IEEE Robotics & Automation Magazine - September 2014 - 120

Speed (°/s)

Resistive
Torque = 0 Nm

Resistive
Torque = 0.5 Nm

Resistive
Torque = 1 Nm

Resistive
Torque = 1.5 Nm

Resistive
Torque = 2 Nm

20

20

20

20

20

15

15

15

15

15

10

10

10

10

10

5

5

5

5

5

0

0

1

2
3
Time (s)

4

0

0

1

2
3
Time (s)

4

0

0

1
2
3
Time (s)

4

0

0

1
2
3
Time (s)

4

0

0

1

2
3
Time (s)

4

(a)

Speed (°/s)

Resistive
Torque = 0 Nm

Resistive
Torque = 0.5 Nm

Resistive
Torque = 1 Nm

Resistive
Torque = 1.5 Nm

Resistive
Torque = 2 Nm

20

20

20

20

20

15

15

15

15

15

10

10

10

10

10

5

5

5

5

5

0

0

1

2
3
Time (s)

4

0

0

1

2
3
Time (s)

4

0

0

1
2
3
Time (s)

4

0

0

1
2
3
Time (s)

4

0

0

1

2
3
Time (s)

4

(b)
Figure 4. The representative speed profiles achieved by subject 5 under all torque and speed condition combinations. The last 20 of
40 trials are plotted in gray, with the final trial in black. The horizontal lines correspond to the target speed levels, and the vertical
lines mark the range (1-4 s) for which the measure CVspeed was calculated. (a) Target speed = 5°/s. (b) Target speed = 10°/s.

torque levels led to a weak and insignificant decreasing speed
trend. It can be observed that variability generally decreases as
the resistive torque level increases. The variability is lower for
the target speed level of 5°/s, but this is simply due to the effect
of scaling. A fair comparison of the variability of speed for different levels of mean speed necessitates the use of the CVspeed
measure that normalizes the SD of speed by mean speed.
Figure 4 shows the raw speed profile data from a representative subject (Subject 5)
from all ten speed and
Our experimental results
torque level condition
combinations. Only proindicate potential novel
files in the last 20 of 40
trials are plotted in gray
methods of human skill
and the final trial in black.
The horizontal lines coraugmentation in delicate
respond to the target
speed levels, and the vertior critical tasks such as
cal lines mark the range
(1-4 s) for which the
surgery.
measure CVspeed was
calculated.
The results of the
ANOVA indicate a significant main effect of speed
6F ^1, 1390h = 465.4, p < 0.05@ and a significant main effect
of torque 6F ^ 4, 1390h = 42.53, p < 0.05@ on CVspeed . The
interaction effect of torque by speed is also significant
6F ^4, 1390h = 5.57, p < 0.05@ . The results of the post hoc
Tukey-Kramer test for pairwise comparison of torque are
120

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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september 2014

summarized in the bar plot in Figure 5. The error bars indicate standard errors. This plot indicates that CVspeed is significantly higher for the no resistive torque condition in
comparison with all other torque levels ^ p < 0.05h . Although
there is initially a decreasing trend for CVspeed with increasing
resistive torque levels, after 1.5 Nm the trend reverses direction and CVspeed starts to increase. CVspeed for Tr = 2 Nm is
significantly higher than it is for Tr = 1.5 Nm.
Figure 6 summarizes the results of pairwise comparison
tests for interaction effects of resistive torque level by speed on
speed variability in an interaction plot format. Although the
CVspeed versus torque level curves under two different target
speed level conditions mostly follow a parallel trend, the overall
interaction effect is significant because of the nonparallel subtrends, such as those observed between Tr = 1 Nm and
Tr = 1.5 Nm.
Discussion
The significant main effect of speed on movement speed
variability is in agreement with findings using movement
intermittency [2], [20] or timing [19] as the measure of variability in the literature. This possibly indicates a single mechanism of variability behind all, as we have proposed in the
"Variability in Slow Movements" section.
The nonmonotonic relationship between speed variability
and resistive torques observed in Figures 5 and 6 is a novel
finding. These experimental results indicate that increased
muscle force variability in low force levels can indeed explain
increased variability or intermittency in slow movements.
Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2014
