaft

+

-

brushes

DC motor

• We can control: the voltage applied

• We want to control: the rotational speed V

V

Low-level control

getting things done even when you can’t control what you’re doing...PID control

N

S

N S

stator

rotor

commutator on shaft

+

-

brushes

DC motor

• We can control: the voltage applied

• We want to control: the rotational speed V

V

Case 1: We trust equations !Case 2: We trust data !

Motor specs

Electrical Specifications (@22°C)For motor type 1624   003S 006S 012S 024

-------------------------- -------- -------- -------- --------- -------nominal supply voltage (Volts) 3 6 12 24armature resistance (Ohms) 1.6 8.6 24 75maximum power output (Watts) 1.41 1.05 1.50 1.92maximum efficiency (%) 76 72 74 74no-load speed (rpm) 12,000 10,600 13,000 14,400no-load current (mA) 30 16 10 6friction torque (oz-in) .010 .011 .013 .013stall torque (oz-in) .613 .510 .600 .694velocity constant (rpm/v) 4065 1808 1105 611back EMF constant (mV/rpm) .246 .553 .905 1.635torque constant (oz-in/A) .333 .748 1.223 2.212armature inductance (mH) .085 .200 .750 3.00

k

motor constant

Open-loop control

desired d

VThe world

dcompute V from the equation

controller Maybe...

V = + k d R k

Case 1: We trust equations !

voltage

load torque

motor resistance

motor constant

rotational speed

Open-loop analysis

We don’t know everything about !

or maybe not!

= guessed torque required a = actual torque required

Guessed voltage

Actual voltage needed

V = + k d a R k

V = + k d R k

The Road Less Traveled

Bang-bang control

Dynamic performance

Desired speed: d = 1

Computed voltage:

V = + k d R k

Actual torque req.:

a = 2

Results

k2 d

2Rwith =

“motoring uphill”

Dynamic performance

Desired speed: d = 1

Computed voltage:

t

V = + k d R k

Actual torque req.:

a = 2

Results

k2 d

2Rwith =

“motoring uphill”

Dynamic performance

Desired speed: d = 1

Computed voltage:

attained speed = 0.5

t

V = + k d R k

Actual torque req.:

a = 2

Results

k2 d

2Rwith =

“motoring uphill”

Dynamic performance

Desired speed: d = 1

Computed voltage:

attained speed = 0.5

t

V = + k d R k

Actual torque req.:

a = 2

Results

k2 d

2Rwith =

“motoring uphill”

dd

Closed-loop control

desired dV

The world

feedback the actual speed

- compute V prop. to the error e

d Error signal

e

Proportional control

V = Kp (d )

V = Kp • e

Proportional control

actual

Case 2: We trust data !

The road to Hana

(k+Kp)

Closed-loop analysis

V = + k a R k V = Kp (d )

controllerthe world

presuming I’ve done the algebra correctly…

= Kp d - a R

k(k+Kp)

(k+Kp)

Closed-loop analysis

V = + k a R k V = Kp (d )

controllerthe world

presuming I’ve done the algebra correctly…

= Kp d - a R

k(k+Kp)

The actual speed lags behind the desired speed -- with both a multiplicative term and an offset.

Closed-loop analysis

But the constant is under our control...

not very close to the desired speed of 1

Kp = 5

Closed-loop performance

Kp = 20

Kp = 200

Kp = 50

Kp = 500

Evaluating the response

How can we eliminate the steady-state error?

steady-state error

settling time

rise time

overshoot

overshoot -- % of final value exceeded at first oscillation

rise time -- time to span from 10% to 90% of the final value

settling time -- time to reach within 2% of the final value

ss error -- difference from the system’s desired value

Errors

Kp = 200 Kp = 50

Idea: translate error time into increased gain...

d

The Integrator...

desired dV

The worldactual

actual speed

- compute V using P and I feedback

d a

Error signal e

Proportional & Integral control

V = Kp (d ) + Ki ∫ (d ) dt

V = Kp • ( e + Ki ∫ e ) ( with a different Ki )

Your average integral control

enthusiast

Control, PI - styleKp = 100

Ki = 50

Magnum, PI

Ki = 200

You’ve been integrated...Kp = 100

resistance is futile (if it’s < .001

instability & oscillation

ringing

What to do?

You’ve been integrated...Kp = 100

resistance is futile (if it’s < .001

instability & oscillation

ringing

What to do?

error

PID control

desired dV

The worldactual a

actual speed a

- compute V using PID feedback

d a

Error signal e

Proportional / Integral / Derivative control

V = Kp (d ) + Ki ∫ (d ) dt + Kd

V = Kp • ( e + Ki ∫ e + Kd )d e dt

d e dt

( redefining Kd )

PID resultsKp = 100 Ki = 200

Kd = 2

Kd = 10 Kd = 20

Kd = 5

PID final control

PID tuning: the untold story

How to get the PID constants ?

(1) Try out different values until some look good.Optimize performance while tuning only one variable, then repeat with another variable. 2-3 iterations should provide reasonable results.

(2) Find values that produce common behavior, then adjust.Using only Proportional control, turn up the gain until the system oscillates w/o dying down, i.e., is marginally stable. Assume that K and P are the resulting gain and oscillation period, respectively.

Then, use

Ziegler-Nichols Tuning

for P control for PI control for PID control

Kp = 0.6 K

Ki = 2.0 / P

Kd = P / 8.0

Kp = 0.45 K

Ki = 1.2 / P

Kp = 0.5 K

Implementing PID

Use discrete approximations to the I and D terms:

• Proportional term: ei = desired - actual

• Integral term: eiti

at time i

i=0

i=now

• Derivative term: ei - ei-1

How could the time-discretization affect performance?

ti = elapsed time

ti

PID wrap-up

• photomultiplier temperature regulation

• automobile cruise control

• pipeline gas flow

• robotics (joint position and velocity)

Widespread control strategy

Summary of the terms’ effects

reaching a desired setpoint

wall-following

Performance depends on tuning and delays in the feedback loop

Kp

Ki

Kd

rise time overshoot settling time steady state error

decreases

decreases

minor effect minor effect

increases

increases

decreases

minor effect

increases

decreases

decreases

eliminates

Short Assignment #3: PD control

Achieving a goal position, given velocity control.

goalstart

2d Motor Schema control

A 2d vector field for controlling robot motion… (a motor schema with an attractor and an obstacle)

How do we use those “forces” to direct the

robot’s motors?

2d Motor Schemas: a thought experiment

The Nomad (and most robots) are limited in their maneuverability -- they can only move forward and backward in the direction their wheels are facing.

Thus, you can control 2 things:the translational velocity of the robotthe rotational velocity of its wheels

Task: Design several strategies for setting the translational and rotational velocities so that the Nomad can efficiently change course to a goal point in 2d.

For example, suppose the Nomad is moving along the negative x-axis to the right (toward the origin) at a velocity vo . Just when the robot reaches the origin, it realizes it wants to be at the point (1000,1000).

What are possible control strategies that will get it there. Consider as many as you can (but at least two). What are their (dis)advantages?

goal

current state

Wall/Corridor following

Achieving a desired offset, given control over turning angle:

L

R = Kp(R-L)

• Absolute limits should be used on !• How would you detect L and R ?

Fire finding

Achieving a desired offset, given control over turning angle:

light-balancing

just one sensor?

QuickTime™ and a YUV420 codec decompressor are needed to see this picture.

L

R

Wrapping Up

Examining robots’ inputs: building & using models of the world

Inverse kinematics: what we would really like to know ...

Forward kinematics: some alternatives to the differential-drive robot

• Short Assignment #3 due Monday

• Lab Project #1 write-up due Sunday night, 2/16 (midnight)

PID control: strategy for effectively controlling one system characteristic with a related (but not identical) one

this is as far as I got in Spring 2003

Perspective

At least you’re not Jar Jar...

pic

Robotic use of EAPs

shape memory alloys

“nitinol” (nickel titanium)

Perspective

If your robot doesn’t do what you want ...

… you can always change what you’re looking for.

to intelligent robots

the MUSES-C project• optical navigation camera• LIDAR

• laser range finder

• Fan beam sensors

g = 0.0001 m/s2

squishy sphere

feature extraction sample

collection

Possible designs

Extinguishers

See example write-up at the CS154 website.

Use pictures to help explain approach and results.Write-up

Dynamic performance

V = + k a R k the

world :

kV = a + k2 RR

torque = inertia acceleration

kV = J+ L + k2 RR

•

external load torque

internal to the motor

There must be a transient and a steady-state response to the

input, V

Motors and Encoders

desired dV

The world

a

actual speed a

- compute V using the error e

d a

Error signal e

Basic input / output relationship:We want to control .

V = + k R k

We can control V.

PID control

Closed-loop control

desired dV

The world

a

actual speed a

- compute V using the error e

d a

Error signal e

Basic input / output relationship:We want to control .

V = + k R k

We can control V.

PID control

Wrapping Up

Examining robots’ inputs: building & using models of the world

Inverse kinematics: what we would really like to know ...

Forward kinematics: some alternatives to the differential-drive robot

• Short Assignment #3 due Monday

• Lab Project #1 write-up due Sunday night, 2/16 (midnight)

PID control: strategy for effectively controlling one system characteristic with a related (but not identical) one