Document [original]

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36

https://doi.org/10.1186/s12984-020-0640-7

RESEARCH Open Access

Adaptive multichannel FES

neuroprosthesis with learning control and

automatic gait assessment

Philipp Müller1* , Antonio J. del Ama2,JuanC.Moreno

3and Thomas Schauer1

Abstract

Background: FES (Functional Electrical Stimulation) neuroprostheses have long been a permanent feature in the

rehabilitation and gait support of people who had a stroke or have a Spinal Cord Injury (SCI). Over time the

well-known foot switch triggered drop foot neuroprosthesis, was extended to a multichannel full-leg support

neuroprosthesis enabling improved support and rehabilitation. However, these neuroprostheses had to be manually

tuned and could not adapt to the persons’ individual needs. In recent research, a learning controller was added to the

drop foot neuroprosthesis, so that the full stimulation pattern during the swing phase could be adapted by measuring

the joint angles of previous steps.

Methods: The aim of this research is to begin developing a learning full-leg supporting neuroprosthesis, which

controls the antagonistic muscle pairs for knee flexion and extension, as well as for ankle joint dorsi- and plantarflexion

during all gait phases. A method was established that allows a continuous assessment of knee and foot joint angles

with every step. This method can warp the physiological joint angles of healthy subjects to match the individual

pathological gait of the subject and thus allows a direct comparison of the two. A new kind of Iterative Learning

Controller (ILC) is proposed which works independent of the step duration of the individual and uses physiological

joint angle reference bands.

Results: In a first test with four people with an incomplete SCI, the results showed that the proposed neuroprosthesis

was able to generate individually fitted stimulation patterns for three of the participants. The other participant was

more severely affected and had to be excluded due to the resulting false triggering of the gait phase detection. For

two of the three remaining participants, a slight improvement in the average foot angles could be observed, for one

participant slight improvements in the averaged knee angles. These improvements where in the range of 4° at the

times of peak dorsiflexion, peak plantarflexion, or peak knee flexion.

Conclusions: Direct adaptation to the current gait of the participants could be achieved with the proposed method.

The preliminary first test with people with a SCI showed that the neuroprosthesis can generate individual stimulation

patterns. The sensitivity to the knee angle reset, timing problems in participants with significant gait fluctuations, and

the automatic ILC gain tuning are remaining issues that need be addressed. Subsequently, future studies should

compare the improved, long-term rehabilitation effects of the here presented neuroprosthesis, with conventional

multichannel FES neuroprostheses.

Keywords: Multichannel neuroprosthesis, unctional electrical stimulation, Iterative learning control, Automatic gait

assessment, Real-time motion analysis, Joint angle tracking, Gait support

*Correspondence: [email protected]berlin.de

1Technische Universität Berlin, Berlin, Germany

Full list of author information is available at the end of the article

International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and

reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the

Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver

(http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 2 of 20

Background

People who had a stroke or have a Spinal Cord Injury

(SCI) experience impaired motor control. Limited loco-

motion function can have a big impact on the health and

overall life quality of these persons. After a stroke or acci-

dent, the persons go through a rehabilitation period in

which they try to regain as much of their former motor

function as possible. After rehabilitation, stroke survivors

or people with SCI might continue to see a physiother-

apist. Over the last several decades Functional Electrical

Stimulation (FES) has proven to be a useful tool in reha-

bilitation [1–3]. FES can help with basic muscle training

[4], can initiate or amplify motion, and can provide sen-

sory feedback [5]. Compared with a passive orthosis, FES

does not limit the range of motion or the use of mus-

cles [6]. While exoskeletons can offer higher forces and

support, FES is comparatively light weight, less expensive

and more physically engaging. The main disadvantages of

FES are the limited amount of achievable force (especially

using non-invasive surface electrodes) [7,8], the complex-

ity of motion control using stimulation, the increasing

discomfort with higher stimulation intensities and the

rapid muscular fatigue of the artificially activated paretic

muscles [9]. FES-based neuroprostheses are therefore best

suited to lightly affected persons or in combination with

robotics.

The first FES-based neuroprosthesis was a drop foot

stimulator introduced by Liberson et al. in 1961 [10], in

which the stimulation of the tibialis anterior muscle was

triggered on and off by a foot switch attached to the per-

son’s heel. Commercial drop foot systems available today

still follow the same basic principle: heel-rise and initial

contact of the foot are detected using either a foot switch

or an inertial sensor, and the stimulation profile is a square

or trapezoidal pattern during the swing phase (e.g., the

Odstock Dropped-Foot Stimulator produced by Odstock

Medical Ltd in the UK).

The single channel tibialis anterior stimulation was later

extended to multichannel neuroprostheses, in which more

muscles of the gait muscle complex were included in

the stimulation [11–13]. In these studies, gastrocnemius,

hamstrings, quadriceps, gluteus maximus, gluteus medius

and even shoulder muscles were stimulated. Kim et al.

were able to show that multichannel stimulation (of glu-

teus medius and tibialis anterior) is superior to single

channel stimulation (of only the tibialis anterior) in terms

of gait improvement [13].

A main issue with this first-generation FES prosthe-

sis is that the stimulation patterns and timings are rigid

and can only crudely and manually be adjusted to the

needs of the individual person. Recent research has tried

to address this issue. One approach is to use more true to

life stimulation patterns, replacing the trapezoid or rect-

angular patterns. O’Keeffe et al. and Breen et al. derived

a stimulation pattern for the tibialis anterior muscle

from Electromyography (EMG) data of healthy subjects

[14,15]. The fixed stimulation pattern was triggered with

a foot switch and resampled to the current estimated step

duration. Meng et al. extended this approach to include

four muscles, the quadriceps, hamstrings, tibialis ante-

rior and gastrocnemius muscles [16]. In a previous study

[17], the EMG muscle activity of ten healthy subjects dur-

ing gait was recorded in relation to five gait events. This

recorded EMG activity was converted to a stimulation

intensity pattern and played back at the corresponding

gait events of each individual participant. The method was

tested on seven healthy subjects.

The remaining issues, however, are that the shapes of

the stimulation patterns are not adjusted to the individ-

ual person’s needs, and that the intensities have to be

manually tuned for each subject. Chia et al. and Ferrante

et al. went one step further by deriving stimulation pat-

terns from the gait EMG activity of the individual subject

[18,19]. This was done in a separate session in which the

EMG activity was measured in relation to six gait events.

By comparing the measured EMG data to data obtained

from healthy subjects, stimulation patterns could be

derived. In a preliminary evaluation with two stroke sur-

vivors, a gait improvement could be shown after four

weeks of training with the stimulation. An advantage of

this approach is that after the extensive calibration ses-

sion, no additional sensors, besides the foot switch or

inertial gait phase detection, are necessary. The stimula-

tion patterns, however, are calibrated to the circumstances

at the time of the measurement, and cannot adapt to

changes in gait caused by factors such as fatigue, mental

focus and longer term rehabilitation improvement.

As well as orthoses, exoskeletons, robotics and FES,

EMG biofeedback is a method to improve rehabilitation

therapy. In EMG biofeedback the EMG activity of one

or multiple muscles is measured and directly fed back to

the subject in the form of audio or video signals. This

enables a direct feedback of the subjects’s performance.

Moreland et al. showed in a review of eight studies, that

EMG biofeedback performs better compared to conven-

tional therapy of the lower extremities [20]. Lourenção

et al. were able to show that combined FES and EMG

biofeedback based rehabilitation performed better than

an exclusive FES therapy for the upper extremities [21].

Cozean et al. showed that applying EMG biofeedback

during gait, together with FES, performed better than

exclusive FES or conventional therapy [22]. Laufer et al.

analyzed the potential of sensory electrical stimulation

in which the stimulation is felt but no muscle recruit-

ment is produced [23]. Laufer et al. concluded, that the

combination of sensory electrical stimulation and active

training has the biggest potential for improved rehabil-

itation. However, due to limited studies the long-term

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 3 of 20

results were inconclusive. The presented studies on EMG

biofeedback suggest that direct feedback of the persons’s

performance is beneficial to therapy and that FES is a valid

choice for biofeedback. The aforementioned neuropros-

theses, which use unchanging (aside from resampling)

gait event triggered stimulation patterns, do not adapt to

the subject’s performance and, therefore, miss out on the

additional therapeutic benefits of biofeedback.

A different FES neuroprosthesis approach is to adapt the

stimulation patterns in real-time to the gait of the subject.

This, however, needs a form of measurement of the cur-

rent gait of the subject, meaning that additional sensors

are necessary. Classical feedback control (e.g., PID con-

trol) is not suitable in gait applications due to the slow

dynamics between stimulation onset and motion. Chen

et al. specified a muscle independent latency of approxi-

mately 0.1 s between stimulation and the generated force

in the muscle [24]; Müller et al. and Seel et al. identi-

fied a delay of 0.2 s between stimulation and joint angle

response [25–27]. For example, for a healthy person walk-

ing at 3 km/h, the duration of the swing phase would be

approximately 0.25 s [28] (assuming a 40 % swing). Thus,

a direct feedback control of the joint angle during gait

cannot be achieved by FES.

Fortunately, gait is a repetitive motion, and therefore

deficits of the last step can be accounted for in the next

step. Using information from the previous cycles to influ-

ence the current cycle is generally referred to as learning

control. Relevant methods of learning control include

Iterative Learning Control (ILC), used for full trajectory

control, and Run To Run Control (R2R), used for single

parameter control [29].

Franken et al. used R2R (in this case is was called cycle-

to-cycle control) to automatically tune the single param-

eter of the stimulation duration of the hip flexor muscle

at every step, by measuring the hip angle range [30]. ILC

was first used together with FES by Dou et al. to control

the elbow flexion/extension angle [31]. Instead of a sin-

gle parameter, the full stimulation pulse width trajectory

was controlled, enabling full control of the elbow flexion.

Nahrstaedt et al. were the first to apply ILC during gait

on the tibialis anterior muscle [32]. Hughes et al., Free-

man et al. and Meadmore et al. further investigated into

ILC strategies for the upper limbs [33–35]. Seel et al. used

ILC to control the tibialis anterior and fibularis longus

muscle, achieving physiological dorsiflexion and eversion

of the foot in walking stroke survivors [26,27]. This was

achieved by identifying the coupling between, on the one

hand, the two muscles and, on the other, the dorsiflexion

and eversion angles. With this knowledge, two separate

ILCs could be used for each joint angle.

For gait applications, so far only ILC control of dorsiflex-

ion muscle groups during the swing phase were achieved.

In a preliminary work, we studied the system dynamics of

the knee flexion/extension angle when stimulating during

different phases of the gait. We established a first version

of an antagonistic knee ILC, which was tested on eight

healthy subjects [25]. We are now developing a learning

FES neuroprosthesis that supports the four antagonistic

muscle groups of the upper and lower leg by assessing

thekneeandfootangle(thebasicsetupcanbeseenin

Fig. 1). In this paper we present the development of an

automatic stepwise joint angle assessment, the develop-

ment of a walking speed independent iterative learning

controller, the implementation of the neuroprosthesis, a

first test with four people with SCI and the evaluation of

the test.

Automatic gait assessment

The purpose of the automatic gait assessment is to provide

the learning control with continuous error signals for the

knee and foot joint. These error signals should encode at

which points in time the subject needs more flexion or

extension. This is comparable to a therapist looking at the

person’s gait and noting in which phase of the gait cycle

deficits occur and of what intensity they are.

A way to systematically measure those deficits is to

measure the joint angles, gait cycle by gait cycle, and to

compare them with a desired reference. Several methods

for measuring joint angles and gait phases using Inertial

Measurement Unit (IMU) data can be found in literature.

To automatically find references that match the different

gaits and step cycle durations of people with pathological

Fig. 1 Placement of the neuroprosthesis (single leg setup) on one of

the participants (left image) and the schematic placement of

stimulation electrodes and sensors (right image). The neuroprosthesis

supports the stimulation of four muscle groups (quadriceps,

hamstrings, tibialis anterior and gastrocnemius) to control the knee

and foot motion during gait. The control of each leg is independent,

and therefore the double leg setup is a duplication of the single leg

setup. Due to the limitations of the wireless sensors, the single leg

setup was used in this work

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 4 of 20

gait proved to be challenging. New methods of automated

reference generation are proposed in this publication.

Measuring joint angles and gait phases

There are multiple IMU-based real-time gait phase detec-

tion algorithms available in literature [36–38]. In this

paper the foot mounted inertial sensor gait phase detec-

tion from Müller et al. was used [39]. This algorithm can

detect four gait events per foot sensor: initial contact,

foot-flat, heel-off and toe-off.

Inferring joint angles from raw IMU data is a well

known procedure, see for example, [40–42]. When com-

pared with optical reference systems, for IMU based joint

angle measurements in the sagittal plane, the precision

was found to be in the range of 3° or lower [40–42]. One

problem is that three dimensional orientations can only

directly be obtained by using magnetometer measure-

ments. Those measurements, however, are often heavily

disturbed. By using mechanical constraints of body and

gait it is possible to omit the use of magnetometers with

certain tradeoffs. Different methods of varying efficacy

are available in literature. Here we will focus on a plain

and robust solution, which has adapted on some of these

previous methods. Due to the plentitude of available pub-

lications, the chosen method will be described very briefly

in this paper.

The sensors are assumed to be aligned (x-axis along the

limb and z-axis facing along the knee joint axis or the

ankle dorsi/plantarflexion joint axis). Errors in the align-

ment can lead to errors in the joint angle measurement,

yet, Fennema et al. found that IMU alignment was accept-

ably repeatable for the knee joint [43]. Depending on only

one sensor, the foot-to-ground angle is expected be less

sensitive to alignment errors.

For the knee angle, the angle between the gravity vector

of the upper leg sensor and the gravity vector of the lower

leg sensor, projected to the sagittal plane, is obtained. The

part of the measured angular velocities of the upper and

lower leg that points along the knee joint axis is sub-

tracted to form the relative knee joint angular velocity.

This value is then integrated and fused together with the

estimated angle, based on the accelerations using a vari-

able weight. The value of the weight is determined by how

close the norm of the accelerations resemble gravity for

the last five samples. This rating ensures that accelera-

tion peaks generated by the gait do not influence the angle

estimation.

The foot-to-ground angle was obtained by integrating

the part of the measured foot angular velocity that points

along the ankle dorsi/plantarflexion joint axis. This value

is set to zero with each foot-flat event. To correct the

drift of the angular velocity measurement, the foot-to-

ground angle vector between two foot-flat events was

retroactively changed so that the first and last joint angle

value equals zero. This could be achieved by subtract-

ing a sloped line from the trajectory. Figure 2illustrates

the definition of the knee and foot-to-ground angle. The

calculated foot-to-ground angle is only correct when the

pitch of the foot during the foot flat phase is close to the

pitch of the previous foot flat phase; ergo, this method

would not be suitable when walking on uneven terrain.

Physiological joint angle reference bands

Inordertobeabletoevaluatepathologicalgait,aref-

erence must first be defined. We chose to measure the

gait of healthy persons and used this data as a reference

for a good gait. Four people (aged 38.5 ±5.5 years) were

asked to walk with four different speeds (1.5, 2, 2.5 and

3 km/h) on a treadmill. The measured joint angles were

cut into gait cycles using the events of the gait phase detec-

tion. Hence, for both, the knee and foot angle, there are

four different options to define the start of the gait cycle.

Since we want to compare the angle of one gait cycle to

a reference, it would be beneficial if the start and end of

the angle trajectory were at a predictable value. For the

foot-to-ground angle, the angle is zero by definition at the

foot-flat event (see Fig. 2). For the knee angle, there is no

phase where the angle is previously known. The heel-off

event was chosen as a reliable event in which the knee is

relatively straight for most subjects, as hinted in Fig. 2.

Each measured joint angle of one gait cycle was resam-

pled to a duration of 100 samples. Using the data of all

subjects, the mean and standard deviation for a "healthy"

foot and knee angle were determined as presented

in Fig. 3.

When using the obtained reference bands to assess the

gait of a person, the setting should be similar to the set-

ting of when the reference bands were recorded. In our

case this would be the walking on level ground with mod-

erate walking speeds. Ascending stairs, shuffling, running

or walking on uneven terrain requires different motion

sequences and, accordingly, different sets of joint angle

references.

Fig. 2 Joint angle definitions of the knee angle αand the

foot-to-ground angle β. The knee angle is defined zero for a straight

leg and positive for knee flexion. The foot-to-ground angle is zero

when the foot is parallel to the ground and positive when the

forefoot is pointing upwards

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 5 of 20

Fig. 3 The knee and foot-to-ground angle reference bands. The

bands are the standard deviations of the mean joint angles obtained

from measurements with healthy subjects. The knee reference starts

and ends at the heel-off event whereas the foot reference starts and

ends at the foot-flat event

The standard way in control engineering is to directly

compare (subtract) the measured trajectory with the ref-

erence trajectory and act on the resulting error. For the

step assessment, two issues arise: firstly, because the sub-

ject freely chooses the walking speed, the step duration

will vary; secondly, a healthy gait varies and does not

exactly follow a fixed trajectory, so there should be no

errors resulting from natural variations. The intuitive

solution to the first issue is to squeeze/stretch (resam-

ple) the reference trajectory to the duration of the current

step. For the second issue instead of a reference trajec-

tory, a reference band can be used which is defined by

the mean and standard deviations of the above measure-

ments. The error of the joint angle in relation to the

reference band is defined as zero when in the band, oth-

erwise it is defined as the distance to the band. This

means that if the joint angle stays within a physiological

range, the error remains zero. For a joint angle trajec-

tory y=[y1...yNstep ]T, and the upper reference trajectory

rupper =[rupper,1 ...rupper,Nstep ]T, and the lower reference

trajectory rlower =[rlower,1 ...rlower,Nstep ]T, the elements of

the error trajectory e=[e1...eNstep ]Tare defined as:

ei=⎧

⎨

⎩

rupper,i−yiif yi>rupper,i

rlower,i−yiif yi<rlower,i

0otherwise

(1)

∀i∈[1...Nstep],

where Nstep isthenumberofsamplesofthemeasured

step.

The effects of applying the resampling to the reference

band of the foot-to-ground angle of a pathological sub-

ject’s gait cycle can be seen in Fig. 4. The introduced

physiological range reference band (upper row) is resam-

pled to the duration of the measured step of the subject

(center left) and the resulting error is shown (lower left).

When looking at the joint angle and the reference it

becomes evident that the motion of the subject follows

Fig. 4 Two methods are proposed to fit the reference bands to the

step of the subject. On the left: the resampling of the reference to the

current duration of the step. And on the right: using dynamic time

warping to adjust the reference to the joint angle of the current step.

The second row shows the measured foot-to-ground angle of a

subject ( ) and the fitted reference bands ( ). The third row

shows the resulting error with respect to the reference bands ( ).

The problematic shift of the joint angle to the reference band

obtained by the first method and the resulting error, is indicated ( ).

The missing dorsiflexion of the subject during the swing-phase is

consistent with the error obtained from the warped reference ( )

almost the same motion as the reference, but is somehow

delayed. The range of motion however is almost identi-

cal, only in the positive plane the motion of the subject

is of smaller range, indicating missing dorsiflexion. Due

to the time shift of the reference to the subject’s angle,

the resulting errors are enormous, suggesting an extreme

amount of push off and dorsiflexion missing in the sub-

ject’s gait. The errors do in no way resemble the subject’s

lack of motion but only the subject’s lag or temporal dis-

tortion of the gait. The aim of the neuroprosthesis is to

support the persons in their individual motions and not

to force them to a completely new pattern. In the previous

works, for example, [26,27], the motion was only rated for

the swing phase and the stimulation was only pulling the

angle in one direction. The reference was also tuned sepa-

rately for each subject. For a general solution, which works

for antagonistic muscle stimulation in all gait phases, a

method that automatically adjusts the reference to the gait

of the individual subject has to be found.

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 6 of 20

Adjusting the reference to the subject’s gait using dynamic

time warping

With the previously presented resampling method, the

reference is sometimes ahead and sometimes lagging in

relation to the measured joint angle, indicating that there

is a problem with the timing of the reference signal.

A well-known method (from signal processing, espe-

cially speech recognition) that addresses the comparison

between two signals that are warped in time, is Dynamic

Time Warping (DTW) [44,45]. By accelerating or decel-

erating the signal time, DTW finds the optimal time

sequence, so that the two signals become the most similar.

This means that a signal can be stretched and squeezed in

the time domain so that it optimally fits to another signal,

while still providing the same sequence of values.

In essence, DTW determines the optimal path in

a matrix in which each element represents the error

between the i’th element of signal 1 and the j’th element

of signal 2. The path through the matrix is a composi-

tion of elementary steps and DTW finds the sequence of

steps which yield the lowest cost. The elementary steps

used in the standard form of DTW are shown in Fig. 5a.

Using these elementary steps allows infinite acceleration

and deceleration of a signal (by going vertical/horizontal)

which can lead to extreme and unnatural results. It is pos-

sible to constrain the solution of DTW: firstly, by limiting

the space where DTW can act inside the matrix (by using

Sakoe-Chiba bands and Itakura parallelograms [44,45]);

secondly, by enforcing a minimum and maximum speed

of time by changing the elementary steps. The first solu-

tion cannot limit the maximum and minimum warping

speed, whereas the second solution is limited by a discrete

selection of steps. The elementary steps which are typi-

cally used with DTW are presented in Fig. 5a. The steps

showninFig.5b limit the warping speed to a minimum of

0.5 and a maximum of 1.5.

Thematrixshowingtheabsoluteerrorsoftwosignalsis

presented in Fig. 6. The participant’s foot-to-ground angle

introduced in Fig. 4is compared to the resampled mean

of the foot-to-ground angle reference presented in Fig. 3.

Fig. 5 Fundamental steps of the dynamic time warping algorithm.

The most common steps (a) allow infinite stretching, whereas the

steps shown in (b) limit the maximum and minimum warping speed

to 1.5 and 0.5, respectively

Fig. 6 The distance matrix between the foot-to-ground angle of one

step of a SCI participant and the mean foot reference angle. Each

sample of the reference is compared to each sample of the

measurement and the distance of the two signals visualized as a pixel

of the matrix. Black indicates no distance and white indicates the

largest distance. The area that can be reached by the DTW is limited

by the chosen fundamental steps. For the steps chosen, the grayed-

out area cannot be reached by the DTW. ( ) is the resulting optimal

warping path and ( ) are two examples of matched samples

The elementary steps from Fig. 5bareused,thisauto-

matically excludes the grayed out area, which can only

be reached by a faster warping speed. The resulting opti-

mal warping path first compresses the reference signal

with the lowest speed possible until the push-off, then

progresses along the valley until terminal swing, where it

stretches the reference with the highest possible warping

speed. If the person, for example, has no distinct dorsi-

flexion during the terminal swing phase, the DTW would

not find a similarity to the foot-to-ground angle of the ref-

erence signal during that phase and would try to skip as

quickly as possible through this section of the reference.

By limiting the warping speed, the DTW cannot skip parts

of the reference that are not showing in the joint angle.

Even when the joint angle does not contain a positive

foot-to-ground angle section, the warped reference will

still contain a (shorter) version of its original section. This

leads to a new reference that adapts to the subject’s gait,

but at the same time enforces the motion of the healthy

reference.

The DTW is always applied to the mean of the joint

angle reference. The obtained warping information is

then applied to the reference band as shown in Fig. 4

(right column). The resulting error now indicates missing

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 7 of 20

dorsiflexion during swing phase, and the warped reference

matches the motion of the participant.

The introduced DTW method can warp a signal in time;

however, the start points of the two signals are defined

to be concurrent, and the same applies to the end points.

Hence, a delay of the joint angle to the reference at the

start point or end point could not be corrected by the

DTW. This problem can be avoided by defining the start

and end points to positions in which the joint angles can

be assumed to be within the reference band. As presented

in the previous subsection, the heel-off event is selected as

a trigger for the knee angle measurement, and the foot flat

event as a trigger for the foot-to-ground angle measure-

ment. With this configuration the foot-to-ground angle

starts at zero per definition and the knee angle can be

assumed to be close to zero.

Resulting gait assessment

The resulting gait assessment procedure is as follows. The

knee angle is cut into heel-off event based cycles and

the foot-to-ground angle is cut to foot-flat event based

cycles. A heel-off event based knee-angle reference band

and a foot-flat event based foot-to-ground angle refer-

ence band was obtained (Fig. 3). These reference bands are

defined by the standard deviations of the measurement of

healthy subjects and are expected to resemble the ranges

of healthy joint angles. For each knee angle cycle and each

foot-to-ground angle cycle the corresponding reference is

resampled to the duration of this cycle. The resampled

reference is then matched to the respective joint angle

using DTW. Fundamental DTW steps were chosen that

limit the allowed warping speed (Fig. 5b). To obtain the

new reference bands, DTW was applied to the mean ref-

erence angle. The upper and lower reference bands are

then warped with the warping information (indexes) of

the warped mean reference angle. The cycle error for

knee and foot-to-ground angle can be acquired using the

respective joint angles and reference bands as defined

in (1).

Basic principles of the neuroprosthesis

The aim of the adaptive neuroprosthesis is to assess each

step of the subject and to adapt the stimulation pattern

for the next step accordingly. The assessment is based on

the knee flexion/extension angle and the foot-to-ground

angle. The stimulation intensity patterns are continuous

signals for all four muscle groups that are stimulated. The

aimistosupportthesubjectduringtheentiretyofthegait,

hence the stimulation patterns span over the entire step

duration and the entire step is evaluated.

For people with remaining sensory function and low

stimulation tolerance levels, the FES can only aid but

never replace the voluntary muscle action. If the sub-

ject is stimulated at significantly different timings than

his natural progression through the gait cycle, the stim-

ulation does not support but disrupt the person. Hence,

in our case, being in sync with the subject’s intentions is

very important. Therefore, the healthy reference bands are

warped to be synchronized with the subject’s gait. Sub-

sequently, the inferred stimulation patterns will help the

subject to reach the same range of motion as the refer-

ence joint angle bands, but cannot help to reach the same

timings.

The gait phases are determined separately for each leg

using the foot-mounted IMUs. This means that the neuro-

prosthesis for one leg is completely independent from the

prosthesis of the other leg. Thus, by simply copying the

soft- and hardware the neuroprosthesis can be extended

from one leg support to double leg support. In this work,

however, due to the wireless bandwidth limitations of the

sensors, we support only one leg (the more affected leg).

As we learned in the previous section, the gait assess-

ment is triggered with the heel-off event for the knee

angle and the foot-flat event for the foot-to-ground angle.

When the gait event arises the gait cycle error of the pre-

vious cycle can be determined for the respective joint

angle. Our aim is to use ILC to determine a stimulation

intensity pattern for the next cycle of the subject by uti-

lizing the previous cycle error. Note that for both, the

knee angle control as well as the foot-to-ground angle con-

trol, two separate stimulation intensity patterns have to be

established due to the antagonistic muscle pairs.

The cycle by cycle assessment, the learning, and the

applying of stimulation are depicted in Fig. 7.Herethe

knee angle cycles, segmented by the heel-off event, and

the foot angle cycles, segmented by the foot-flat event, can

be seen. With each event, the step assessment and ILC is

applied and a new stimulation pattern determined for the

next cycle. Ideally the assessment and generation should

happen in less than one sampling period, so that the new

stimulation pattern can be immediately applied and the

stimulation will not be interrupted. As stated before, when

supporting two legs, a second copy is running in parallel,

as implied by the second layer in the figure.

An issue with the triggered stimulation patterns is that

step cycle duration variations can lead to timing errors

with the stimulation intensity pattern. For example, if a

step of the subject is much faster than previous steps, the

stimulation in the middle of this step comes too late. Much

of the stimulation happens during the swing phase. The

foot-flat event is relatively far from the beginning of the

swing phase compared with the heel-off event. For per-

sons showing big gait variations the current version of the

foot-to-ground angle control can lead to timing errors.

For this group, a second version of the foot control was

introduced and is shown in Fig. 8. The gait assessment is

triggered, as usual, with the foot-flat event, but the ILC is

triggered later at the heel-off event. The error trajectory

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 8 of 20

Fig. 7 The basic workings of the neuroprosthesis: The knee angle is

recorded and, with the heel-off event, passed to the gait assessment.

The ILC learns new stimulation patterns from the resulting error of the

assessment. These stimulation patterns are instantly applied until the

next heel-off trigger (or the end of the pattern). The foot-to-ground

angle control is working equivalently, but is triggered by the foot-flat

event When supporting both legs, a counterpart is running at the

same time for the other leg, using the gait events and joint angles of

this leg

Fig. 8 Second version of the foot control. Due to the duration from

the foot-flat event to the stimulation during the swing phase, timing

problems can arise in persons with irregular gait. This alternative

triggers the stimulation at the heel-off event, which is closer to the

swing phase, to ensure correct timing. This sacrifices the ability for

push-off support since much of the support happens before the

heel-off event

from the gait assessment is shortened by the number of

samples that passed from foot-flat to heel-off, and there-

fore the ILC creates a shorter stimulation pattern starting

from heel-off. This solves the previous timing problems,

at the cost of having no stimulation between the foot-flat

and heel-off event. Hence, most of the subject’s push-off

cannot be supported by stimulation in this case.

ILC design

Two independent ILCs are used to control the antago-

nistic muscle pair of the knee and the foot of one leg.

Each ILC is triggered with a gait event and provided with

the error trajectory of the previous cycle from the gait

assessment. The resulting control signals of each ILC are

transformed into two stimulation intensity patterns for

the two antagonistic muscles, using an input mapping

strategy.

As in previous works [25–27,32,34], a P-type ILC

is used (as thoroughly explained in [29]). In this work,

however, two novel extensions are made: a new control

strategy that is independent of the cycle duration, and an

adaptation to reference bands.

Input mapping

In order to use one Single Input Single Output (SISO)

ILC controller per joint angle, each of the two antagonis-

ticmusclepairshastobemappedtoonecontrolsignal.

This control signal can be positive and negative, whereas

the stimulation intensities of the muscles can be only pos-

itive. Dead zones can be avoided, and some joint stiffness

gained by using cocontraction around the switching zone

of one muscle to the other. A similar mapping was pre-

viously used in [25] and a detailed study of coactivation

strategies can be found in [46]. The mapping is defined by

qa,i=qa0+1

kauiif qa0+1

kaui>0

0otherwise (2)

qb,i=qb0+1

kbuiif qb0+1

kbui<0

0otherwise,

where uiis the control input at sample i,qa,i≥0andqb,i≥

0 are the corresponding stimulation intensities of the first

and second muscle, qa0≥0andqb0≥0arethedead-

zone stimulation intensities for a control input uiof 0, and

ka>0and 1

kb>0 are the stimulation gains in relation to

the control input. This strategy allows cocontraction for

low intensities, and fading to single stimulation for higher

intensities. The input mapping can act as a static system

inverse by setting qa0and qb0to the identified stimula-

tion thresholds of the first and second muscle and kaand

kbto the identified steady state gain of the corresponding

muscle. Having a static system inverse as the input map-

ping means, that the ILC can be tuned to a system with an

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 9 of 20

assumed gain of one and does not have to be customized

for each subject (unlike the input mapping).

The validity of the static system inverse depends on

the identified parameters. Different conditions (for exam-

ple under load in contrast to swinging freely, or flexed

in contrast to extended) can alter the properties of mus-

cle groups. Müller et al. investigated the properties of

the antagonistic knee muscles during different times of

the gait cycle and compared them to a sitting pose [25].

Parameter identification experiments with 5 healthy sub-

jects were conducted during walking and while sitting.

Although noticeable variations of the identified parame-

ters could be observed, it could be shown that the vari-

ations were still within the robustness margins of the

applied ILC. Hence, parameters obtained from a sitting

pose can be used to tune the ILC.

The stimulation intensity used in this publication is

defined in the following way: since the intensity can be

increased by increasing the stimulation pulse width or the

stimulation current, the product of both, the charge, is

chosen as intensity parameter. For a given charge q[μAs],

the stimulation current I[mA] and the stimulation pulse

width pw[μs] are defined as:

I:=200 q,pw:=800 q.(3)

Step duration independent control

The different forms of ILC control as described in [29]do

not account for variable cycle duration. A straightforward

modification is to choose a large enough ILC buffer and,

during each cycle, to fill the error vector with zeros, so

that it fits the buffer size. Seel et al. used this approach

and were able to prove ILC stability (for a fixed refer-

ence) in this case [27]. This approach is a basic, if limited,

way to deal with variable step durations. However, if a

change from a small step duration to a bigger step dura-

tion occurs, this ILC-type will still apply the stimulation

for short steps and has to learn the stimulation pattern of

the now longer steps. Depending on the ILC tuning, this

can take many iterations. This means that until the new

stimulation pattern is learned, the stimulation timings will

be out of sync with the subject’s gait, and the gait will not

be supported and could be disrupted.

To address this problem, we designed an ILC that acts

in the Gait Cycle Percentage (GCP) domain instead of the

time domain. In the GCP domain, independent of the step

duration, the step starts at 0 % and ends at 100 %. The

error from the step assessment is transformed to the GCP

domain, where the learning and storing of the ILC control

signal also takes place. In order to apply the control signal,

it has to be transformed back to the time domain using the

current estimated step duration. Since we cannot foresee

the duration of the next step, the estimation is based on

the duration of the last step. Thus, the learning in the GCP

domain will always be with the correct timings, since the

previous step duration is known. However, the correctness

of the scaling of the control signal is dependent on the step

duration estimation.

The error from the previous cycle is acquired, as shown

in the previous section, using the stepwise fitted reference

bands. The first step is to limit the error, which ensures

that unreasonable errors cannot have too much impact

and also limits the rate of the learning:

ek=+emax

sat

−emax

(ek),ek=[ek,1 ...ek,Nstep,k]T,(4)

where ±emax defines the bounds of the error considered

during the learning, ekis the error vector from the previ-

ous cycle, Nstep,kis the number of samples of the last cycle

and ¯

ekthe limited error.

The purpose of a Q-filter in ILC is to smooth out the

control signal and thereby improve robustness. It was

decided that the Q-filter should be applied in the time

domain (as opposed to in the GCP domain). This ensures

that short steps cannot produce steeper stimulation pat-

terns compared with long ones. Applying the Q-filter and

learning gain to obtain the new difference ukto the

control signal:

uk=λQ¯

ek,(5)

where Qis the matrix of the Q-filter and λthe learn-

ing gain. This difference is now transformed to the GCP

domain.

u∗

k=resamp

NGCP

(uk),u∗

k∈RNGCP ,(6)

where u∗

kis the control signal difference in the GCP

domain, resamp is linear resampling and NGCP is the

number of samples in the GPC domain.

The learning of the new control signal now takes part in

the GCP domain:

u∗

k+1=umax

sat

umin u∗

k+u∗

k,(7)

where u∗

k+1is the control signal for the upcoming cycle

k+1. Since the stimulation intensities are limited to the

preferences of each person, the control signal is limited

in the same way (by choosing umin and umax correctly) to

avoid ILC-windup.

To apply the control signal in the next cycle, it has

to be transformed back into the time domain using the

currently estimated step duration:

u†

k+1=resamp

Nstep,k+1

(u∗

k+1),(8)

where u†

k+1=[u†

k+1,1 ...u†

k+1, ˆ

Nstep,k+1]Tis the control sig-

nal and ˆ

Nstep,k+1the estimated step duration.

One advantage of iterative learning control is that con-

stant time delays can be easily compensated due to the

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 10 of 20

prior knowledge of the error. In the classic ILC this is

done by shifting the error vector ekby msamples. In this

case, after joining the error, the control signal vector is

resampled to the GCP domain and subsequently resam-

pled to the estimated next step duration. Hence, a shift in

the error vector can lead to a different shift in the applied

control signal. Therefore, the control signal u†

k+1has to be

shifted after the resampling is applied:

ˆu†

k+1=⎡

⎢

⎣

ˆu†

k+1,m

ˆu†

k+1, ˆ

Nstep

⎤

⎥

⎦

,(9)

where ˆu†

k+1is the shifted control signal. When applying

the control input during the next step, it can happen that

the step continues for more than ˆ

Nstep −msamples. After

Nstep−msamples have passed, the control input is defined

to be zero. For a constant step duration, this means los-

ing control over the last msamples of the stimulation

trajectory.

Control signal decay

With these new extensions that we have just described,

the ILC is able to produce a control signal that pushes

the system inside of the defined reference bands. How-

ever, when the system stays inside of the reference bands

using a nonzero input, it is impossible to tell if the sys-

tem would also be able to stay within the bands using

a smaller control signal. When applying the ILC to FES

there are many reasons to use only as little stimulation as

is needed. To solve this problem, an iterative way is cho-

sen: for all points in the control signal where the error is

zero at the same point, the control signal is lowered by

a certain amount toward zero. Thus, the control signal

always decays toward zero on points where the error is

zero.

To achieve this, first the error signal is transformed to

the GCP domain:

e∗

k=resamp

NGCP

(ek). (10)

A control signal decay vector d∗

k=[d∗

k,1 ...

d∗

k,NGCP ]Tis defined as

d∗

k,i=

⎧

⎨

⎩

−min(|u∗

k,i|,d)if u∗

k,i>0∧e∗

k,i=0

+min(|u∗

k,i|,d)if u∗

k,i<0∧e∗

k,i=0

0otherwise

∀i∈[1...NGCP],

where dis the amount of decay towards zero with each

cycle. When u∗

k,iis closer to zero than d,itissettozero.

The decay signal is not necessarily smooth, hence it also

has to be Q-filtered to guarantee ILC robustness:

ˆ

d∗

k=Q∗d∗

k, (11)

where Q∗is a second Q-filter matrix, matching to the size

of the signals in the GCP domain and ˆ

d∗

kis the filtered

decay signal.

The learning rule (7) now has to be changed to

u∗

k+1=umax

sat

umin u∗

k+u∗

k+ˆ

d∗

k. (12)

ILC framework

The resulting ILC framework is depicted in Fig. 9.For

the knee angle and foot angle control of one leg, two

independent copies of the established ILC are used. The

knee angle ILC and foot angle ILC are both triggered by

their respective gait events (heel-off and foot-flat). When

triggered they each supply the control input for the next

gait cycle in the gait cycle percentage domain. Together

with the respective trigger event, this control signal is

then resized to the current estimate of the cycle dura-

tion and played back, sample by sample, in real time. The

two real-time control signals are mapped by the respec-

tive mapping strategies into stimulation intensities for the

antagonistic muscle pairs. Here, qa,knee is the stimulation

intensity for the quadriceps muscle, qb,knee the hamstring

muscle, qa,foot the tibialis anterior muscle and qb,foot the

gastrocnemius muscle.

Experimental setup

The proposed neuroprosthesis was implemented,

parametrizedandtestedwithfourpeoplewithanambu-

latory incomplete SCI. For each participant, an automatic

parameter identification procedure was conducted while

sitting. Subsequently, each participant was asked to walk

on a treadmill while wearing the neuroprosthesis. During

this time, the prosthesis was switched on and off in one

minute intervals.

Hardware and software implementation

The hardware used in the experiment was a four-channel

stimulator (Rehamove 3, Hasomed GmbH, Germany),

three 9-DOF Bluetooth IMUs (RehaGait, Hasomed

GmbH, Germany) and a standard PC.

Due to the wireless bandwidth limits of the Bluetooth

IMU sensors, the setup could only assess and stimulate

one leg. Using wired IMU sensors or a different wire-

less implementation would enable a symmetric two leg

version of the neuroprosthesis. In the experiments, the

more affected side of each participant was chosen for

stimulation.

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 11 of 20

Fig. 9 Schematic of the ILC. The knee assessment and ILC are triggered by the heel-off event. The error of the last knee angle cycle gets passed to

the ILC, which generates the new control input. The control input is in the gait cycle percentage domain and has to be resized to the estimate of the

duration of the next cycle. The resized control input is played back sample by sample and transformed to stimulation intensities for the antagonistic

knee muscles. Equally the foot assessment and ILC are triggered by the foot-flat event

The gait phase detection, joint angle estimation,

step assessment and ILC were implemented in Mat-

lab/Simulink (partly using C/C++). The Simulink diagram

was converted to C/C++ code using the Simulink Embed-

ded Coder and run in a soft Linux real-time environment

on a PC. The IMU data was sent from the sensors via

Bluetooth with a frequency of 100Hz. The joint angle esti-

mation and gait phase detection were run at the same

frequency of 100Hz; the ILC and step-assessment was run

with the stimulation frequency of 50Hz. The Stimulator

received and executed stimulation commands via USB at

a constant frequency of 50 Hz. A biphasic pulse form was

chosen in which the two pulses had the current ampli-

tude Iand −Irespectively and each of the pulses the

pulse width pw. Frequencies of 20–30 Hz are often seen as

an optimum for minimizing fatigue [47]. When working

with people with an incomplete SCI or a stroke, the max-

imum achievable force is mainly limited by the person’s

comfort limits. Choosing higher stimulation frequencies

increases the produced force with the same pulse setting

[48]. Due to the potentially low comfort limits, the abil-

ity to generate sufficient force was favored above having

a good fatigue to force trade-off. Hence, the stimulation

frequency was set to a relatively high value of 50 Hz.

At the end of each cycle, the new stimulation patterns

for the next cycle should be instantly calculated. This

means that the DTW calculations, together with the ILC

update, can take a maximum of one sampling instance

50 Hz =0.02 s. Due to the high computational complex-

ity of DTW (approx. O(N2),see[45]), this goal could not

be achieved. A compromise was found in which the ILC

and DTW calculations were done in two sampling steps

(0.04 s) and the stimulation was zero for the first sample of

each cycle.

Participants

Four people with a SCI were asked to participate in a

first test of the neuroprosthesis. The participants were

recruited at the Hospital Nacional de Paraplejicos Toledo,

Spain. The inclusion criteria were: incomplete SCI; at least

three months of clinical treatment and stable clinical con-

dition; age between 18 and 70 years; tolerance to standing;

walking ability with walker and/or crutches without assis-

tance for at least 10 minutes, at a minimum speed of

1 km/h; spasticity in plantar/dorsal ankle flexors and knee

flexors/extensors less than or equal to two of the Modified

Ashworth Scale; and ability to follow instructions.

The exclusion criteria were: peripheral neuropathy that

interferes with the effect of electrical stimulation or con-

traindication; metal implant or implanted medical electri-

cal equipment; antecedents of previous surgeries in the

last six months; comorbidities that affect walking and the

application of electrical stimulation; history of frequent

falls; debilitating disease; alteration of mental functions

that prevent the subject from following instructions; and

refusal to sign informed consent.

All the subjects were informed about the study and

a written consent was obtained before the session. The

experimental study has been carried out after the formal

approval of the local ethical committee of the hospital,

Hospital Nacional de Parapléjicos-Toledo, Spain (C.E.I.C

– 368).

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 12 of 20

Experimental procedure

The positioning of the stimulation electrodes can be seen

in Fig. 1. The following passive gel electrodes (Axelgaard

ValuTrode) were chosen for stimulation: two 5 x9cmelec-

trodes for the quadriceps, two 5 x9cmelectrodesforthe

hamstrings, two oval 4 x6.4 cm electrodes for the tibialis

anterior and two 4 x9 cm electrodes for the gastrocne-

mius. The IMUs were attached using straps and an elastic

bandage for the foot mounted IMU.

Before starting the walking experiment, an automatic

procedure was conducted to identify the ILC parameters

as well as the maximum painless stimulation intensities

for each muscle of the individual participant. First, the

participant was asked to sit on a high surface so that the

concerned leg was able to swing freely. The stimulation

intensity was then slowly ramped up for each channel

until terminated by verbal indication of the participant.

This was repeated three times for each participant. Dur-

ing the procedure the foot and knee angles were recorded

together with the stimulation intensity. From this data,

astaticgainK[°/μAs], a stimulation threshold q0[μAs]

and the maximum stimulation qmax [μAs] for each mus-

cle was determined. This could be achieved by fitting a

piecewise linear curve (constant until the threshold, then

a linear gain) to the stimulation intensity/joint angle data.

In the case that the participant showed very little reac-

tion to the stimulation, q0was limited to a maximum

of 5.00 μAs. For higher values of q0, the constant cocon-

traction stimulation can feel uncomfortable. The esti-

mated static system gain Kwas limited to a minimum of

0.12 °/μAs. Since Kis inverted in the static system inverse

(2), values closer to zero can lead to unreasonable high

and rapidly-changing stimulation intensities. This limit-

ing of q0and Kwas carried out after the parameters were

identified.

The neuroprosthesis experiment was conducted in the

following way. When conducting the experiment we

always chose the foot-flat based version of the foot angle

control first. In the case of timing problems, the experi-

ment was restarted with the heel-off based version. The

participant was asked to stand upright on the treadmill,

this instance was used to define a knee angle of 0°. To

ensure the safety of the participant, all participants were

securedbyaharnessaswellasaccompaniedbyathera-

pist. First, the speed was slowly increased while consulting

with the participant, until a comfortable, self selected,

pace was found. The participant walked then for one

minute without any stimulation. Then, the neuropros-

thesis was activated and the stimulation patterns were

adapted and applied (changing with every gait cycle) for

another minute. This two minute procedure was repeated

until the participant was tired or the therapist declared

the end of the rehabilitation session. After every two

minute repetition, the ILC was reset and started anew

with stimulation patterns of zero intensity. A photograph

oftheactualmeasurementcanbeseeninFig.10.

Parameters

For both, the knee and the foot ILC, the same set of fixed

parameters were chosen (see Table 1). Having a person-

independent set of ILC parameters was possible by setting

the parameters for the input mapping so that the map-

ping resembles the static system inverse. The ILC can then

assume a system with a static system gain of 1. The input

mapping parameters ka,kb,qa0and qb0were set to the

identified parameters of the preliminary ramp identifica-

tion experiment. With this parameterization, and due to

the system inverse, the control signal ˆu†

khas the same

unit as the measurement signal, namely degree, unlike the

actual stimulation intensity signals qaand qb, which are

giveninμAs.

We assumed a delay between the stimulation and joint

angleresponseof0.2s(see“Background” section and

[25–27]). With the sampling frequency of 50 Hz, this lead

to a plant delay of m=10 samples.

Fig. 10 Picture of one of the people with a SCI during the experiment.

The participant is walking on a treadmill. On the right leg, the

stimulation electrodes and IMU sensors are partly visible. A detailed

illustration of the electrode and sensor placement is given in Fig. 1

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 13 of 20

Table 1 For all experiments, the ILC was tuned with the

following parameters

ILC Parameters

Plant delay m10

Max samples Nstep, max 300

GCP domain samples NGCP 200

ILC gain λ1

Decay factor d1

Error limit emax 10°

ILC Qfilter Q: 1st order backward-forward butterworth,

fcuttoff =5Hz

ILC decay Qfilter Q*: 1st order backward-forward butterworth,

fcuttoff =5Hz

The parameters for the individual participants were contained in the input mapping

and set by the automatic parameter tuning procedure

The ILC was limited to allow a maximum of samples per

cycle Nstep, max. With the chosen setup the maximum cycle

duration is 6 s. The decay factor was chosen so that when

the joint angle stays within the reference bands and the

stimulation is at maximum intensity, a complete decay to

zero intensity requires 15 cycles.

The ILC Q-filter matrix was created by composing a

lifted system filter matrix Fof the first Nstep, max impulse

responses of the filter (see [29] for details). To achieve an

acausal backward-forward filtering, the Q-filter matrix Q

was chosen to be FFT.

Since the ILC decay Q-filter Q∗filters signals in the GCP

domain, as opposed to the time domain, there is no mean-

ingful unit for the sampling time. We chose to assume an

average step duration of 1 second, as a consequence the

sampling time is chosen 0.01 s for an NGCP of 200.

Results

For all four participants, the parameter identification was

conducted while sitting, before starting the walking exper-

iment. This procedure took an average of 139 s. For the

first three participants, the joint angles changed signifi-

cantly when ramping up the stimulation intensity, channel

after channel. These three participants showed discom-

fort only at high levels of stimulation or no discomfort at

all. For participant 3, an unusually high level of hamstring

stimulation (10.49 μAs, note the difference from Table 2

in which the parameter q0was limited to 5.00 μAs) was

necessary to induce notable motion. Participant 4 expe-

rienced an increased pain sensation and therefore dis-

comfort was felt at low levels of stimulation intensity (see

Table 2). As a result, no visible motion could be induced

except when stimulating the quadriceps. Table 2shows the

identified parameters from the automatic parameter iden-

tification for each participant. The identified system gains

were set to a minimum of 0.12 °/μAs, to remain within

Table 2 The automatically identified parameters

qa0Kaqamax qb0Kbqbmax

[μAs] [°/μAs] [μAs] [μAs] [°/μAs] [μAs]

Quadriceps Hamstrings

Participant 1 5.00 1.55 12.20 5.00 0.28 10.03

Participant 2 3.28 2.36 8.57 2.10 0.16 14.36

Participant 3 5.00 1.92 18.00 5.00 0.49 20.99

Participant 4 5.00 1.26 9.11 3.84 0.12 10.81

Tibialis Anterior Gastrocnemius

Participant 1 3.25 1.66 8.40 4.23 1.43 7.14

Participant 2 2.24 3.42 11.38 3.05 1.45 12.15

Participant 3 3.70 1.49 13.05 3.89 0.32 15.18

Participant 4 4.29 0.12 6.52 4.23 0.12 5.68

qa0and qb0are the stimulation intensity thresholds of one antagonistic muscle pair,

Kaand Kbthe identified steady state gains and qamax and qbmax the maximum

comfortable stimulation intensities for the individual muscle pair and participant. In

order to translate the given charge (μAs) to the applied current and pulse width,

please refer to Eq. (3)

a reasonable range. Participant 4 could only surpass this

minimum with the quadriceps muscle.

Participant 1 was the most severely affected out of the

four. His weight had to be supported by a harness, and a

therapist walking together with the participant helped sta-

bilizing the torso. Due to the insecurity and shaking of the

leg of the participant during the stance phase, the heel-

off event was triggered multiple times during each stance

phase. This led to triggering of the ILC at the wrong time,

leading to disruption of the gait by the resulting uncom-

fortable stimulation patterns. The output of the gait phase

detection during this measurement is shown in Fig. 11,in

which the back and forth triggering between heel-off and

foot-flat can be observed. The experiment was canceled

due to the inability of the gait phase detection.

With participant 2, when using the foot-flat triggered

ILC for the foot angle, the participant confirmed that

there were problems with the timings and the stimulation

did not feel supportive. The foot ILC had to be switched

to the heel-off triggered version (as described in Fig. 8),

Fig. 11 Gait phase detection issues with participant 1. Due to the

many false positive heel-off detections the ILC was triggered at the

wrong times and the experiment had to be aborted

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 14 of 20

and therefore a push-off support was not possible. For

participant 3 and 4 the foot-flat triggered foot ILC was

used. Participants 2, 3 and 4 confirmed that the stimu-

lation was coming at the right times and felt supportive.

When activating the knee ILC for participant 2, unrea-

sonable stimulation patterns occurred during the stance

phase. Because of this issue, for participant 2, the knee

angle reference band was widened during the stance phase

ascanbeobservedinFig.13 (compared with the orig-

inal reference presented in Fig. 2). For participant 4 the

stimulation limits had to be lowered further during the

experiment due to discomfort.

In Figs. 12 and 13 one example of the knee ILC and

one of the foot ILC is shown during the measurement.

The shown recording of the foot ILC starts shortly before

the ILC is switched on, so that the learning process can

be observed. The upper row shows the measured foot

angle and the generated reference bands; the second row

shows the foot error produced by the automatic gait

assessment. Note that the reference and the error sig-

nal is shown in an acausal way, since the automatic gait

assessment produces the entire reference and error vector

after each step. The stimulation input (seen on the bot-

tom rows) is shown as applied to the participant by the

ILC during the experiment. When looking at the error,

it can be noted that in almost every step, the participant

lacks push-off during the pre-swing phase as well as dor-

siflexion during the terminal swing phase. The applied

stimulation control signal converges step by step to a

fixed pattern.

A similar example is shown of the knee ILC (Fig. 13)

where the stimulation control signal also converges. This

time the assessment suggests too little knee flexion during

swing and the ILC is stimulating the hamstring muscles

during swing with the maximum tolerated stimulation.

As experiments were alternated with one minute of no

FES and one minute of activating the neuroprosthesis,

for each of the minute intervals, the joint angles were

averaged and shown together with their standard devi-

ations. Figure 14 shows the result for participant 2 and

Fig. 15 for participant 3. Along with the mean and stan-

dard deviations, reference bands are shown that were used

in the respective experiments. These reference bands were

warped (by using the same method as in the assessment)

to match the presented mean joint angles. With partic-

ipant 2, the foot dorsiflexion during the terminal swing

phase, as well as the knee flexion during the swing phase

is visibly increased when the stimulation is turned on. For

participant 3, both foot dorsiflexion during terminal swing

and push-off are increased, whereas no improvements can

be seen in the knee angle. In addition to the joint angles,

the mean and standard deviations of the stimulation con-

trol signal are shown below the respective joint angle. The

presented control signal was normalized to the maximum

allowed stimulation intensities. The stimulation patterns

indicate hamstring stimulation during knee flexion for

participant 2, and hamstring stimulation during the stance

phase of participant 2 and 3. The push-off of participant 3

is supported by gastrocnemius stimulation and the termi-

nal swing of participant 2 and 3 are supported by tibialis

Fig. 12 Continuous time experiment data of the foot ILC. The foot-to-ground angle and the stimulation signal are shown as seen during the

experiment. The reference bands and the error signal are plotted in an acausal way, since the assessment for each cycle is done at the end of the

cycle. The shown data is part of the experiment with participant 3. Note that the positive plane of the stimulation control signal was normalized to

the maximum tibialis anterior stimulation intensity qtib

max (13.05 μAs) and the negative plane to the maximum gastrocnemius stimulation intensity

qgast

max (15.18 μAs). Due to the cocontraction mapping strategy, a stimulation control signal of zero still leads to a certain stimulation. The vertical lines

() mark the foot-flat events

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 15 of 20

Fig. 13 Continuous time experiment data of the knee ILC. The knee angle and the stimulation signal are shown as seen during the experiment. The

reference bands and the error signal are plotted in an acausal way, since the assessment for each cycle is done at the end of the cycle. The shown

data is part of the experiment with participant 2. Note that the positive plane of the stimulation control signal was normalized to the maximum

quadriceps stimulation intensity qquad

max (8.57 μAs) and the negative plane to the maximum hamstrings stimulation intensity qham

max (14.36 μAs). Due to

the cocontraction mapping strategy, a stimulation control signal of zero still leads to a certain stimulation. The vertical lines ( ) mark the heel-off

events

stimulation. Due to the low levels of stimulation and the

lacking change of gait, a figure for participant 4 is not

presented.

These results are also numerically presented in Table 3.

The mean Root Mean Square (RMS) error, as well as the

mean minimum and maximum error, are shown sepa-

rately for the times with and without stimulation. Addi-

tionally, the ratio of the RMS error with and without

stimulation is shown. As the RMS error is calculated over

the entire step circle, low values are to be expected since

the errors arise only during short periods (for example,

push-off and terminal swing). With the knee angle, a high

Emax means a lacking knee flexion and a high negative

Emin a lacking knee extension. With the foot-to-ground

angle, a high Emax means a lacking dorsiflexion and a high

Emin a lacking push-off (plantar flexion). Thus, for partic-

ipant 2, the foot dorsiflexion was increased by an average

maximum of approximately 4°, and the plantarflexion was

increased by a average maximum of approximately 2°. For

participant 3 these average maximum improvements were

approximately 3° and 4°, respectively. The knee flexion

of participant 2 was increased by an average maximum

of approximately 4°. No further significant improvements

could be measured. Furthermore, the self selected tread-

mill walking speeds of the participants, as well as the

passed gait cycles are presented in the table.

Discussion

In a first test, four people with a SCI were asked to walk

with the proposed neuroprosthesis. For three of the par-

ticipants, the stepwise-generated stimulation patterns felt

supportive and well timed. For two participants, slight

changes towards the desired reference bands could be

measured; one participant was more severely impaired

which led to a false positive detection of heel-off events

and one participant could not be functionally stimulated

due to high pain sensation.

The automatic parameter identification includes the

essential setting of the participant’s comfort limits and

prevents any manual setting of parameters. With an aver-

age duration of 139 s, it can be realistically included into a

rehabilitation setting.

The measurement with participant 1 was quickly

aborted due to the false positives of the gait phase detec-

tion. The gait phase detection from [39]canbetunedby

many parameters and the problem could have been likely

solved by raising the threshold (αPS) for the heel-off detec-

tion. However, manual tuning of the gait phase detection

is not an aim for a practical setting of the neuroprosthe-

sis. As with the other three participants, the gait phase

detection worked as expected, as the four gait phases were

passed consecutively in the correct order throughout the

experiment.

The proposed gait assessment was able to adapt the

reference joint angle bands to the individual gait of the

participant. The reference bands naturally follow the foot

and knee angle of the participants (as shown in Figs. 12

and 13), and therefore meaningful joint angle errors can

be provided. Matching the reference to the joint angles of

the participant is an organic process that makes a quanti-

tative evaluation difficult. The errors reflecting the typical

drop foot problem during swing phase and the lacking

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 16 of 20

Fig. 14 Mean and standard deviations of the knee and foot joint angles of participant 2 during the first six minutes of the experiment. For the first

minute the neuroprosthesis was turned off, for the second minute it was turned on, and so forth. The joint angles were all resampled to the gait

cycle percentage domain. The green areas in the background are the reference bands that were used during the experiment (for participant 2 a

wider knee reference band was used). The reference bands are fitted to the mean joint angles using DTW similarly to how the reference is fitted to

each individual step in the real-time gait assessment. In this representation, the gait cycle is started with the heel-off event for both the knee and the

foot angle. Below the joint angles, the respective stimulation control signals (mean and standard deviation) are presented. For the knee a positive

control signal implies quadriceps stimulation and a negative signal hamstring stimulation. For the foot control signal, positive values imply tibialis

stimulation and negative values gastrocnemius stimulation. The positive and negative planes of the control signal were scaled to the maximum

tolerated stimulation for the respective muscle of the participant (the values can be found in Table 2)

push-off during pre-swing, as well as the resulting logical

stimulation patterns, indicate a success of the proposed

gait evaluation method.

The knee and the foot ILC converge to a repeating non-

trivial stimulation pattern. When looking closely at the

pattern of the foot (Fig. 12) it can be observed that it

reaches the maximum gastrocnemius stimulation in the

pre-swing phase and toward approximately a third of the

maximum stimulation of the tibialis anterior muscle dur-

ing swing phase. This closely resembles the natural activa-

tion of these muscle groups during gait (see for example,

[49]).

The new stimulation control pattern, which is generated

for every step, is shorter than the expected step duration

due to a time shift to compensate the slow FES dynam-

ics, see (9). Hence, for the last samples of most steps, the

stimulation control signal is set to zero. A sudden change

of stimulation intensity could disrupt the current motion

or could feel unpleasant. Due to the choice of gait events

for the triggering of the ILC (foot-flat or heel-off), we

expected little or no control action during this time. As

canbeobservedinFigs.12 and 13 there was no issue with

sudden drops of the stimulation intensity at the end of an

ILC cycle.

As we have already described, for the knee angle reset

the participants were asked to stand straight and the angle

was defined to be zero in this position. The knee angle

assessment turned out to be very sensitive to this reset.

If the participant slightly hyperextended or slightly flexed

thekneeduringreset,itwashardforthetherapistto

notice. This change of a few degrees often meant that

during loading response and mid-stance, the knee angle

was slightly above or below the reference band, leading

to increased stimulation in this phase. When examining

the recorded joint angle it was hard to see if the angle

was wrongly calibrated or if the gait of the participant

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 17 of 20

Fig. 15 Mean and standard deviations of the knee and foot joint angles and stimulation control signals of participant 3 during the first six minutes of

the experiment. In this representation, the gait cycle is started with the heel-off event for both the knee and the foot angle

deviated from the norm. As we have already mentioned,

the knee reference band had to be widened during the

stance phase for participant 2 (see Fig. 13) to account

for this problem. Widening the reference bands, however,

reduces the FES support during stance phase (a wider

reference leads to a smaller or no error). Consequently,

optimal knee FES support during stance phase is not reli-

ably possible with the current solution. In Figs. 14 and 15 it

is evident that often, the knee angle is below the reference

during stance phase, indicating knee hyperextension. This

lead to a stimulation of the hamstrings during the stance

phase by the ILC. While this stimulation pattern might

seem counterintuitive for weight acceptance, Springer et

al. could show that FES of the hamstrings is beneficial for

people with knee hyperextension [50].

When looking at the knee stimulation pattern in Fig. 13,

aproblemwiththeILCgaincanbeseen.Thestimula-

tion pattern jumps from almost no stimulation in one step

to the maximum amount of stimulation in the next. As

shown in the method section, the error of the ILC is lim-

ited, which means that the amount of input change from

step to step is also limited. The aim of this neuropros-

thesis is to learn a stimulation pattern and to not react

Table 3 Mean values of the RMS error of each step (ERMS) taken

with and without stimulation

Participant 2 Participant 3 Participant 4

Minutes 5 5 7 7 7 7

Status Off On Off On Off On

Knee ERMS [°] 1.58 0.77 2.41 2.42 2.48 2.49

Ron/off [%] 48 % 100 % 100 %

Emax [°] 7.85 3.46 4.83 4.89 3.67 5.38

Emin [°] -0.15 -0.27 -5.02 -5.2 -7.30 -6.35

Foot ERMS [°] 3.78 2.93 3.15 2.03 6.99 6.50

Ron/off [%] 78% 65% 93%

Emax [°] 15.03 10.79 5.33 3.47 21.99 20.30

Emin [°] -2.76 -5.77 -13.23 -8.60 -4.08 -3.92

Cycles 288 625 403

Speed [km/h] 1.3 1.9 1.0

Ron/off is the ratio of (ERMS) with stimulation to without stimulation of the

corresponding participant. Mean maximum error values of each step (Emax)taken

with and without stimulation. Mean minimum error values of each step (Emin)taken

with and without stimulation. The cycles are the total gait cycles passed during the

experiment and the speed is the chosen walking speed on the treadmill by the

participant

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 18 of 20

extremely to a single odd step. This means that the ILC

gain in this scenario was chosen too high by the auto-

matic system identification. As we have explained before,

the ILC gain is chosen for each muscle individually by esti-

mating the static system gain of each muscle. This resulted

in a parametrization of the ILC, which proved not to lead

to the desired ILC learning rate in many cases. A bet-

ter method might be to tune the ILC so that with the

maximum allowed error, the maximum allowed stimula-

tion is reached after a set number of steps (for example,

five). This would also further simplify and shorten the

identification procedure.

In the classic ILC applications, with every cycle the

error is supposed to decrease, eventually reaching a cer-

tain minimum level. When looking at the two examples,

it is evident that the error fluctuates with every step and

does not necessarily decrease. Since the applied stimu-

lation control input was repetitive and well timed, it is

safe to assume that the error fluctuation emerges from

the complex gait process and voluntary muscle interac-

tion. Therefore, it should not be individually analyzed but

rather statistically processed, as was done in Figs. 14 and

15 and Table 3. If the learning gain of the ILC is low

enough, the statistical properties can be smoothed out and

the control signal can converge as it did in the presented

measurements.

In the statistical evaluations of Figs. 14 and 15 and

Table 3, slight improvements of the averaged joint angles

could be observed for participant 2 (knee and foot) and

participant 3 (foot improvements only). These averaged

maximum improvements were in the range of 4°. For par-

ticipant 4, as would be expected with the non-functional

stimulation levels, the joint angles could not be improved.

The increased standard deviations in the minutes with

stimulation can be explained by the slow learning of the

ILC. This slow learning leads to changing stimulation pat-

terns (and therefore reactions) during the first part of the

minute.

Altogether, relatively small statistical changes of the gait

were achieved. However, cyclically decreasing errors or

big angular improvements could not be observed. The

change of, for example, the mean maximum foot error of

participant 2 from 15.03° to 10.79° might not seem like

a big change, but should be seen in the context of the

aim and limitations of the proposed FES neuroprosthesis.

Firstly, it can be seen that, if necessary, the prosthe-

sis increases stimulation intensity up to the maximum

allowed amount (see Figs. 12 and 13). If the maximum

achievable support by FES is reached, if the timing is cor-

rect, any other control strategy can not push the joint

angles further towards the desired gait trajectory. Sec-

ondly, rehabilitation is not a sudden change but a process.

Guiding the pathological gait of a person more towards

the gait of a healthy person is our main aim and can, to

some extent, be achieved by this neuroprosthesis. Pro-

viding the participant with a direct biofeedback that is

not only felt, but that also acts on four important mus-

cle groups of the gait process, can be a step towards

improved rehabilitation. The proposed neuroprosthesis

directly reacts to any change of the gait of the participant

and supplies new customized stimulation patterns with

every step. This dynamic and direct feedback to the partic-

ipant distinguishes this research from the prevalent simple

triggered stimulation approaches.

Conclusion

In this paper the first approach for an adaptive full-cycle

full-leg support FES neuroprosthesis was presented. This

neuroprosthesis can be seen as a next step to the pre-

viously published FES solutions. Learning of stimulation

patterns was already achieved in [26,27,32], in which a

single muscle (tibialis anterior) or a synergetic muscle pair

(tibialis anterior and peroneus longus) were controlled

exclusively during the swing phase. In both cases, the

reference could not adapt to the pace or way of gait of

the participants. In works including the stimulation of

the full leg [11–13,16,18,19], the stimulation patterns

were fixed (in shape and intensity) and could not adapt

to any changes in the gait of the participants (aside from

adaptions to step duration).

A first test was conducted with four people with ambu-

latory incomplete SCI walking on a treadmill. The mea-

sured data showed that the neuroprosthesis could assess

the joint angles and generate suitable individual stimula-

tion patterns for the four targeted muscle groups of the

participants. Two participants reported that they felt sup-

ported by the stimulation at the right times. For those

participants, slight improvements of the averaged joint

angles could be observed. A steady gait and a minimum

level of muscle activation by the FES proved to be essen-

tial for an effective neuroprosthesis; these factors were

not present with the two participants who did not feel

supported by the neuroprosthesis. Remaining problems

include the sensitivity to the knee angle reset, timing prob-

lems in participants with significant gait fluctuations, and

the automatic ILC gain tuning.

Future studies should investigate a two-sided imple-

mentation of the neuroprosthesis on a higher number of

people with a SCI, and a one-sided implementation for

people with a stroke. In the tests presented here, only one

measurement was conducted per participant. However, in

future, measuring over a longer period of time and com-

paring with a control group could show more significant

gait improvement.

A novel method of gait assessment has been proposed

in this paper that allows an immediate continuous joint

angle assessment for each step of the participant. This

method could be applied to achieve automated clinical

Müller et al. Journal of NeuroEngineering and Rehabilitation (2020) 17:36 Page 19 of 20

gait assessment, biofeedback, or gamification of rehabil-

itation training. Future work could investigate recording

different sets of reference joint angles with a bigger num-

ber of subjects, for different age groups, and for a wider

range of walking speeds.

Abbreviations

DTW: Dynamic time warping; EMG: Electromyography; FES: Functional

electrical stimulation; GCP: Gait cycle percentage; ILC: Iterative learning

control; IMU: Inertial measurement unit; R2R: Run to run control; SCI: Spinal

cord injury; SISO: Single input single output

Acknowledgements

The authors would like to acknowledge Axelgaard Manufacturing Co., Ltd., for

donating the stimulation electrodes. We acknowledge support by the Open

Access Publication Fund of TU Berlin.

Authors’ contributions

PM designed and implemented the assessment and control of the

neuroprosthesis, prepared the manuscript and conducted the experiment. TS

led the research project and helped with the development and testing of the

applied methods. AA and JM hosted, organized and assisted the experiment.

All authors provided critical feedback on the manuscript. All authors read and

approved the final manuscript.

Funding

Not applicable.

Availability of data and materials

The datasets used and/or analysed during the current study are available from

the corresponding author on reasonable request.

Ethics approval and consent to participate

The experimental study has been carried out after the formal approval of the

local ethical committee of the hospital, Hospital Nacional de

Parapléjicos-Toledo, Spain (C.E.I.C – 368). All the subjects were informed about

the study and a written consent was obtained before the session.

Consent for publication

Written informed consent for publication was obtained from the participants

involved in the study.

Competing interests

Thomas Schauer ist co-founder of the startup SensorStim Neurotechnology

GmbH which aims at the development of non-invasive stimulation systems.

Author details

1Technische Universität Berlin, Berlin, Germany. 2Universidad Rey Juan Carlos,

Madrid, Spain. 3Instituto Cajal, Spanish National Research Council (CSIC),

Madrid, Spain.

Received: 6 May 2019 Accepted: 31 December 2019

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