Measuring the Allocation of Control
in a 6 Degree-of-Freedom Docking Experiment
Introducing the M-metric
Maurice R. Masliah and Paul Milgram
Ergonomics in Teleoperation and Control (ETC) Lab
Department of Mechanical and Industrial Engineering
University of Toronto, Ontario, Canada, M5S 3G8
http://etclab.mie.utoronto.ca
{moman, milgram}@etclab.mie.utoronto.ca
Motivation
(Images courtesy of Shumin Zhai and Ravin Balakrishnan)
Measures/Definitions of “Coordination”
•
•
•
•
•
•
time-on-target (“not very suitable” [Poulton ‘74])
accuracy  speed [Behbehani et al. ‘88]
spatial or temporal invariance [Morrison & Newell ‘98]
cross-correlations [Vereijken et al. ‘92, Zhai et al. ‘96]
integrality [Jacob et al. ‘94]
inefficiency [Zhai & Milgram ‘98]
Hypothetical Trajectories : 2 DOF
A
B
C
Goal Position
D
Goal Position
Start Position
Start Position
Goal Position
Goal Position
Start Position
Start Position
E
F
G
Goal Position
Goal Position
Goal Position
Start Position
Start Position
Start Position
Integrality vs. Inefficiency
Amount of Movement Over Time
10
Amount of Movement
• Integrality is a measure of
simultaneity
(in the time domain)
8
6
4
2
0
Time
• Inefficiency is a measure of
distance traversed
(in the space domain)
A
B
The M-metric
• Measures the allocation of control across DOFs
•
“Control” = any movement which reduces error
•
“Error” = the difference between the goal position and
the current position
• M-metric
= (control simultaneity) × (control efficiency)
Error Reduction
Definition of Control Simultaneity
DOF "X"
Area under
DOF curve = 1
DOF "Y"
IN
ERROR
Error Increase
Normalized
Error
Reduction
CHANGE
Time
Area of overlap,
intersection
between the DOFs.
Control Simultaneity Examples
control
simultaneity  0
control
simultaneity  1
Control Efficiency
a
Start
Position
c
Goal
Position
Efficiency =
b
c
a+b
Efficiency =the weighted average of the ratios
of the length of the “optimal” trajectory for
each DOF divided by the actual trajectory
M-metric: Primary Features
•
•
•
•
measures the allocation of control
= simultaneity  efficiency
values between 0 and 1
computed for any number of DOFs ( 2)
•
(also subsets of the total available DOFs)
• computed across DOFs encompassing
different measurement units (cm, degrees)
Experimental Design
8 subjects total (between subjects design)

2 input devices :
Spaceball
 216 docking trials per session

5 one hour sessions
= 8640 total trials
Finger-ball
Isometric vs. Isotonic
Resistance Continuum
Isometric
Elastic
Force sensing (input device does not move)
Isotonic
Position sensing (input device moves
without resistance)
Hypothesis for 6 DOF docking tasks
• Non-equal allocation of control across DOFs
• Novices
•
•
will allocate their control between translation and
rotation DOFs
will switch control back and forth
• As expertise develops:
•
•
will continue to allocate their control between
translation and rotation DOFs with improved control
will develop uniform allocation of control across all
6 DOFs
Results: Task Completion Times
40
35
Session Means
30
25
20
15
10
5
Task Completion Time (seconds)
40
Task Completion Time (seconds)
Docking Performance over Time
Isometric Rate Device
Docking Performance over Time
Isotonic Position Device
35
Session Means
30
25
20
15
10
5
0
0
0
200
400
600
Trial Number
800
1000
0
200
400
600
Trial Number
800
1000
Results: M-metric Scores
2-way Comparisons
within translation
0.6
between translation
within rotation
& rotation
Average M-metric Value
for all Two-Way Comparisons
0.5
0.3
0.2
0.1
YR
Z
Z
R
Y
XR
R
XR
Z
R
ZR
Y
ZR
X
ZR
Z
YR
Y
YR
X
YR
Z
XR
Y
XR
X
XR
YZ
XZ
0.0
XY
M-metric
0.4
Results: M-metric Scores
3-way Comparisons
within translation
between translation
within rotation
& rotation
-metric Value for all Three-Way Comparisons
Average M
0.6
0.4
0.3
0.2
0.1
R
Y
XY
R
Z
XZ
R
X
XZ
R
Y
XZ
R
Z
YZ
R
X
Y
ZR
Y
YZ
R
XR Z
XR
XR Y
XR
XR Z
YR
YR Z
XR
YR Y
XR
YR Z
YR
ZR Z
XR
ZR Y
XR
ZR Z
Y
R RZ
XR
YR
Z
R
X
XY
XY
Z
0.0
XY
M-metric
0.5
Results: M-metric Scores Over Time
0.6
Isotonic Position Y-Z-RY
Isometric Rate Y-Z-RY
Isotonic Position RX-RY-RZ
Isometric Rate RX-RY-RZ
0.5
within rotation
M-metric
0.4
0.3
Isotonic
0.2
between translation
& rotation
Isometric
0.1
0
1
2
3
Session (Time)
4
5
M-metric Summary
•
•
•
•
new metric for measuring allocation of control
optimal trajectory must be identified/defined
tested in a longitudinal 6 DOF docking task
subjects allocated allocated unequally control across
all 6 dofs
• subjects controlled rotation & translation separately
• separation of control for the isometric device greater
than for the isotonic device
Future Work
• In docking, any trajectory which accomplishes the
docking goal is acceptable.
• Next experiment : test M-metric on a dynamic 6
DOF tracking task.
• Expand M-metric definition to include tracking,
tracing, and target acquisition tasks.
Taxonomy of Manual Control Tasks
Time Domain
Externally Paced
Self-Paced
(Time Matching) (Time Minimizing)
Single
Location
Distributed
Location
Space Domain
Target Acquisition Target Docking


ball catching
instrument
playing at a
tempo
Dynamic
Tracking


target
gunnery
driving at a
speed limit


menu
selection
peg-in-hole
tasks
Tracing


drawing
marking
menus
[Masliah ‘99]
Conclusion:
In a multi-degree of freedom
continuous movement task:
• the M-metric provides a measure of how
control is allocated across available DOFs
• it is possible to have two movements with
equal performance scores, but with very
different time-space trajectories
Acknowledgements
• Institute of Robotics and Intelligent Systems
(IRIS)
• Natural Sciences and Engineering Research
Council (NSERC)
• Shumin Zhai, IBM Almaden Research
• Ravin Balakrishnan, University of Toronto