Manual Control

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Manual Control

• chapter 10

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Intro to calculus

• Derivatives change (subtraction)
• 0-order position
• 1st-order speed (change in position)
• 1st derivative of position
• 2nd-order acceleration (change in speed)
• 1st derivative of speed
• 2nd derivative of position

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Derivatives

• Derivative change in something per unit time

change in something
unit of time
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Position
position p(t) p(1) 20 p(2) 28 p(3) 32,
etc
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Speed
speed s(t)
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Speed
speed s(t)
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Acceleration
acceleration a(t)
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Acceleration
acceleration a(t)
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Integration

• Integration addition (summation)
• So, speed at time 4 (constant acceleration
  example)
• integrate acceleration up to time 4

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Manual Control

• Previously, we looked at discrete responses
• stimulus perception decision selection
  execution
• open loop (environmental feedback)
• discrete movements
• focus on response selection rather than execution
• Manual Control focuses on response execution
• discrete open- and closed-loop
• continuous closed-loop responses

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Open- Closed-loop systems

• Closed Loop
• Feedback based on directly measuring errors
• That is, the action taken is dependent on the
  output of the system.
• Output produces some error
• Error is feedback to the system
• next decision then takes that error into account

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Open- Closed-loop systems

• Closed Loop
• Heat-seeking missile
• Missile constantly measures source of heat.
• Source of heat relative to heading changes,
  producing error.
• Missile uses error to correct its course

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Open- Closed-loop systems

• Open Loop
• Output of system does not affect subsequent
  actions
• There is no feedback ballistic in nature
• Canon example
• Shell is fired, but it can not correct its
  course
• Trajectory is determine by initial inputs only
• elevation, amount of charge used, etc.

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Discrete Movement Time

• Fitts Law
• Speed/accuracy trade-off for making ballistic
  (open-loop) movements
• Only describes the latency of the movement
• Trade-off is a function of
• distance
• target sizes
• Mouse movement
• target size size of icon
• distance distance of mouse movement

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Fitts Law

• MT movement time (latency) a b are irrelevant
  constants
• A distance
• W target width
• So, if target size is held constant, difficulty
  increases as distance increases.
• Likewise, if distance is held constant,
  difficulty decreases as width increases.

Index of difficulty
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Fitts Law

• Why are menu bars that are placed at the top of
  the screen accessed more quickly than menu bars
  at the tops of windows?

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Fitts Law

• Because the menu bar is bounded at the top of the
  screen, it has infinite height.
• Users can toss the cursor to the top while being
  confident that the pointer will not overshoot the
  menu bar.

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Fitts Law

• Since it is a speed-accuracy trade-off, if speed
  and target width are held constant and distance
  increases, then accuracy must decrease.
• Fitts Law only describes the latency to initiate
  a movement, rather than speed of the movement.

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Models of Discrete Movement

• Movements are rarely completely ballistic in
  nature
• even saccades can be corrected in mid-flight
• However, the corrections take some time, and are
  not continuous.
• If the movement is long enough, several discrete
  corrections might occur.
• If the movement is too fast, there might not be
  enough time to make a correction.
• Makes movements appear open-loop

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W
A
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Closed-loop corrections

• How do we know if a change that occurs during a
  movement is a closed-loop correction?
• If the calculation for the correction is made
  before the movement is initialized, the frame of
  reference for the movement will be off

E
E
E
S
S
S
Error
Closed-Loop, in-flight correction
open-Loop, pre-flight correction
Correct
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Motor Programs Schema

• Feedback for well-learned skills
• Feedback is not visual, but proprioceptive or
  vestibular (motor senses)
• tying shoe laces
• balancing while walking
• The pattern of desired muscle movements is stored
  in LTM and occur as an open-loop motor program.
• Motor programs are relatively automatic and
  therefore require little attention
• Riding a bicycle

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Motor Programs

• Single Response Selection
• Each program is considered a single reponse
• i.e., although the program consists of many
  intricate muscle movements, only the program
  itself is considered a single action
• Each decision is considered a single action
• i.e. Shift from 2nd to 3rd gear consists of 3
  movements
• forward gt right gt forward

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Motor Programs

• Single Response Selection
• Because each motor program is considered a single
  response, the latency for launching the program
  is unaffected by program complexity.
• However, the complexity of making the decision
  does affect latency.

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Motor Schemas

• Schemas
• Motor program implies a very consistent series of
  muscle movements.
• What appears to be consistent is the result of
  the movements, rather than the actual movements
  themselves.
• Example
• signing your signature on a paper placed on a
  desk vs. a clipboard on a wall.
• Both produce similar outcomes, but the patterns
  of muscle movements are quite different

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Motor Schemas

• Schemas
• This suggests that what is being recalled from
  LTM is not an exact set of muscle commands, but a
  generic process in how to produce correct result.
• i.e. what is stored in LTM is how the ballistic
  problem can be solved.
• analogous to the equations for coming up with a
  firing solution.
• given these different variables, what
  adjustments do I need to make to come up with the
  correct result?

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The Tracking Loop
o(t)
i(t)
e(t)
f(t)
u(t)
Display
Operator
Control
System

• Command input i(t) task demands, curve of
  road, item that needs to be tracked
• Display e(t) display of information,
  perception
• Human Operator f(t) decision maker,
  controller
• Control u(t) joystick, steering wheel
• Systrem o(t) output from machine, steering
  rack movements, elevators flaps.

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Transfer Functions

• Transfer Functions
• Represent the mathematical relationship between
  input and output of the system.
• In the case of humans, we care about u(t), or the
  position of the control.
• That is, the result of the muscle output
  (signature), rather than the muscle outputs
  themselves.
• Control Order
• The number of integrations performed by the
  transfer function.

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Two Parameters

• Gain
• degree of amplification (multiplication)
• Ratio of input to output
• Pure Gain
• High-gain sports car steering
• Low-gain moving van

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Two Parameters

• Lag
• Pure Time Delay
• Output is delayed, but otherwise unaltered
• Example - simulators and video games have an
  inherent time delay(computations, refresh rate)

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Two Parameters

• Lag
• Exponential Lag
• Lag is not pure delay
• Result appears to home in on final result
• Early power-steering systems

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Order and controls

• Zero Order (Position controller)
• Example computer mouse or graphics tablet
• Types
• Pure gain - (mouse speed in control panel)
• Pure time delay - (refresh rate and processing
  time)
• Exponential lag
• Good For
• Systems designed to control position precisely
• Controllers w/o a natural zero-point

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Order and controls

• 1st Order (Velocity controller)
• Single integration over time
• Example car steering wheel
• Angle of wheel affects the speed at which the
  heading changes.
• Angle of wheel determines the change in heading,
  not the heading itself.
• If the wheel is cocked 5 degrees (assume wheels
  are cocked 5 degrees)
• Then the heading will change 5 degrees with each
  passing unit of time
• So, heading constantly changing, even though
  control remains in a constant position.

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Order and controls

• Good For
• Systems designed to control velocity (angular, in
  the case of steering a car)
• Controllers w/ a natural zero-point
• joysticks, steering wheels, etc.

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Order and controls

• 2nd Order (Acceleration controller)
• Example car brakes or gas pedal
• Input displacement is equal to acceleration
• A brake pedal press 25 will slow the car down
  less than when it is pressed 75 of its travel.
• Because of inherent inertia in the system,
  tracking tends to be unstable, often producing
  oscillations.
• Not a big deal in the case of braking, because
  the braking point is constant and not a moving
  target.

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Human limits in tracking

• Processing time
• When performing tracking, there is always some
  time delay between when an error occurs and a
  response is made.
• Lags are shortest for 0-th and 1st-order systems
  (150-300 ms), and longer for 2nd-order (400-500).
• These delays reflect the complexity of the
  error-correction decision.
• Delays can lead to problems of instability,
  especially oscillatory behavior.

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Lag and Oscillations

• How overcorrecting oversteer leads to fishtailing

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• Car begins to oversteer
• Driver countersteers to the left
• Car straightens, but driver still counter
  steering
• Car fishtails in opposite direction
• Driver corrects oversteer by countersteering to
  the right.
• rinse, repeat

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Human limits in tracking

• Bandwidth
• For unpredictable signals, the upper limit for
  human tracking is 1-2 Hz (up to 2 corrective
  decisions per second).
• If signals are predictable, number of corrections
  increases to 2-3 Hz
• Upper-limit of Hz limited by the speed at which
  responses can be generated.
• e.g. simple RTs (go no-go) less than 100 msec are
  considered an error
• Choice RTs take longer than simple RTs

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Human limits in tracking

• Prediction and anticipation
• When there is a lag in system output, people must
  anticipate the resulting error.
• Example steering a ship (or a really overloaded
  shopping cart at Home Depot).
• Inertia means that there is a lag before the
  inputs lead to a course correction.

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Human limits in tracking

• Prediction and anticipation
• Inertia means that there is a lag before the
  inputs lead to a course correction.
• So, the operator must make inputs now based on
  future errors.
• Since predictability goes down as lag increases,
  errors increase.
• In addition, humans are poor at perceiving
  changes in velocity (acceleration) and
  acceleration (degree of acceleration).

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Effects of Tracking Displays

• Preview
• Goal is to eliminate effects of lags or
  higher-order systems
• Preview displays help to improve input
  predictability
• Example on a clear day, the driver can see the
  road winding ahead and has several seconds of
  preview
• On a foggy or rainy day, that preview is reduced
• The greater the preview (of future demands) the
  more accurate the tracking.

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Effects of Tracking Displays

• Output Prediction and Quickening
• Predictive displays
• Computer estimates future position and adds a
  symbology to the display representing this future
  position (prediction span)
• Quickened displays
• Same as predictive, but w/o current position

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Future flight path based on current inputs and
system status