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
(Images courtesy of Shumin Zhai and Ravin Balakrishnan) 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
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
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)
Definition of Control Simultaneity Area of overlap, intersection between the DOFs. Normalized Error Reduction Area under DOF curve = 1 CHANGE IN ERROR
Control Simultaneity Examples
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
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 : 216 docking trials per session 5 one hour sessions Spaceball Finger-ball = 8640 total trials
Isometric vs. Isotonic Isotonic Isometric Resistance Continuum Elastic Position sensing - (input device moves without resistance) Force sensing - (input device does not move)
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
Results: M-metric Scores 2-way Comparisons within translation between translation & rotation within rotation
Results: M-metric Scores 3-way Comparisons within translation between translation & rotation within rotation
Results: M-metric Scores Over Time Isotonic within rotation Isometric between translation & rotation
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 [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