Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 22–27___________________________________________________________________________________________________________A Human Reaching Movement Model for Myoelectric Prosthesis Control
Go Nakamura *, Taro Shibanoki †, Yuichiro Honda*, Akito Masuda ‡, Futoshi Mizobe §, Takaaki Chin* and Toshio Tsuji ***Robot Rehabilitation Center in The Hyogo institute of Assistive Technology, †Ibaraki University,‡
Kinki Gishi Corporation, §Hyogo Rehabilitation Center Hospital, **Hiroshima University
E-mail: g_nakamura@assistech.hwc.or.jp

Abstract
This paper proposes a reaching movement model for the generation of desired trajectories within a myoelectric
prosthesis training system. First, an experiment was performed to observe reaching movements with a non-impaired
subject and a myoelectric prosthesis user. Reaching movements made by the prosthesis user were then adopted toconstruct a model based on a logistic function. The proposed model can be used to generate three trajectory types
with a bell-shaped speed profile with the adjustment of only a few parameters.
Keywords: Myoelectric prostheses, Motion planning, Logistic functionof an evaluation method and such a system requires theconstruction of a model capable of generating humanreaching movement trajectories. A clinically applicabletraining system with such a model requires thefollowing features: (1) high adaptability for generationof optimized and other trajectories (as myoelectric
prosthesis users do not have the reaching movement of
non-impaired people due to wrist-related limitations);(2) adjustability of hand velocity (movement time) in
consideration of individual differences and variations in
trainees’ operational ability; (3) easy and intuitive
trajectory adjustment for use in clinically applicabletraining; and (4) real-time trajectory generation for use
in training. A number of studies on human reaching
movement have been conducted [2] – [4] to clarify thehuman motor planning mechanism. By way of example,

1. Introduction
The prescription of myoelectric prostheses to upperlimb amputees supports everyday living and opens up
new possibilities for rehabilitation. However, months oftraining is needed until such prescription can be made.
Before being able to use a myoelectric prosthesis,
patients must learn the skills necessary to perform tasks
with natural posture (e.g., the direction of grasping
approach and the manner of forearm usage) in addition
to smooth hand opening/closing [1]. However, there iscurrently no quantitative evaluation method or training
system for prosthesis control with natural posture.
Against such a background, the authors sought tosupport myoelectric prosthesis prescription by
developing a training system (Fig. 1). The establishment

Copyright © 2017, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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the minimum-jerk model [2], the minimum torquechange model [3] and the minimum-variance model [4]have all been proposed and found to be capable ofgenerating human trajectories accurately. However, thetrajectories in these studies were determined via
optimization calculation; it is difficult to generate
trajectories in real time. For control of machinery suchas manipulators and vehicles, real-time trajectory
generation models have been proposed [5] – [7]. As an
example, Tsuji et al. proposed a real-time trajectory
generation model based on an artificial potential field
and a time base generator (TBG) involving a scalarsignal with a controllable finite duration and a bellshaped velocity profile. However, these models areaccompanied by problems such as the difficulty ofadjusting the many related parameters, which are
determined by trial and error.
This paper proposes a human reaching movement
model for myoelectric prosthesis control training. The
model has high adaptability and can be used to generate
three hand trajectory types (straight-line paths, circulararc paths and S-shaped paths) with a bell-shaped speed
profile in near-real time with the adjustment of only afew parameters.

Fig. 1. Concept of the training system for myoelectric
prosthesis control using the prosthetic arm trajectory model

was repeated five times. A 3D position sensor (Isotrak
II, Polhemus Corp.) was attached to the right cubital
fossa
of each subject, and their elbow positions(accuracy: ± 2.4 mm) andpostures (Eulerian angle)(accuracy: ± 0.75 ) were measured at 60 [Hz]. The
hand trajectories and hand velocity were evaluated by
calculating the hand position
from themeasured elbow position and posture. The hand position
is defined as follows:(1)

2. Human Reaching Movement for Myoelectric
Prostheses

Here, is the forearm length as determined in advance.
However, the two subjects had different degrees of
freedom in the wrist because the wrist joint of a
myoelectric prosthesis is fixed, making evaluation on alevel playing field difficult. Accordingly, the location of
the wrist joint was defined as the hand position. Hand
velocity was estimated using a second order
Butterworth low-pass filter (cut-off frequency: 10 [Hz]),and was then calculated using a low-pass differential
filter. As the study focused on reaching for and picking
up a cup, a two-dimensional trajectory model wasconstructed as a first step.

2.1. Experimental conditions
A monitoring experiment was conducted with a nonimpaired subject (25 years old, male) and an
experienced myoelectric prosthesis user (49 years old,male; MyoBock hand) toward the development of areaching movement model for myoelectric prosthesis
control. The prosthesis user was a right upper-limb
amputee (amputation site: 14 cm below the elbow), andhad used a myoelectric prosthesis for 14 years. His
average score for the Box and Block Test [8] wasapproximately 40 blocks, which exceeds the average of
normal-level users. His performance was more efficientthan that of most myoelectric prosthesis users.
The subjects were asked to sit on a chair and pick up acup from one of nine locations on a table, lift it to theirmouth and return it to its original location. Each task

2.2. Results
Figures 2 shows scenes of reaching tasks for the nonimpaired subject and the myoelectric prosthesis user,
respectively. Figure 3 shows trajectories observed inreaching for the cup, with origin coordinates based on
the initial hand position. The trajectories represent the
average of five trials for each subject. The dashed lines
represent the standard deviation for five sessions. The
figure shows linear trajectories for both subjects. The

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 22–27___________________________________________________________________________________________________________

trajectories of the skilled myoelectric prosthesis user
exhibit characteristics similar to those of the nonimpaired subject, but several distinctive differencessuch as different end points are also observed. The
myoelectric prosthesis user also approached the cup
placed in the nearest row (lower right, bottom and lowerleft) after pulling back his elbow, and the trajectories
show downward movement. This can be attributed to
the fixed wrist joint of the myoelectric prosthesis, whichmeant that the end points and trajectories for the cup in
the nearest row were affected by wrist flexion/extension
limitations. The two subjects exhibited different wrist
postures at the time of grasping (Fig. 2).
Figure 4 shows hand velocity results based on averagesof five trials for each subject. Velocity for the
myoelectric prosthesis user was lower than that for the
non-impaired subject, but both exhibit bell-shaped
velocity profiles. This is because the myoelectric
prosthesis user was able to approach the target while
opening his hand within the series of motions, andperformed the tasks without reducing hand velocity.
Figure 2 shows that the myoelectric prosthesis user
opened the hand at the start of the approach. These
results indicate that the myoelectric prosthesis user
performed the tasks with smooth control and handvelocity similar to that of the non-impaired subject.
The hand position and posture data are characterized
by a monotonously increasing/decreasing function or a
combination thereof, and a similar tendency for all data
was observed. The next step in the study was toconstruct a human reaching movement model using alogistic function.

Fig. 2. Subjects approaching the cup with upper-rightplacement

Fig. 3. Measured hand trajectories for the non-impaired
subject and myoelectric prosthesis user

3. Trajectory Generation Model for Myoelectric
Prostheses
The proposed model is designed to highlight theappropriate trajectory to a target in a training system. As
this study focused on accurately reproducing measured
hand trajectory and velocity, the model was not basedon the human movement mechanism.
3.1. Logistic function
The study involved the proposal of a human reaching
movement model using a logistic function.

Fig. 4. Measured hand velocities for the non-impaired
subject and myoelectric prosthesis user

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 22–27___________________________________________________________________________________________________________

(2)
(3)
Here,
and

is the end point.

,andbehavior.

is the start point,
is defined as.

are parameters determining function

Fig. 5. Straight-line path dependence on the parametersand3.2. Spatial trajectory model
The study involved the proposal of a human reaching
movement model using a logistic function.
andare defined as(4)(5)

Fig. 6. Circular-arc path dependence on the parameters

To derive an equation for trajectory on the XY plane,for (4) and (5) is eliminated. The
the parameter
trajectory on the XY plane can be represented as(6).
Here, is defined as
To prevent the denominator from being 0, (6) can betransformed by multiplying the numerator anddenominator by:

Fig. 7. S-shaped path dependence on the parameters

For S-shaped paths, trajectories are generated underand. These paths
the conditions of
can be controlled by adjusting only the ratio of
maintained. Figure 7 shows time histories
with
. The
of spatial trajectory based on the parameterscurvature gradually increases the farther the ratio ofis from 1.0.

(7)Here, the condition is given by.
The proposed model can be used to generate three
hand trajectory types (straight-line paths, circular-arc
paths and S-shaped paths) featuring a bell-shaped speed
profile with the adjustment of only the two ratios of
and
.
and
Straight line paths can be generated by setting
under the conditions ofand.
Figure 5 shows time histories of spatial trajectory basedand .
on the parameters
For circular arc paths, trajectories are generated underand. These paths
the conditions of
can be controlled by adjusting only the ratio of
maintained. Figure 6 shows timewithhistories of spatial trajectory based on the parameters. The curvature gradually increases the farther theis from 1.0.
ratio of3.3. Bell-shaped velocity profiles
The proposed model can be used to generate bellshaped velocity profiles. Single-peaked (unimodal)
profiles, double-peaked (bimodal) profiles and othertypes can be expressed only with adjustment of.
andUnimodal profiles can be generated under the. These profiles can be controlled
conditions ofwithby adjusting only the ratio of
maintained. Figure 8 shows time histories of spatial. Kurtosis
trajectory based on the parametersisgradually increases the farther the ratio offrom 1.0.

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 22–27___________________________________________________________________________________________________________

4. Simulation Experiment
A simulation experiment was conducted to evaluate
the proposed model’s propensity for hand trajectoryandwere set as the times at which thegeneration.
andwere nearest to
observation values of, respectively. The parameter
was theandandwere given
measured movement time, andusing (9). was set as = 0.01.
Figures 10 and 11 show reaching hand trajectories andhand velocity for each subject, respectively. Solid lines
represent hand velocity based on the averages of five
trials for observation and generation using the proposedmodel, and dashed lines represent the standard deviation
for five sessions. Although approximation errors areseen with the reaching hand trajectories and handvelocity of the myoelectric prosthesis user for the cup
placed in the nearest row, the simulated hand
trajectories and hand velocity both correspond to theobservations, and the simulated and observed lines arealmost identical. Approximation error for the nearest
row arises because that the observed time-series data are
a combination of an increasing/decreasing function, andthe proposed model based on a monotonously
increasing/decreasing function was not capable ofaccurate replication. With this in mind, the authors plan
to introduce methods for appropriate combination withthe proposed model. From these results, it can beconcluded that the proposed model is capable ofgenerating hand trajectories and hand velocity data bothfor non-impaired subjects and for myoelectric prosthesis
users.

Fig. 8. Unimodal profile dependence on the parameters

Fig. 9. Bimodal profile dependence on the parameters

Bimodal profiles can be generated under the conditions. These profiles can be controlled byof. Figure 9 shows time
adjusting only the ratio of
histories of spatial trajectory based on the parameters. The inter-peak distance gradually increases theis from 1.0.
farther the ratio of
3.4. Adjustment of movement time
This subsection outlines how movement time for the
proposed model is adjusted. For the logistic function, it
is difficult to specify the convergence time because it is
not necessarily a finite period. To address this problem,
was set. Thea small arbitrary positive constant, and the logistic
movement time is defined asatcan be expressed
functionsas

5. Conclusion
This paper proposes a human reaching model for
myoelectric prosthesis control. In the study, the authors
performed an experiment to observe reaching
movements with a non-impaired subject and amyoelectric
prosthesis
user.
The
distinctive
characteristics of reaching movements made by theprosthesis user were identified and adopted to support
the construction of a model. A simulation experiment
was also performed, with results indicating that the
proposed model was capable of successfully generating
hand trajectories for both subjects.
In future work, the authors plan to introduce methods
for combination with the proposed model and expand it
model will also be applied for use with a training
system.

(8)
and, whichSolving (8) gives the parametersspecify the movement time. The issue of their mutual
dependence is solved by fixing as the time at which
the function is . can then be easily estimated frommeasurement values. In addition, a rational value for=even when it iscan be obtained because
difficult to obtain a measurement value. Accordingly,
is calculated as
is fixed in advance and(9)Here, the condition is given by
and.
allows setting of the desired movement
Specifying
time.

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 22–27___________________________________________________________________________________________________________

Generated hand trajectories by the proposed model
Mesured hand trajectories−60 −40 −20

0.91)

(2.31

0.85)

60
60
(1.11 0.52)(1.54 0.11)
40
40
20
20
0 x [cm]
0 x [cm]
0 −20 20 −60 −40 −20 0 −20 20 −60 −40 −20(a): A prosthesis user

0.07)
0.05)

−60 −40 −20
(0.68
(0.62

60
40
20
0 x [cm]
0 −20 20

0.08)
0.09)

−60 −40 −20(0.95 0.07)
60(0.96 0.06)
40
20
0 x [cm]
0 −20 20 −60 −40 −20

60
40
20
0 x [cm]
0 −20 20

(0.89

0.15)

60
(0.89 0.13)4020
0 x [cm]
0 −20 20 −60 −40 −20

y [cm]y [cm]

60(0.97 0.05)(0.98 0.04)
4020
0 x [cm]
0 −20 20 −60 −40 −20

y [cm]

60
40
20
0 x [cm]
020−20

y [cm]

(0.96
(0.97

0.06)

(1.12

y [cm]

60
40
20
0 x [cm]
0 −20 2060
(1.12 0.08)4020
0 x [cm]
0
20 −60 −40 −20−20y [cm]y [cm]y [cm]y [cm]y [cm](1.46(1.11 0.10)
60(1.08 0.08)4020
0 x [cm]
0 −20 20 −60 −40 −20

0.03)

(1.82

0.55)

y [cm]

0.17)
0.10)

60
40
20
0 x [cm]
0 −20 20 −60 −40 −20−60 −40 −20

(1.03

60
(1.04 0.03)4020
0 x [cm]
0
20 −60 −40 −20−20y [cm]

(1.32
(1.17

0.07)
0.06)

0.05)
0.04)

y [cm]−60 −40 −20

(1.23
(1.21

(1.03
(1.02

60
40
20
0 x [cm]
020−20

y [cm]

0.06)
0.07)

y [cm]

(1.13
(1.13

y [cm]−60 −40 −20(1.05 0.02)(1.11 0.13)
6060(1.06 0.03)(1.13 0.18)
40
40
20
20
0 x [cm]
0 x [cm]
0
20 −60 −40 −20 0
20 −60 −40 −20−20−20

y [cm]

0.06)
0.05)

y [cm]

(1.08
(1.07

Generated hand trajectories by the proposed model
Mesured hand trajectories

60(1.31 0.09)4020
0 x [cm]
0 −20 20 −60 −40 −20

60
40
20
0 x [cm]
0 −20 20(b): A non-impaired subject

Fig. 10. Observed and simulated hand trajectories for the myoelectric prosthesis user and the non-impaired subject

0.5 1.0 1.5 2.0
Time [s]

200
150
100
50
0
0

(2.31
(1.54

0.85)
0.11)

0.5 1.0 1.5 2.0
Time [s]Velocity [cm/s]

200
150
100
50
0
0

(a): A prosthesis user

(0.96
(0.97

0.07)
0.05)

0.5 1.0 1.5 2.0
Time [s]
(0.68
(0.62

0.08)
0.09)

0.5 1.0 1.5 2.0
Time [s]Velocity [cm/s]

0.5 1.0 1.5 2.0
Time [s]

200
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(1.03
(1.04

0

0.5 1.0 1.5 2.0
Time [s]
(0.97
(0.98

0

0.05)
0.04)

0.5 1.0 1.5 2.0
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(0.89
(0.89

0

0.03)
0.03)

0.15)
0.13)

0.5 1.0 1.5 2.0
Time [s]Velocity [cm/s]

0

0.91)
0.52)

0.10)
0.08)

0.05)
0.04)

200
150
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0
0

Velocity [cm/s]

(1.46
(1.11

(1.11
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(1.03
(1.02

Velocity [cm/s]

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0.07)
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Velocity [cm/s]

0.17)
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(1.23
(1.21

(1.11
(1.13

Velocity [cm/s]

(1.32
(1.17

0.5 1.0 1.5 2.0
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0.5 1.0 1.5 2.0
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Generated hand trajectories by the proposed model
Mesured hand trajectories

Velocity [cm/s]

0.06)
0.07)

(1.05
(1.06

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(1.13
(1.13

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Generated hand trajectories by the proposed model
Mesured hand trajectories

200
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(b): A non-impaired subject

(1.12
(1.12

0.06)
0.08)

0.5 1.0 1.5 2.0
Time [s]
(0.95
(0.96

0.07)
0.06)

0.5 1.0 1.5 2.0
Time [s]
(1.82
(1.31

0.55)
0.09)

0.5 1.0 1.5 2.0
Time [s]Fig. 11. Observed and simulated hand velocity for the myoelectric prosthesis user and the non-impaired subject
5. A. Badawy, Dual-well Potential Field Function for
Articulated Manipulator Trajectory Planning, Alexandria
Acknowledgements
Engineering Journal 55 (2) (2016) 1235–1241.
This work was partially supported by a Grant-in-Aid for6. T. Tsuji, Y. Tanaka, P. G. Morasso, V. Sanguineti and M.
Kaneko, Bio-mimetic Trajectory Generation of Robots
Young Scientists B Number 26730111.
via Artificial Potential Field with Time Base Generator,
References
IEEE Transaction on Systems, Man and Cybernetics 32
1. T. Chin, Kinden Gishiyu Kunren Maniyuaru, All-Japan(4) (2002) 426–439.
Hospital Publication Association Ltd. (2006), p. 83. (in7. T. Weerakoon, K. Ishii and A. A. F. Nassiraei, An
Japanese).
Artificial Potential Field Based Mobile Robot Navigation
2. T. Flash and N. Hogan, The Coordination of Arm
Method to Prevent from Deadlock, Journal of Artificial
Movements:
An
Experimentally
Confirmed
Intelligence and Soft Computing Research 5 (3) (2015)
Mathematical Model, Journal of Neuroscience 5 (7)189–203.
(1985) 1683–1703.
8. V. Mathiowetz, G. Volland, N. Kashman and K. Weber,
3. Y. Uno, M. Kawato and R. Suzuki, Formation and
Adult Norms for the Box and Block Test of ManualControl of Optimal Trajectory in Human Multi-joint Arm
Dexterity, The American Journal Occupational Therapy.
Movement, Biol. Cybern. 61 (1989) 89–101.
39 (6) (1985) 386–391.
4. C. M. Harris and D. M. Wolpert, Signal-dependent Noise
Determines Motor Planning, Nature 394 (1998) 780–784.

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