Journal of Medical Engineering & Technology, 2011; 35(6–7): 314–321
Copyright © 2011 Informa UK, Ltd.
ISSN 0309-1902 print/ISSN 1464-522X online
DOI: 10.3109/03091902.2011.591480

Innovation

Fuzzy FES controller using cycle-to-cycle control for repetitive movement
training in motor rehabilitation. Experimental tests with wireless system
Naoto Miura1*, Takashi Watanabe1,2, Satoru Sugimoto1, Kazunori Seki3, and Hiroshi Kanai1,2

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1

Graduate School of Engineering, Tohoku University, Aoba-ku, Sendai, Japan, 2Graduate School of Biomedical Engineering,Tohoku University, Graduate school of biomedical engineering, Sendai, Japan and 3Tohoku University Graduate School of
Medicine, Sendai, Japan
has been utilized as an orthotic and therapeutic aid in the
rehabilitation of the upper and lower limb motor functions.
The therapeutic effects during rehabilitation with FES havebeen shown to improve muscle strength [1–3] and muscle recruitment [3–4]. The repetitive movement therapy mediatedby the electrical stimulation also has the potential to facilitate
motor relearning [5].
In motor rehabilitation, goal-oriented repetitive movement training of the paralyzed limbs has been applied. One of
the therapeutic effects is motor relearning, which is reacquisition of previously learned motor skills after central nervous
system injury. In general, assistance provided by therapists
is required to perform repetitive execution of identical orsimilar movements of the limbs in the rehabilitation training.
On the other hand, several large-scale robotic systems havebeen developed to reduce the workloads for the therapists
and improve repeated training for patients [6]. However,these equipments are large and expensive, which are installedin hospitals or rehabilitation centers, and therefore generally
unsuitable for home rehabilitation and daily exercise.
For motor rehabilitation with FES, surface electrical stimulation would be useful because of its noninvasive nature.
However, the electrical stimulator for surface FES is usuallyrequired to generate high stimulation intensity pulses, whichleads to an increase of size and power consumption of thestimulator. In addition, wired connection between controller and stimulators and between controller and sensors are
sometimes cumbersome and can obstruct the movement of
the limb. Therefore, this study focused on miniaturizing theelectrical stimulator and on removing the connection codeusing wireless technology.
In training with FES for rehabilitation, repetitive movements of limbs have to be controlled appropriately by stimulating the relevant muscles. Closed-loop FES control is required
to suppress variations of initial position and muscle response,and muscle fatigue in the exercise and to derive benefit from

A prototype of wireless surface electrical stimulation system
combined with the fuzzy FES controller was developed forrehabilitation training with functional electrical stimulation(FES). The developed FES system has three features forrehabilitation training: small-sized electrical stimulator forsurface FES, wireless connection between controller andstimulators, and between controller and sensors, and the fuzzy
FES controller based on the cycle-to-cycle control for repetitive
training. The developed stimulator could generate monophasicor biphasic high voltage stimulus pulse and could output
stimulation pulses continuously more than 20 hours with
4 AAA batteries. The developed system was examined withneurologically intact subjects and hemiplegic subjects in knee
joint control. The maximum knee joint angle was controlled byregulating burst duration of stimulation pulses by the fuzzycontroller. In the results of two experiments of knee extension
angle control and knee flexion and extension angle control, themaximum angles reached their targets within small numberof cycles and were controlled stably in the stimulation cycles
after reaching the target. The fuzzy FES controller based on thecycle-to-cycle control worked effectively to reach the target
angle and to compensate difference in muscle properties
between subjects. The developed wireless surface FES system
would be practical in clinical applications of repetitive
execution of similar movements of the limbs for motor
rehabilitation with FES.
Keywords: Cycle-to-Cycle Control, Functional Electrical
Stimulation, Rehabilitation, Surface Electrical Stimulation,
Wireless System

Introduction
Functional electrical stimulation (FES) can be an effective
method of assisting or restoring paralyzed motor functions
caused by spinal cord injury or cerebrovascular disease. FES*Corresponding author. E-mail: naoto.miura@bme.tohoku.ac.jp314

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Fuzzy FES controller for motor rehabilitation315

the rehabilitation. Tracking control of joint angles of the lower
limb is a difficult problem because of nonlinearity and significant time delay, both affecting the responses of the musculoskeletal system to electrical stimulation. For this purpose, thefuzzy FES controller based on the cycle-to-cycle control [7–9]
was modified and implemented in the wireless FES system
for rehabilitation in this study. The cycle-to-cycle control isa control method for restoring cyclic movements such as gaitby using FES [10–11]. Each muscle contraction is controlled
by single burst of stimulation pulses with constant pulse amplitude, pulse width and frequency to induce joint movement
reaching the target joint angle, in which the stimulation burst
duration is regulated.
The purpose of this study is to show the effectiveness of thewireless FES system in which the fuzzy cycle-to-cycle control
was implemented for repetitive movement control throughcontrol tests with neurologically intact and hemiplegic subjects. In this paper, the wireless surface electrical stimulation
system combined with the fuzzy FES controller based on thecycle-to-cycle control was developed. The developed wirelessfeedback FES system was examined in knee joint control. First,
the maximum knee extension angle control stimulating one
muscle was performed to find the basic performance of theclosed-loop control with the wireless system with neurologically intact subjects and hemiplegic subjects. Then, the maximum knee flexion and extension angle control was performed
as a preliminary test of controlling a sequence of movements
stimulating two muscles with neurologically intact subjects.

frequency in the wireless transceiver module and transmitted to the fuzzy FES controller through wireless transceivermodule as feedback signal. It is possible to receive the sensor
data of up to 4 channels simultaneously. The topology of wireless communication is the point-to-point connection between
the controller and the stimulator and between the controller
and the sensor, in which the original protocol (the packet consisting of the data of Preamble, Address, Payload and Cyclic
Redundancy Check) is used. The bit rate and the latency of
the transceiver module are up to 250 kbit/s and about 2 ms,
respectively.
Electrical stimulator consists of the wireless transceivermodule, the boost converter and the stimulation pulse generator. The boost converter stores electric charges in a tankcapacitor and generates high voltage pulse required for thesurface electrical stimulation (maximum output voltage:
128 V). The stimulator generates monophasic or biphasic
pulse. The maximum stimulation frequency was 520 Hz. In
usual FES control, stimulation pulses with a constant stimulation frequency smaller than about 100 Hz are used. Highfrequency stimulation pulses are sometimes used in research
work as a doublet or a triplet [12–13], in which stimulation
frequency is about up to 300 Hz. The overall size of the produced stimulator was 70 × 55 × 30 mm. The stimulator’s poweris supplied by 4 AAA batteries. The electrical stimulator could
output stimulation pulses continuously more than 20 hours(monophasic pulse train, frequency: 20 Hz, pulse width:
0.3 ms, pulse amplitude: 80 V).

Wireless surface electrical stimulation system

Outline of fuzzy FES controller based on cycleto-cycle control

The wireless surface electrical stimulation system consistsof three parts: the fuzzy FES controller implemented on thePC, surface electrical stimulator and sensor. For wirelesscommunication between the controller and the stimulator
and between the controller and the sensor, a 2.4 GHz wireless transceiver module (WCU-241, K2-denshi) was used.
The stimulus data determined by the fuzzy FES controller istransmitted to the stimulator through the wireless transceivermodules. The stimulator generates electrical stimulation
pulses immediately after receiving the stimulus data. The data
was composed of stimulus voltage, stimulus pulse width andmonophasic/biphasic pulse type. The current system can send
the stimulus data of up to 4 channels together. The sensor data
are digitized by a 10 bit A/D converter with 40 Hz of sampling

The block diagram of the fuzzy FES control for repetitive
movement is shown in figure 1. Output of the fuzzy controller
was automatically adjusted by two parameters: error-based
output adjustment factor (E-OAF) and sensitivity-based
factor (S-OAF). Therefore, the burst duration of stimulation
pulses of a current cycle TB[n] is regulated by the following
formula:TB[n] = TB[n-1] + ΔTB[n]where TB[n-1] is the stimulation burst duration for thecycle just before the current one and ΔTB[n] is the output of
the fuzzy controller adjusted by the 2 factors.
The fuzzy controller was designed as multi-input singleoutput (MISO) controller with two inputs of ‘error’ andFigure 1. Block diagram of the Fuzzy FES control for repetitive movement. S-OAF, sensitivity-based output adjustment factor; E-OAF, error-based
output adjustment factor; θT, target maximum angle; θmax, maximum joint angle produced by TB; θch, joint angle change produced by TB.
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Naoto Miura et al.

‘desired range’. The ‘error’ was defined as the difference
between the target angle and the maximum angle elicitedby the burst stimulation pulses. The ‘desired range’ wasdefined as the difference between the target angle and theangle at the stimulation onset. The E-OAF is determinedby the error of the cycle just before the current cycle, which
increases the output value of the controller if the error islarge, and decreases if the error is small. The S-OAF is determined by joint angle production ratio that is defined as
the ratio of joint angle change to stimulation burst duration,
θch/TB, which means sensitivity of the muscle to electricalstimulation.
figure 2 shows an example of input and output membership functions of the fuzzy controller for knee extension
angle control. Input membership functions were expressed bytriangular and trapezoidal fuzzy sets. The membership functions of the ‘error’ and ‘desired range’ comprised 7 and 3 linguistic terms, respectively, and that of the output variable wasexpressed as 11 fuzzy singletons. The membership functionsof the E-OAF comprised 5 linguistic terms, and the output
variable was expressed as 5 fuzzy singletons. The membershipfunctions of the S-OAF comprised 3 linguistic terms, and theoutput variable was expressed as 3 fuzzy singletons.
The fuzzy inference was accomplished by using the Mamdani method. Center of gravity (COG) was used in the defuzzification process. Parameter values of the fuzzy controller
were determined based on control results and values obtainedin our previous studies [7–9], which were fixed during theexperiments.

Knee extension angle control withneurologically intact subjects and hemiplegic
subjects
Experimental methods
The vastus muscles were stimulated through surface electrodes (SRH5080, SEKISUI PLASTICS), and maximum knee
extension angle was controlled by the surface electrical stimulation system (figure 3). Two neurologically intact subjects(subject A, B) and two hemiplegic subjects caused by cerebral
apoplexy (subject C: 76-year-old right sided hemiplegic malepatient, subject D: 38-year-old left sided hemiplegic malepatient) participated in the experiments. Subjects’ consent toparticipate in the experiment was obtained.
The subject seated in the chair (GT-30, OG Giken) andrelaxed his legs during experiments. To maintain the sitting
position, the trunk of hemiplegic subject was fixed to the chairwith band. The sitting position of the neurologically intact subjects was determined by themselves and that of the hemiplegic
subject was determined by adjusting the back of the chair in
the forward and backward direction for appropriate knee joint
movement. Consequently, the initial joint angle was about 65°
in neurologically intact subjects and about 80° in hemiplegic
subjects (0° means full knee extension). The target angle was
30° (range of knee extension angle was about 35°) for neurologically intact subjects and was 70° or 65° (range of knee
extension angle was about 10° or 15°) for hemiplegic subjects.
The target angle was determined based on the maximum
knee extension angle developed by electrical stimulation. The

Figure 2. Input/Output membership functions of the fuzzy controller. Input membership functions were expressed by triangular and trapezoidal
fuzzy sets. The membership functions of the ‘error’ and ‘desired range’ comprised 7 and 3 linguistic terms, respectively, and that of the output
variable was expressed as 11 fuzzy singletons. The membership functions of the E-OAF comprised 5 linguistic terms, and the output variable wasexpressed as 5 fuzzy singletons. The membership functions of the S-OAF comprised 3 linguistic terms, and the output variable was expressed as 3
fuzzy singletons. S, small; M, medium; L, large; NL2, negative large 2; NL1, negative large 1;NL, negative large; NM, negative medium; NS, negativesmall; Z, zero; PS, positive small; PM, positive medium; PL, positive large; PL1, positive large 1; PL2, positive large 2.
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317

Figure 3. Experimental setup of the knee extension control.

v­ alues of fuzzy membership functions for neurologically intact subjects were determined in previous experiments withother subjects [8,9]. The values of fuzzy membership functions for hemiplegic subjects were determined after adjusting
their values of neurologically intact subjects from the resultsof preliminary experiments.
In one experimental session, 100 cycles were performed
with neurologically intact subjects, and 35 cycles were performed with hemiplegic subjects to reduce physical load.
The knee joint angles were measured with an electric goniometer (M180, Penny & Giles). The output signal of thegoniomenter was digitized by a 10 bit A/D converter with40 Hz of sampling frequency. Pulse width and pulse frequency was fixed at 0.3 ms and 20 Hz, respectively. Stimulus
pulse amplitude was determined so as to develop target
joint angle without pain before the experiment. Initial valueof TB was 0 s.

Results
An example of control results with a hemiplegic subject (Subject C) was shown in figure 4. Stimulation burst duration TB
increased as the number of cycles increased, and then the
maximum extension angle was reached to the target angle atthe 4th control cycle. In the first few cycles, the value of EOAF was large, which shows the E-OAF worked effectively inearly cycles in order to reach the targets with small number ofcycles. The value of S-OAF was large at the most cycles, whichshows the S-OAF compensated for the weak muscle responseof this subject.
For evaluating control results, settling index (SI), mean error (ME) and mean variation (MV) were calculated (table 1).
SI was defined as the number of cycles that were required toreach the target joint angle with absolute error that was lessthan or equal to 3°. ME was mean value of the absolute error
between the target angle and the produced maximum extension angle in cycles after reaching the target. MV was mean of
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the difference in controlled joint angles between two consecutive cycles after reaching the target. The number in parentheses in table 1 shows the result for the first 35 cycles that is thesame evaluation condition as the hemiplegic subjects. As seen
in table 1, SI was 3–5 cycles, ME was less than 1° for all trials and MV was approximately 1°. The evaluation indices forthe hemiplegic subjects showed similar values as those for theneurologically intact subjects.
The developed system performed well in the knee extension control with all subjects. However, there were somecases that the value of S-OAF did not change dynamicallyto the change in the sensitivity. Figure 5 shows relationshipbetween the sensitivity and the S-OAF of each cycle after
reaching the target in the knee extension angle control. The
value of sensitivity was about between 20° and 50°/s in thehemiplegic subjects and about between 50° and 90°/s inthe neurologically intact subjects. The value of sensitivity
in the hemiplegic subjects was small compared to those of
neurologically intact subjects, because muscle responses
to electrical stimulation were weak with the hemiplegic
subjects. The controller used in the experiments adjusted
output values (TB) by the S-OAF for subject A (0.7–1.0) andC (1.2–1.5). For Subjects B and D, values of the S-OAF wereabout 1.0, which shows little adjustment by the S-OAF. The
role of the S-OAF is to compensate variation of the muscle
properties between subjects, change in muscle response andmuscle fatigue. In the control tests, parameter values for the
S-OAF were determined based on the previous results [8].
That is, for paralyzed subjects, considering weak muscle
responses to electrical stimulation, values of sensitivity forthe input membership function (M) were set between 10°/s
and 70°/s with 40°/s for the center. Those sensitivity values were similar to those for a neurologically intact subject
whose muscle responses were considerably weak [8]. Since
the adjustment of the S-OAF was little with one hemiplegic
subject and one neurologically intact subject compared with

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318

Figure 5. Evaluation results of sensitivity and S-OAF in knee extension
angle control.
Table 1. Evaluation results of knee extension control.

Subject range ofextension
A 35°
B 35°
C 10° (trial 1)
C 15° (trial 2)
D 15°

Max. knee extension control
SI (cycle)
ME (deg)533430.8 (1.2)
0.7 (0.7)
0.6
0.8
0.9

MV (deg)
1.0 (1.4)
0.9 (1.0)
0.8
0.8
1.0

The number in parentheses shows the result for the first 35 cycles that is the sameevaluation condition as the hemiplegic subjects.

­ eurologically intact subjects because of safety for hemiplegicnsubjects in positioning during control.

Figure 4. An example of control results of the maximum knee extension
angles (Subject C trial 2).

the change in sensitivity, the modification of the S-OAF will
be necessary.

Knee flexion and extension control withneurologically intact subjects
Based on the results of the previous section, the range of values of input and output membership functions of the S-OAF
were expanded, and the number of terms were increased inorder to adapt to changes in these muscle responses. The maximum knee flexion and extension angle control was examined
as a sequence of movements stimulating two muscles with		

Experimental methods
The maximum knee flexion and extension angles were controlled in one cycle stimulating the hamstrings and the vastus
muscles by the surface electrical stimulation system with 7
neurologically intact subjects (figure 6). Subject’s consent toparticipate in the experiment was obtained. The subject sat on
the equipment keeping his position by his upper limbs. The
initial knee joint angle (neutral position) was approximately
30° and target angles were 45–70° for knee flexion and 10° forextension (the maximum angle of knee extension is defined
as 0°). Starting condition for each control cycle was when the
difference of knee joint angle between two consecutive cycles
is less than 0.3° for the 20 consecutive samples after 6 seconds from the time when the maximum extension angle was
detected in the previous control cycle. The hamstrings were
stimulated first and then the vastus muscles were stimulated
after detecting the maximum flexion angle.
Pulse width was fixed at 0.2 ms. Other electrical stimulation condition and the measurement method of knee joint
angle were same as the experiment of knee extension control.
Initial value of TB is 0 s and 35 cycles were performed ineach control session. Three control sessions were performed
for each subject with the time interval between 20 min and
30 min.
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Fuzzy FES controller for motor rehabilitation

319

Figure 6. Experimental setup of the knee flexion and extension control.

For the hamstrings, the fuzzy model of the S-OAF waschanged to have 7 linguistic terms for input membershipfunction and 7 singletons for the output variable. For the vastus muscles, the fuzzy model of the S-OAF was changed tohave 4 linguistic terms for input membership function and 4
singletons for the output variable.

Results
Both maximum joint angles were controlled with five subjects,
but sufficient knee flexion angle was not produced by the electrical stimulation with two subjects. One example of control
results is shown in figure 7. The maximum flexion and extension angles reached their targets with small number of cycles (3for the flexion and 4 for the extension, respectively) and were
controlled stably during the stimulation cycles after reaching
the target. As shown in the case of knee extension control, the
E-OAF worked effectively in early cycles and the burst duration
was adjusted appropriately by regulating the value of S-OAF(about 1.2 for flexion and about 0.8 for extension, respectively)
to compensate for different muscle responses.
For evaluating control results, SI, ME and MV were calculated (table 2). SI was 3–5 cycles, ME was less than 4° forflexion control and less than 2° for extension control. MV wasless than 5° for flexion and less than 2.5° for extension.

Discussions
The developed wireless surface electrical stimulation system
combined with the fuzzy controller performed well in the knee
angle controls. The system realized reaching the target within
about 5 cycles. In most of trials, the mean error after reaching
the target was less than about 3°, and the mean variation after
reaching the target was less than about 3°. These control results
were similar to the results in our previous reports [9], whichwere obtained by using previous wired stimulation system.
In addition, under the condition of the longer control cycles
than the previous report [9], the maximum knee ­extension
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angle was controlled stably with neurologically intact subject.
Therefore, the wireless surface electrical stimulation system
combined with the fuzzy controller was considered to function effectively as a closed-loop controller.
The developed system worked well with hemiplegic subjects in the knee extension control. Although the muscle response produced by the electrical stimulation with the hemiplegic subjects was weak compared to those of neurologicallyintact subjects, the ability of fuzzy FES controller based on
the cycle-to-cycle control is considered to be appropriate toreach the target angle and to compensate difference in muscle
properties between subjects. Therefore, the developed system
is expected to be practical in clinical applications.
Stimulation burst duration (TB) was adjusted appropriately, and the knee joint angle was controlled stably by the
fuzzy controller with two parameters of the E-OAF and the SOAF in both control tests. For large error between the control
angle and the target angle in early cycles, the E-OAF worked
effectively to reach the target with small number of cycles inall subjects. After reaching the target angle, the E-OAF was
small because the error of the obtained knee joint angle wassmall. In contrast, the S-OAF worked to compensate for thedifferent muscle responses during all the stimulus cycles
automatically based on the value of sensitivity. These results
showed that both of the E-OAF and S-OAF would be effective
in controlling the repetitive execution of similar movements
for rehabilitation.
In the knee extension angle control, the value of S-OAF
did not change dynamically to the change in sensitivity withsome subjects. Therefore, the range of values of input andoutput membership functions of the S-OAF was expanded
and the number of terms was increased, and then the knee
flexion and extension angle control was examined. Figure 8
shows the sensitivity and the S-OAF of each cycle after reaching the target obtained in the knee flexion and extension angle
control. The value of the S-OAF changed dynamically as thesensitivity changed. It may be better to expand the range of the320

Naoto Miura et al.

Table 2. Evaluation results of knee flexion and extension control.

SI ± SD (cycle)

Max. knee flexion control
ME ± SD (deg)MV ± SD (deg)

E
F
H
J
K
Average

4.0 ± 1.0
2.7 ± 0.6
3.0 ± 0.0
4.0 ± 1.0
3.7 ± 0.6
3.5 ± 0.8

2.3 ± 0.1
3.3 ± 0.5
1.3 ± 0.2
2.3 ± 1.3
2.1 ± 1.2
2.3 ± 0.9

2.9 ± 0.2
3.7 ± 1.1
1.6 ± 0.4
3.4 ± 1.6
2.9 ± 1.7
2.9 ± 1.2

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Subject

Max. knee extension control
SI (cycle) ± SD
ME ± SD (deg)
3.7 ± 0.6
3.3 ± 0.6
3.0 ± 0.0
2.7 ± 1.6
3.0 ± 0.0
3.1 ± 0.5

1.3 ± 0.2
0.9 ± 0.1
0.9 ± 0.2
1.4 ± 0.5
1.5 ± 0.1
1.2 ± 0.3

MV ± SD (deg)
1.2 ± 0.3
1.1 ± 0.2
1.3 ± 0.4
1.7 ± 0.8
2.0 ± 0.1
1.5 ± 0.5

Figure 8. Evaluation results of sensitivity and S-OAF after reaching thetarget in knee flexion and extension angle control.

Figure 7. An example of control results of the maximum knee flexionand extension angles (Subj. K, 1st trial).
		

input and output membership functions of the S-OAF for thevastus muscles because of the slight saturation of the S-OAF
of the vastus muscles in both the lower and higher sensitivity,
if necessary.
The S-OAF using the sensitivity, which is the ratio of joint
angle change to stimulation burst duration, worked effectively
in both hemiplegic subjects and neurologically intact subjects.
However, the sensitivity obtained by this method may containother effects such as movements of other parts of the body or
gravitational effect. For optimal movement control, it is required to modify by using directly measured muscle activity
such as surface electromyogram elicited by electrical stimulation (M-wave).
The developed wireless surface FES system by using thewireless transceiver module is expected to improve ease of use.
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Fuzzy FES controller for motor rehabilitation
However, the wireless communication has problems such as
delay and interference. The delay of wireless communication
between the wireless modules used in the developed system
was small (2 ms) enough compared to the sampling period of
ADC (25 ms) and the stimulus period (50 ms). Therefore, it
is considered that the influence of the delay of the wirelesscommunication on the performance of the cycle-to-cycle
controller was small in this system. The interference in wireless communication was not caused in the experiments using
the wireless transceiver module for the 2.4 GHz (Industrial,
Scientific and Medical: ISM) band. However, the interference
problem does not always cause in the wireless communication. It is necessary to deal with the problem of the wirelesscommunication by modifying the communication software
including time management within each module, the retransmission processing and so on.
The setting of the goniometer for movement measurements
is not so easy for rehabilitation training because of limited attachment position and requirement of complicated calibration
process. The measurement of movement using wearable sensor
such as a gyroscope and accelerometer [14] would be suitablefor clinical application of feedback FES control system.

Conclusion
In this study, the small surface electrical stimulator was designed, and then the wireless surface FES system combinedwith the fuzzy controller based on the cycle-to-cycle control
was developed. In order to show the effectiveness of the wireless FES system implemented the fuzzy cycle-to-cycle control
for repetitive movement control, the developed wireless FES
system was examined in knee joint controls with neurologically intact and hemiplegic subjects. The developed system
performed well in the knee joint angle controls adjusting
stimulation burst time appropriately as a closed-loop controller with both hemiplegic subjects and neurologically intact
subjects, which shows that the wireless FES system can realize stable control. The wireless surface electrical stimulation
system would be practical in clinical applications of ­repetitive
execution of similar movements of the limbs for motor­rehabilitation with FES.

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321

Declaration of interest: This work was supported in partby the Ministry of Education, Culture, Sports, Science andTechnology of Japan under a Grant-in-Aid for Scientific
Research (B), and the Saito Gratitude Foundation.

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