1. When Uncertainty Matters: The Selection of Rapid, Goal-Directed Movements
J. Trommershäuser, L. T. Maloney , M. S. Landy, Psychology and Neural Science, New York University
VSS 2003 TALK
Sarasota, FL
Movement under Risk
Experiment 1
Results:
MEGaMove Model: Effect of Motor Uncertainty
Mean movement end points with
stimulus configurations at different
orientations.
The MEGaMove* Model predicts that subjects will take account of their own motor uncertainty in planning movements.
Here we report the outcomes of
two experimental tests of the model in
simple environments where there are explicit gains and losses associated with the outcomes of movements.
Our results indicate that humans take both costs and their own movement uncertainty into account in planning movement.
: -500
: 100 points (2.5 ¢)
: -500
: 100 points (2.5 ¢)
y (mm) 1 2 3 4
R = 9 mm
100 points
-32 points
100 points S1 S2
100 points
3070 points
-400 points
y (mm)
y (mm)
-32 points
2 penalty conditions:
0 and -500 points
x (mm)
x (mm) S3 S4
 = 4.83 mm
 = 4.83 mm
5 “practiced movers”
1 session: 12 warm-up trials,
6x2x16 trials per session,
24 data points per condition
x (mm)
In this simple task, a motor
strategy is characterized by
the distribution of end points
around a mean end point.
Each mean end point corresponds
to an expected gain. This expected
gain depends only on the subject’s
motor uncertainty and the rewards
and penalties present in the
environment.
We can compute, for any subject,
an expected gain surface.
Kassi Price, 2001 US Nationals
Expected Gain Surface
exp., penalty = 0
The Experimental Task
exp., penalty = 500
model, penalty = 500 x
points
per trial
-10 -5 -0 5 10
The green target is hit: +100 points S5
Speeded movement:
Hit targets, with
Fingertip, avoid
penalties.
700 ms time limit. 90
x (mm)
100 60
100
y (mm) L 30
-30
The red target is hit: -500 points
<-60
Results:
-10 -5 5 10 15 20
Experiment 2
target: 100
penalty: -500
x (mm)
-500
 = 4.83 mm
Mean movement end points with
more complex configurations.
y (mm)
MEGaMove Model: The Expected Gain Surface
MEGaMove* Model for Movement under Risk S1 S2
penalty: 0
penalty: 100
penalty: 500
Key assumption:
The mover chooses the motor strategy that maximizes the expected gain  , taking into account motor uncertainty.
x (mm)
x (mm) 90
100
-500 60 30
2 penalty conditions:
0 and -500 points
y (mm)
y (mm)
Consequence:
The choice of motor strategy depends on
the reward structure of the environment
the mover's own motor variability.
-30
points per trial S3 S4
<-60 y x y x y x
5 “practiced movers”
1 session: 12 warm-up trials,
6x2x16 trials per session,
24 data points per condition
x (mm)
x (mm)
x, y: mean movement end point [mm]
exp., penalty = 0
exp., penalty = 500
y (mm)
Trommershäuser, Maloney, Landy (2003) JOSA A, in press.
Trommershäuser, Maloney, Landy (2003) Spatial Vision, 16,
Maloney, Trommershäuser, Landy (2003) VSS
model, penalty = 500 x
y [mm]
y [mm]
y [mm] S5
x (mm)
*: Maximum Expected Gain Model of Movement planning
x [mm]
x [mm]
x [mm]
Supported by NIH EY08266 and HFSP RG0109/1999-B, J.T. funded by the DFG (Emmy-Noether Programm)
 = 4.83 mm