Iterative learning control of drop footstimulation with array electrodes for

selective muscle activation

M. Valtin ∗ T. Seel ∗ J. Raisch ∗,∗∗ T. Schauer ∗

∗ Control Systems Group, Technische Universitat Berlin, Berlin,Germany (e-mail: valtin@control.tu-berlin.de)

∗∗ Systems and Control Theory Group, Max Planck Institute forDynamics of Complex Technical Systems, Magdeburg, Germany

Abstract: Disorders of the central nervous system like stroke often lead to a paresis of themuscles responsible for dorsiflexion and eversion of the foot during swing phase. Functionalelectrical stimulation (FES) is commonly used to improve the foot movement. A preciseplacement of two single surface electrodes on the shank as well as a manual tuning of heel-switch triggered stimulation is required when using standard drop-foot stimulators. In this work,the use of automatically tuned array electrodes for selective nerve/muscle stimulation and theapplication of iterative learning control for adjusting stimulation intensities are investigatedwith the aim to obtain an optimal foot movement. The stimulation effect is observed by meansof two inertial measurement units mounted on the foot and shank, respectively. Two arrayelectrodes are placed over the areas covering the peroneal nerve and the muscle tibialis anterior.A fast identification procedure finds three suitable sets of array elements, forming so-calledvirtual electrodes, in both arrays. Two stimulation channels are established over the threevirtual electrodes. Both channels produce dorsiflexion, but one promotes eversion and the otherinversion. A decoupling matrix is applied to the stimulation intensities of both channels in orderto obtain independent control over dorsiflexion and eversion. Finally, two independent iterativelearning controllers are employed to achieve desired angle profiles. The proposed stimulationand control scheme is initially tested on a healthy person sitting on a table with the shank andfoot free to swing. A tracking RMS error of less than one degree is achieved within six walkingsteps.

Keywords: Iterative Learning Control, Biomedical System, Array Electrodes, MIMODecoupling, Virtual Electrodes, Functional Electrical Stimulation

1. INTRODUCTION

About one million strokes occur each year in the EuropeanUnion (Sudlow and Warlow, 1997). Many people havewalking deficits after a stroke. Ineffective dorsiflexion andeversion during the swing phase (drop foot) is present inabout 20% of ambulatory stroke survivors (Wade et al.,1987). Functional electrical stimulation for correction ofdrop foot was introduced by Liberson et al. (1961). Stim-ulation systems available to patients use either a pair ofsurface electrodes, placed over the peroneal nerve and mus-cle tibialis anterior, or a two channel implanted nerve cuffelectrode, to produce dorsiflexion and eversion during theswing phase of gait. The stimulation is usually triggeredby a simple heel switch. Only one commercially availablesystem involves an inclination sensor at the shank.

The electrode placement for transcutaneous stimulationrepresents a difficult and time consuming procedure. Thestimulation response is highly sensitive, especially to theplacement of the nerve stimulation electrode, and changes

? This work was funded by the German Federal Ministry of Edu-cation and Research (BMBF) within the project APeroStim (FKZ01EZ1204B).

from day to day. To solve this problem, several researchgroups are investigating the use of array electrodes thatallow a more selective nerve and muscle stimulation (Helleret al., 2012; Azevedo-Coste et al., 2007; Elsaify, 2005).Typically, all elements are individually stimulated and thecorresponding foot movements are monitored by sensorsmounted at the foot/shank. Elements with good responsesare used to form so-called virtual electrodes inside thearray electrodes.

None of the commercially available drop foot stimulatorsoffer closed-loop control of the foot movement. The userhas to adjust the stimulation intensity manually to achievesufficient foot clearance in the swing phase. To be on thesafe side, the user is tempted to choose a higher intensitythan necessary. However, this leads to more rapid fatigueof the electrically stimulated muscle, which is a majorlimitation in functional electrical stimulation (FES).

First simple feedback control systems for dorsiflexion havebeen presented in (Negard, 2009; Mourselas and Granat,2000; Hayashibe et al., 2011). While the control methodsused therein yield sufficient foot clearance, they do notguarantee a natural foot motion in form of a desired dor-

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Copyright © 2014 IFAC 6587

siflexion angle trajectory. That this additional objectivecan be achieved by the use of Iterative Learning Control(ILC) was demonstrated in (Nahrstaedt et al., 2008; Seelet al., 2013c) through simplified experiments with healthysubjects and in (Seel et al., 2013a) with stroke patientswalking on a treadmill.

All mentioned closed-loop control approaches require ameasurement of the foot-to-ground angle or of the dor-siflexion angle of the ankle joint, i.e. the angle betweenthe foot and shank. The former can be determined usingan inertial measurement unit 1 on the foot (Negard, 2009).In contrast, determining the joint angle requires a secondIMU on the shank (Seel et al., 2013a), or alternatively a go-niometer (Mourselas and Granat, 2000) or bioimpedancemeasurements (Nahrstaedt et al., 2008). In case inertialsensors are used, the heel switch can be replaced by a gaitphase detection that uses the measured accelerations andangular rates instead (Kotiadis et al., 2010; Negard, 2009;Seel et al., 2013b; Heliot et al., 2013).

This contribution is concerned with the development of adrop foot stimulator that allows, for the first time, controlof dorsiflexion and eversion during the swing phase by twodecoupled iterative learning controllers. The stimulationchannels are realised by automatically tuned array elec-trodes that cover the peroneal nerve and the muscle tibialisanterior. The proposed stimulation and control scheme areexperimentally evaluated with a healthy subject.

2. METHODS

2.1 Experimental Setup

Electrode arrays with 30 and 24 elements are placed overthe areas of the peroneal nerve and the muscle tibialisanterior, respectively. The flexible-PCB based arrays arecustom-made. A single hydro-gel patch (AG702 Stimulat-ing Gel, Axelgaard Manufacturing Co., Ltd., USA) with avolume resistivity of 1500 Ωcm is placed between electrodeand skin covering all elements of an array. In this case,stimulation selectivity is ensured by a limited conductivityof the gel. The element size is 8x8 mm and 12x12 mm forthe nerve and muscle array, respectively. The inter-elementdistance for both arrays is 3 mm in all directions. Fig. 1shows the placement of the two array electrodes.

The slightly modified stimulation system DeltaStim (HA-SOMED GmbH, Germany) (Valtin et al., 2012) is used todeliver monophasic pulses between two virtual electrodes,one per array. Each virtual electrode is formed by anarbitrary subset of array elements with the help of ademultiplexer. The configuration of the virtual electrodesas well as the pulse intensities are manipulated in real-time from a PC running Linux with the Rtai-extension 2 .The controller design and implementation is performed inScilab/Scicos 4.1.2 using the HART-toolbox 3 . This tool-box supports automatic real-time code generation basedon Rtai-Lab. The GUI QRtaiLab 4 is used for signal mon-itoring and parameter updates.1 i.e. typically a combination of accelerometers, gyroscopes, andmagnetometers2 http://www.rtai.org3 http://hart.sf.net4 http://qrtailab.sf.net

muscle arrayelectrode

nerve arrayelectrode

IMUs

Fig. 1. Experimental setup showing the array electrodesand inertial motion units (IMUs) at the left leg.

dorsi-flexioneversion

inversion

adduction

abduction

plantarflexion

α

β

Fig. 2. Definition of fundamental movements of the foot.

When applying monophasic pulses, the majority of muscleaction potentials will be generated under the array actingas cathode (active electrode), especially for a large anodic(passive) counter electrode (Reilly and Diamant, 2011). Allpulses are current-controlled and the injected charge q isdefined as stimulation intensity. The muscle contractionis adjusted by this control signal. The charge itself isdefined as product of the current amplitude I and thepulsewidth pw. In this application, a given charge isequally distributed to pulsewidth and current amplitude(normalised to their maximal values) as follows:

pw =

√q pwmax

Imax, I =

√qImax

pwmax, 0 ≤ q ≤ (Imax pwmax),

where pwmax = 500µs and Imax = 60mA are the chosenupper limits for pulse width and current amplitude.

Two inertial measurement units (IMUs) (RehaWatch, HA-SOMED GmbH, Germany) are mounted on the shank andfoot to determine the dorsiflexion angle α as well as theeversion angle β of the foot. Data are transmitted viaBluetooth from the sensors to the PC.

Since the IMUs are attached in arbitrary orientation to theshank and foot, a calibration movement is used to iden-tify the sensor specific rotation matrices which transformthe 100 Hz measurement data from the sensor coordinatesystems into shank- and foot-related coordinate systems.

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The rotated accelerometer, gyroscope, and magnetometerdata are used to calculate each sensor’s orientation usinga direction cosine matrix (DCM) algorithm. The resultingEuler angles describe the sensor orientations in a commonglobal earth coordinate system. In order to obtain the footdorsiflexion angle α (cf. Fig. 2), the pitch angles from thefoot and shank sensor are subtracted. The eversion angleβ is calculated by subtraction of the roll angles of bothsensors.

2.2 Identification of Virtual Electrodes

The following procedures are carried out automaticallywhile the subject is sitting on a table with the shank andfoot free to swing:

Determine a stimulation intensity for the identifi-cation: In a first step, a suitable stimulation intensity isdetermined which will later be used for identifying goodelements in both muscle and nerve array. The chosenintensity should yield, at least for some array elements,sufficient dorsiflexion without discomfort when stimulat-ing exclusively over these single elements. Usually thedorsiflexion related to nerve stimulation is less than theone related to muscle stimulation. Therefore, we find thisstimulation intensity for nerve stimulation using the entiremuscle array as passive counter electrode while applying asequence of monophasic stimulation pulses to all individualelements of the nerve array in a loop. Every nerve arrayelement is stimulated with three pulses at 25 Hz beforeswitching to the next element. The stimulation intensitystarts at 0.05 µAs and is increased in steps of 0.05 µAs af-ter every completed loop until the continuously measureddorsiflexion exceeds ten degrees. The so found stimulationintensity is called qident.

Identifying suitable array elements: In a second step,suitable elements for the muscle and nerve stimulationare selected. For each array electrode, elements with gooddorsiflexion are identified by applying monophasic pulsesat 25 Hz for 0.5 s with intensity qident to each elementwhile using the entire other array as counter electrode.Monophasic impulses guarantee almost pure nerve andmuscle stimulation, respectively. A pause of 1.5 s is usedbetween the stimulation of the individual elements to allowthe foot to return to the rest position. For both thenerve and the muscle array, the four elements with thehighest dorsiflexion form a virtual electrode, the virtualnerve and muscle electrode, respectively. For the nervearray electrode, a second set of electrodes, which doesnot show a stimulation effect, is identified and used toform a virtual passive counter electrode for the musclestimulation. Based on these results, two time-multiplexedmonophasic stimulation channels are obtained: A musclestimulation channel with the virtual electrode on themuscle as cathode and the virtual passive counter electrodeover the nerve as anode; as well as a nerve stimulationchannel employing the virtual electrode on the nerve ascathode and the virtual electrode on the muscle as anode.The changing polarities guarantee a certain degree ofcharge balance with respect to the entire array electrodes.

Both channels produce dorsiflexion, but muscle stimula-tion promotes usually a small amount of inversion whilenerve stimulation promotes eversion. The stimulation in-

β

α

(αn, βn)

(α, β)(αm, βm)

(αm + αn, βm + βn)

Fig. 3. Theoretically feasible FES-actuated area of dorsi-flexion and inversion/eversion.

tensities of the muscle and nerve stimulation are qm andqn, respectively.

2.3 Decoupling of Stimulation Channels

The two stimulation channels will be statically decoupledto enable independent control of dorsiflexion and eversion.Let q

nand q

mbe the stimulation intensities at which the

foot starts to move. The stimulation intensities qn andqm describe the maximal stimulation intensities that arewell tolerated by the user and that yield enough functionaldorsiflexion. No saturation effects in the foot angles shouldbe visible. For the defined stimulation intensity ranges, alinear static relation between the stimulation intensitiesand the resulting angles is assumed:(α− αβ − β

)=

(cα,m cα,ncβ,m cβ,n

)(qm − qmqn − qn

),

qm≤ qm ≤ qm

qn≤ qn ≤ qn

Here, α and β are the minimal angles observed at minimalstimulation intensities q

nand q

m. A typical feasible region

for α and β is depicted in Fig. 3. In order to identifythe coefficients ci,j , i ∈ α, β, j ∈ n,m, the angles(αm, βm) and (αn, βn) at maximal pure muscle stimulation(qm, qn) and nerve stimulation (q

m, qn) are measured.

Choosing(qmqn

)=

(cα,m cα,ncβ,m cβ,n

)−1(uα − αuβ − β

)+

(qmqn

)=:

(cm,α cm,βcn,α cn,β

)(uα − αuβ − β

)+

(qmqn

)(1)

with the new inputs uα und uβ , statically decouples thesystem. The new inputs must lie inside the rhomboidshown in Fig. 3 to yield unconstrained stimulation inten-sities.

2.4 Iterative Learning Control

Iterative learning control is a method that aims at improv-ing the performance of a system which executes the sametask multiple times. These improvements are achieved bylearning from previous trials/iterations/passes (Bristowet al., 2006). Due to the repetitive nature of gait, ILC isa promising tool for the control of drop foot stimulation.Since we decoupled the stimulation dynamics, two separateSISO ILC problems can be formulated for dorsiflexion andeversion, respectively. Due to the inherent need of datastorage, discrete-time is considered the natural domain forILC analysis (Bristow et al., 2006).

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With ν being the relative degree of the two decoupledsingle-input single-output systems, let

ui,j = [ui,j(1), ui,j(2), . . . , ui,j(N)]T ∈ RN ,yi,j = [yi,j(1 + ν), yi,j(2), . . . , yi,j(N + ν)]T ∈ RN ,vi = [vi(1 + ν), vi(2 + ν), . . . , vi(N + ν)]T ∈ RN

be the lifted signal vectors (i.e. the vectors of N sequentsample values) of the input signals, of the output signals,and of unknown, but iteration-invariant, disturbance sig-nals for both control problems i ∈ α, β, respectively.Furthermore, N ∈ N is the pass length and j ∈ N0 is theiteration/trial/pass index. The output signals of iterationj are yα,j(k) = αj(k) and yβ,j(k) = βj(k), k = 1, · · · , N ,respectively. Angle errors ei,j = (ydi − yi,j) ∈ RN are de-

fined with respect to desired outputs ydi ∈ RN , i ∈ α, β,and the goal of the ILC is to reduce the error (in somenorm) to a small number from pass to pass. To this end,we employ the following input update laws

ui,j+1 = Qi (ui,j + Li ei,j ), i ∈ α, β , (2)

where Qi,Li ∈ RN×N are the so-called Q-filters andlearning gain matrices, respectively.

The Qi-filter matrices are designed in form of non-causalsecond-order low-pass filters with a cut-off frequency of2.5 Hz to obtain smooth stimulation intensity profiles andto increase robustness (Bristow et al., 2006).

Furthermore, a diagonal learning matrix L is used:

Li(λ) := λiI, λi ∈ R, i ∈ α, β.The values of λα and λβ are chosen and adapted exper-imentally based on experience from previous work (Seelet al., 2013c,a).

When implementing the two ILCs, the feasible range forthe reference signals (cf. Fig 3) and control signals, eithertransformed control inputs or original stimulation intensi-ties, have to be taken into account. For the transformedcontrol inputs, we formulate the two ILC update laws asfollows:(uα,j+1

uβ,j+1

)=

(Qi 0N0N Qi

)[(uα,juβ,j

)+

(Li 0N0N Li

)(eα,jeβ,j

)],

where 0N is the zero matrix of dimension N × N . Weexpress the transformed control signal vectors uα,j anduβ,j by the stimulation intensity vectors

qi,j = [qi,j(1− ν), qi,j(2− ν), . . . , qi,j(N − ν)],

i ∈ n,m,and use(

uα,juβ,j

)=

(cm,αIN cm,βINcn,αIN cn,βIN

)︸ ︷︷ ︸

˜C

−1(qm,j − qm1N×1

qn,j − qn1N×1

)

+

(β1N×1

α1N×1

),

where 1N×1 is a ones vector of dimension N × 1 andIN is the identity matrix of dimension N × N . Withthis, we rewrite the above ILC input update law forstimulation intensities. Furthermore, we introduce anti-windup to account for saturation of stimulation intensities.Thereby, the following modified ILC input update law isobtained:

(q∗m,j+1

q∗n,j+1

)= C

(Qi 0N0N Qi

)[C

−1(qm,j − qm1N×1

qn,j − qn1N×1

)+

(β1N×1

α1N×1

)+

(Li 0N0N Li

)(eα,jeβ,j

)]− C

(β1N×1

α1N×1

)+

(qm

1N×1

qn1N×1

)with

qi,j+1(k) = sat(q∗i,j+1(k))

=

qi , q∗i,j+1(k) > qiq∗i,j+1(k) , q

i≤ q∗i,j+1(k) ≤ qi

qi

, q∗i,j+1(k) < qi

∀k = 1, . . . , N, i ∈ n,m.

3. RESULTS

In a series of experiments, which were approved by theEthics Committee at Charite Berlin, we evaluated theproposed stimulation and control system with a healthysubject. The person was sitting on a table with the shankand foot free to swing.

Figs. 4 and 5 illustrate the results for a virtual elec-trode identification, which took 108 seconds. The observedmaximal changes in dorsiflexion/plantarflexion and ever-sion/inversion with respect to the rest position of thehanging foot are plotted for each individually stimulatedelement as a vector. The length of the vector represents theamount of dorsiflexion/plantarflexion. If a vector pointsupwards then dorsiflexion occurred, otherwise plantarflex-ion was observed. Vectors pointing to the left indicateinversion and vectors to the right indicate eversion. Thechosen virtual electrodes are indicated as well.

Fig. 6 shows exemplary stimulation responses for theorginal, non-decoupled system. System inputs and outputsfor muscle stimulation are reported in the left graphs.The results for nerve stimulation are shown in the rightsubplots. The coupling of the stimulation channels isclearly visible. The Relative Gain Array (RGA) (Bristol,1966) is given by

RGAoriginal =

(ρα,qm ρα,qnρβ,qm ρβ,qn

)=

(0.777 0.2230.223 0.777

).

In Fig. 7, input step responses of the decoupled systemwith the new inputs uα and uβ are presented. The corre-sponding RGA matrix is

RGAnew =

(ρα,uα ρα,uβρβ,uα ρβ,uβ

)=

(1.03 −0.03−0.03 1.03

).

The expected decoupling effect can be clearly observed.

The iterative learning control of dorsiflexion and eversionwas tested for simulated swing phases with a duration of1.2 s. A pause of two seconds was inserted between ILCiterations (swing phases) to allow the foot to return to therest position and to delay fatigue.

The learning gains λα and λβ have been set to 0.5 and 0.2,respectively. This value has been chosen based on previousresults for pure dorsiflexion ILC (Seel et al., 2013c).

Figs. 8 and 9 illustrate the performance of the ILCs.The reference profiles for both angles guide the footsmoothly from the rest position to desired positive values

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123456

789101112

131415161718

192021222324

muscle electrode array (left leg)

med

ial

(con

nec

tor

sid

e)

lateral

40virtual muscle

electrode

eversion (β > 0)inversion (β < 0)

plantarflexion (α < 0)

dorsiflexion (α > 0)

Fig. 4. Result of virtual electrode identification in themuscle array electrode.

12345678910

11121314151617181920

21222324252627282930

nerve electrode array (left leg)

60virtual nerve

electrodevirtual passive muscle

counter electrode

anterior (connector side) posterior

Fig. 5. Result of virtual electrodes identification in thenerve array electrode.

of dorsiflexion and eversion. The stimulation starts 200 msbefore the actual foot movement due to the approximaterelative degree ν = 5 at a stimulation sample period of40 ms. It should be noted, that the stimulation intensityqm for the muscle stimulation temporary saturated at6µAs in the shown trials three and five. Despite this fact,convergence to a non-saturated control signal profile wasachieved. The RMS error for both angle profiles decreasedbelow one degree within six iterations.

4. CONCLUSIONS

We proposed the first closed-loop control system for dropfoot stimulation that allows simultaneous regulation ofdorsiflexion and eversion. Virtual stimulation electrodeswithin two array electrodes have been automatically de-termined by monitoring the stimulation effect with inertialmeasurement units at the shank and foot. A physiolog-ical foot movement in the swing phase was achieved bymeans of two decoupled ILCs in a few “walking” steps. Asimple linear static model was assumed for designing the

2

3

4

5

6

7

0 1 2 3

q man

dq n

[µA

s]

Step in qm

qmqn

2

3

4

5

6

7

0 1 2 3

q man

dq n

[µA

s]

Step in qn

qmqn

-10

0

10

20

30

0 1 2 3

Ang

lesα

andβ

[deg

]

Time [s]

Step in qm

αβ

-10

0

10

20

30

0 1 2 3

Ang

lesα

andβ

[deg

]

Time [s]

Step in qn

αβ

Fig. 6. Input step responses of the non-decoupled originalsystem.

-10

0

10

20

30

0 2 4 6

u αan

du β

[deg

]Step in uα

uαuβ

-10

0

10

20

30

0 2 4 6

u αan

du β

[deg

]

Step in uβ

uαuβ

-10

0

10

20

30

0 2 4 6

Ang

lesα

andβ

[deg

]

Time [s]

Step in uααβ

-10

0

10

20

30

0 2 4 6

Ang

lesα

andβ

[deg

]

Time [s]

Step in uβ

αβ

Fig. 7. Input step responses of the decoupled system.

decoupling. The accuracy of this model is questionable,especially for large dorsiflexion angles inside the rhomboidof Fig. 3. However, the reported input step responses ofthe open-loop decoupled system and the ILC results indi-cate the usefulness of this model for moderate dorsiflexionwhich is present during natural foot movements.

The assumption of a constant pass length N will not holdfor real walking. A first step towards an extension of theclassical ILC theory for systems with variable pass lengthhas already been developed in (Seel et al., 2011, 2013c) andcan be used. An investigation of the proposed stimulationand control scheme with stroke patients walking on atreadmill is subject of our current research.

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-5

0

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Dor

sifle

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ref.j = 0j = 3j = 5j = 7j = 9

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