Uncertainty in Catching Balls

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Uncertainty in Catching Balls

• Chris Cramer

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How do you catch a fly ball?

• Catching involves many issues with very little
  time. There are many areas where uncertainty can
  effect behavior
• The key is to employ a Control Strategy, i.e. a
  method for using optical information to control
  the subjects movement, but which one?

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A Control Strategy requires information from
optical sources

• Before an explanation of the sources that are
  used in each model, lets review some common terms

Most experimental evidence derives from
experiments where a ball is moving toward an
Interception Point (IP).
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Tau
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Optical variables specify where the ball will
cross

• (?)Tau is the inverse of the relative rate of
  dilation of a projected image
• ie. This is the size an object appears on your
  eye as it approaches you
• The crossing distance can be geometrically
  determined based on the inverse of Tau and the
  size of the ball

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Find the right location

• In order to move the hand to the correct
  location, there are a few things which the
  subject must know.

Passing distance - where the ball is going to
pass, often referred to as the crossing distance
(XC)
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Optical variables will also specify when the ball
will cross

• The Time To Pass (TTP) can be determined
• Y is the optical angle at the eye subtended by
  the current location of the ball and the
  interception point (IP) and ? is the balls
  angular subtense

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Binocular correlates

• So far I have shown the information available to
  a monocular view.
• Actually binocular viewing provides additional
  information

The retinal disparity relative to a fixed
reference point (F) combined with the distance
between the eyes (I) provides additional
information (binocular disparity)
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Uncertainty

• The various sources of optical information
  produce both uncertainty in location, and
  uncertainty of time with respect to catching a
  moving target.
• This means choosing an optimal Control Strategy
  will be difficult

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The 2 most generally accepted Control Strategies

• Predictive
• Estimate TTP and XC on the visual information
  available
• Make a ballistic movement of the hand to the
  future location of the ball
• Some versions allow for continuous updating of
  TTP and XC

• Prospective
• No prediction, and no preprogrammed ballistic
  hand movement.
• A dynamic relationship between the hand and an
  optical variable is established which leads to
  interception if the relationship is maintained

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Two Approaches

• Predictive - you see an object and predict when
  and where it is going to end up
• Prospective - you match a variable in the
  environment and maintain it until the object
  reaches the interception point

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Predictive
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Prospective
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Theoretical support for each approach

• First, a brief review of pros and cons of each
  strategy
• Then we explore the support for one of these
  approaches, the Prospective control strategy

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Pro

• Predictive

• Prospective

Pepers approach angle effects
Information on passing distance, time to pass,
and direction of motion in depth are all available
Montagnes movement reversals
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Con

• Predictive

• Prospective

Fails to explain movement reversals or approach
angle effects
Gray reports that Peper and Montagne have been
constrained to one dimension
Doesnt explain judgements of catchableness Does
nt explain compensation for perceptual motor
delay
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Re-evaluation of previous findings

• The strongest arguments for Prospective control
  come from arguments against Predictive control.
• Prospective control claims there are biases in
• 1) Perception of passing distance
• 2) Perception of direction of motion in depth
• and these explain why Predictive control cannot
  be correct

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The history of the Prospective Strategy

• First Paper
• Peper Bootsma
• Laid the ground work for the Prospective
  Strategy approach
• Second Paper
• Montagne
• Developed further support by demonstrating
  Movement Reversals

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Paper 1

• Peper measured both judgement of passing distance
  (so called catchability) and catching

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Optical information available

• Peper was interested in which optical variables
  were involved in catching.
• Using only optical information it must be
  possible to determine where the ball will cross
  the frontoparallel plane

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Derivation of formulas

• If you assume velocity is constant, then tc is
  equal to the ? margin
• ? margin is specified by ?, the inverse of the
  relative rate of dilation of the projected image

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• .

The crossing point is determined by size of the
ball (R) and the the ratio of the velocity of the
sideward displacement of the center of expansion
? and the rate of expansion of the object image r
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Pepers swinging balls

• Methods
• No leaning
• Look straight ahead
• Shutter glasses provide sight for only 700 ms
• Monocular

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So what?

• Peper shows mathematically optical variable that
  could be involved.
• The hypothesis that subjects would judge critical
  passing distance based on ball size alone, was
  supported.

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Nice finding . . . not necessarily groundbreaking

• The follow up to this experiment changed the
  approach angle, while holding the ball size
  constant
• The hypothesis was that the judgments should be
  the same since the ball does eventually arrive at
  the same location

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NOT SO FAST!

• The approach angle had a significant effect on
  the judged distance
• More experiments were conducted to further test
  this surprising finding

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Follow up experiment
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Results

• They found that people were affected by whether a
  ball was approaching on an inward vs. outward
  angle to the target.

hand
subject
Inward solid line Outward dotted line
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Passing distance and estimation of TTC

• The difference in passing distance estimation
  could be attributed to an error in judging TTC.
• If the approach angle lead to an underestimation
  of time to contact then that would explain the
  passing distance differences.

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Time to Contact not underestimated

• Notice the trend to greater error as the angle of
  approach increases

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Pepers conclusion

• Perhaps subjects do not first estimate passing
  distance and then make a programmed response.
• They might find an optical variable in the
  environment and then move based on it.

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A new approach

• Peper noticed that subjects moved their hand at a
  rate which would have it reach the target
  location 450 ms before the ball
• This movement rate matched the lateral movement
  of the ball

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Development of Prospective Models

• Peper later formally developed the Required
  Velocity Model (RVM)
• This RVM served as the basis for an even more
  advanced models.
• Bullock developed Relative and Required Vector
  Integration to Endpoint model (RRVITE) as an
  extension to the Vector Integration to Endpoint
  model.

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Paper 2

• Montagne
• was interested in the findings of Bootsma and
  Peper and took the new Model a step further

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Experiment
The subjects were constrained along a track and
told to intercept the ball
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Predictions

• If subjects used the Predictive Strategy then
  they would estimate where the ball was going to
  cross and simply go directly there
• According to the Prospective Strategy the
  subjects would find a variable in the environment
  and match their movements to it

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Movement Reversals

• Montagne found subjects would move their hand
  past the interception point and then back, (hence
  movement reversal)

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L/R reversal
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The -4 is outward The 4 is inward Since the
ball arrives at the same point, ideally
the path would be a straight line
The position of the hand over time for the
different Approach angles further supports the
prospective approach
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Montagnes Conclusions

• The results suggest that a Predictive Strategy
  can not be correct

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Conclusions

• Which is the optimal Control Strategy to use
  has been examined, and the information from these
  two papers would suggest that the Predictive
  Strategy is not a good model.
• The proposed Prospective Strategy has flaws which
  I look to explore in my research

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THE END

• fin