1. 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
{moman,

2. (Images courtesy of Shumin Zhai and Ravin Balakrishnan)
Motivation
(Images courtesy of Shumin Zhai and Ravin Balakrishnan)

3. 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]

4. Hypothetical Trajectories : 2 DOF

5. Integrality vs. Inefficiency
Integrality is a measure of simultaneity (in the time domain)
Inefficiency is a measure of distance traversed (in the space domain) B A

6. The M-metric Measures the allocation of control across DOFs M-metric
“Control” = any movement which reduces error
“Error” = the difference between the goal position and the current position
M-metric
= (control simultaneity) × (control efficiency)

7. Definition of Control Simultaneity
Area of overlap, intersection between the DOFs.
Normalized Error Reduction
Area under DOF curve = 1
CHANGE IN ERROR

8. Control Simultaneity Examples

9. Control Efficiency a b c c a + b
Start
Position
Goal b
Position c c
Efficiency =
a + b
Efficiency =the weighted average of the ratios of the length of the “optimal” trajectory for each DOF divided by the actual trajectory

10. 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)

11. Experimental Design 8 subjects total (between subjects design)
 input devices :
 216 docking trials per session
 one hour sessions
Spaceball
Finger-ball
= total trials

12. Isometric vs. Isotonic Isotonic Isometric Resistance Continuum Elastic
Position sensing - (input device moves without resistance)
Force sensing (input device does not move)

14. 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

15. Results: Task Completion Times

16. Results: M-metric Scores 2-way Comparisons
within translation
between translation & rotation
within rotation

17. Results: M-metric Scores 3-way Comparisons
within translation
between translation & rotation
within rotation

18. Results: M-metric Scores Over Time
Isotonic
within rotation
Isometric
between translation & rotation

19. 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

20. 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.

21. Taxonomy of Manual Control Tasks
[Masliah ‘99]

22. 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

23. 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