On the use of FES to attenuate tremorby modulating joint impedance

Antônio Padilha Lanari Bó, Christine Azevedo-Coste, Philippe Poignet, Christian Geny, Charles Fattal

Abstract— In this paper, we describe a closed-looppathological tremor attenuation system using Func-tional Electrical Stimulation (FES). The proposedstrategy, which is based on the modulation of jointimpedance using FES, was developed after experi-mental evidence was obtained on open-loop trials withtremor patients. The method relies firstly on an onlinetremor estimation algorithm, which also filters thevoluntary motion performed by the patient. Basedon this information, the impedance of the tremblingjoint may be increased accordingly by applying theappropriate stimulation parameters on a pair of antag-onist muscles that act on the joint, thus attenuatingthe effects of tremor. An experimental evaluation ofthe system, which involved 4 healthy subjects and 1tremor patient, is also presented.

I. Introduction

Tremor, which may be defined as an involuntary, ap-proximately rhythmic, and roughly sinusoidal movement,is one of the most common movement disorders [1]. It canaffect the different body parts, but presents particularlyhigh incidence on the hands. Although it is not a life-threatening pathology, it often decreases significantly theperson’s quality of life, since patients present reducedability to perform simple daily tasks, such as drinkinga glass of water or opening a door.

An absolutely effective treatment for pathologicaltremor is not yet available, since current pharmacologicaland surgical alternatives still present limitations withrespect to effectiveness, risks, and costs. A differentapproach is the use of assistive technologies, such asrobotic devices [2], upper limb exoskeletons [3], andthe use of Functional Electrical Stimulation (FES) [4].Nevertheless, the design of active tremor compensationsystems presents several challenges. Such a device mustbe able, for instance, to distinguish between voluntaryand pathological motion and also to react to changes inthe trembling motion, since tremor often presents highlytime-varying dynamics. Furthermore, tremor compensa-tion must be accomplished while minimizing the inducedfatigue, pain, and discomfort.

In his pioneer work [4], Prochazka proposed a single-joint tremor compensation system using FES in which apair of antagonist muscles were stimulated in anti-phase

During this work, Antônio P. L. Bó (e-mail: anto-nio.plb@gmail.com), Christive Azevedo-Coste and PhilippePoignet were with the LIRMM, Montpellier, France. Currently,Antônio P. L. Bó is at the Universidade de Braśılia, Brazil.Christian Geny is with the CHU Montpellier, France. CharlesFattal is with the Centre Propara, Montpellier, France.

with respect to tremor. The controller was designed insuch a way that the closed-loop gain of the system wasmaximized for the tremor frequency. A simple modelof a FES-actuated joint was used, but the possibilityto provide long-term tremor suppression using electricalstimulation was demonstrated.

In this work, however, we are not especially interestedin controlling joint motion to counteract tremor. Instead,we are mainly interested in increasing the FES-inducedjoint impedance in order to reduce tremor amplitudeand also to provide an extra stability to support theperson’s intended motion. This additional impedancemay be provided using FES to co-contract antagonistmuscles, while producing minimum joint displacement.

In preliminary experiments, this alternative has beenevaluated on trials involving tremor patients, where thevalidity of the approach has been confirmed. In theseexperiments, the stimulation levels that provide suitableimpedance for that particular tremor were set manu-ally or in open-loop schemes. An improved closed-loopsolution would require the addition of other features,such as estimation of tremor time-varying intensity anda method to compute the appropriate stimulation levels.In a previous paper [5], both problems were addressed.

In this paper, firstly we describe briefly the neu-romusculoskeletal principles and preliminary open-loopexperiments conducted to validate the approach. Next,the closed-loop tremor attenuation strategy is presented,including both methods of online tremor estimation whilefiltering voluntary motion and the FES controller thatmodulates joint impedance. Section IV presents thenthe experiments designed to evaluate the solution, whichwere conducted on healthy subjects with no neurologicalimpairment, but under the effects of a FES-inducedtremor, and on one tremor patient. A discussion on thepotential advantages and drawbacks of the method closesthe section, while the final remarks are presented in thelast section.

II. Evidence on open-loop experiments

From consolidated knowledge in motor control [6], itis known that humans co-contract their muscles whenperforming specific tasks. Indeed, although it may be asan inefficient approach in terms of energy consumption,simultaneously contracting antagonist muscles is one ofthe strategies employed by the CNS in tasks that requiremore precision and stability, since the joint impedance isincreased.

2011 50th IEEE Conference on Decision and Control andEuropean Control Conference (CDC-ECC)Orlando, FL, USA, December 12-15, 2011

978-1-61284-801-3/11/$26.00 ©2011 IEEE 6498

−0.4

−0.2

0

0.2

0.4G

yro

X [ra

d/s

]

0 5 10 15 20 25 30 35 40−0.4

−0.2

0

0.2

0.4

Gyro

Y [ra

d/s

]

Time [s]

FES off FES offFES on

Fig. 1. Patient 1. Effect of FES with fixed stimulation parameterson tremor intensity. Motion measured in 2 axis are represented.

In terms of musculoskeletal dynamics, increasing jointimpedance without producing any residual joint motionis possible when antagonist muscles deliver the same,but opposing torques to the joint. In this condition,impedance may be modulated by the muscles activationlevel due to either intrinsic and proprioceptive contri-butions to muscle active viscoelasticity [7]. Since thisproperty is also valid for muscles activated using FES, itmay be inferred that artificially inducing co-contractionis one of the simplest strategies to reduce the effects ofpathological tremor.

Simulation studies were conducted to validate themethod [8], but in order to provide experimental sup-port for the strategy, experiments were conducted withpatients diagnosed with Essential Tremor (ET), a pathol-ogy in which tremor amplitude often during voluntaryaction. In these experiments, which were approved bythe local medical research council, a commercially avail-able stimulator (Cefar Physio 4) was used to stimulatemuscles related to the pathological motion presented bythe patient. Since inter-subject variability is high amongpatients, before each trial the muscles were carefullychosen and the corresponding stimulation levels weretuned manually.

In Fig. 1, we illustrate one of the results obtainedwith patient 1, who presentes a mild tremor at thefingers, particularly at the thumb. For that reason, wehave chosen to stimulate the muscles concerned withthumb abduction-adduction (Abductor Pollicis Brevis,APB, and Adductor Pollicis, AP). In the figure we mayobserve the pathological motion measured using a 2-axisgyrometer in periods with and without the compensatorystimulation. Since the stimulation level was tuned man-ually, an Electromyography (EMG) system was used todetect those moments when FES was on.

The data illustrated shows that when no FES wasapplied, tremor was highly variable. However, once thestimulator was turned on and correctly tuned, tremor in-tensity decreased significantly. After the trial, the subjectreported that the extra stability due to the FES-induced

co-contraction was a positive effect. Also, no particularremarks on discomfort due to stimulation were made,which may indicate that using less varying stimulationmay be more comfortable to the patient with respect tothe method presented in [4].

In trials with other patients, other issues related tothe method have became evident, such as problems dueto incorrect placement of the electrodes and the difficultyto effectively evaluate tremor reduction, considering thattremor itself is highly variable. On the other hand, thevalidity of the proposed method has been illustrated onseveral patients.

III. Tremor attenuation strategy

The results described on the previous section indicatethat this approach may be applied to portable FESsystems designed to provide effective functional benefitto tremor patients. Nevertheless, in order to design sucha device, additional capabilities must be integrated to thesystem.

Since tremor is often highly nonstationary, an essentialfeature is to detect tremor onset based on measurementsfrom sensors of motion or muscular activity. Additionally,online tremor estimation while filtering the voluntarymotion simultaneously performed by the patient is poten-tially useful, since more advanced compensation systemsmay be designed. Such algorithm is described in Sec. III-A. The following subsection is devoted to the closed-loop compensation system, in which the tremor stateestimation is used to compute the FES parameters thatwill provide the additional joint impedance in order toreduce tremor amplitude.

A. Online Tremor Tracking

To perform online tremor characterization, but consid-ering that the sensor used for that purpose also measuresthe intentional motion performed, we first assume thatthe measured data may be modeled by

s(k) = st(k) + sv(k) + νs(k), (1)

where st is the tremor component, and sv is the voluntarymotion. s is measured by a motion sensor, which may bean inertial sensor, an optical tracking system, digitizingtablets. νs is an additive white Gaussian noise, νs ∼N(0, σ2s), that represents sensor error.

Different solutions [9], [3] have already been proposedto accomplish the online estimation of both tremor andvoluntary motion from the readings of a noisy sensor.Here, we briefly present a method which was originallypresented in our previous works [10], [11], where a deeperpresentation of this problem may be found.

In our approach, both tremor and voluntary motionare modeled as nonstationary signals. Since tremor maybe seen as a quasi-periodic motion, truncated Fourier

6499

series have been chosen to represent it, i.e.,

st(k) =

Nt∑n=1

[an(k) sin

(n

k∑g=1

ω(g)

)+ (2)

bn(k) cos

(n

k∑g=1

ω(g)

)],

where ω is the time-varying fundamental frequency, anand bn are the coefficients and Nt is the number of har-monics, the model order. νst, an additive white Gaussiannoise, νst ∼ N(0, σ2st), represents modeling errors. ω, an,and bn are time-varying parameters.

Regarding voluntary motion, although it is a slowermovement, it does not present the regular features ofthe tremor motion. Hence, it was modeled as an Auto-Regressive Moving Average (ARMA) model, with fixedfilter parameters tuned to represent the low frequencybehavior assumed for voluntary motion, i.e.,

sv(k)−Nv∑n=1

cnsv(k−n) =

Nv−1∑n=0

dnνsv (k−n), (3)

where νsv is a white Gaussian noise, νsv ∼ N(0, σ2sv ), andNv is the model order.

In order to apply the recursive algorithm to simultane-ously estimate both motions and the tremor parameters,the referred models must be represented in a stochasticstate space form. With respect to tremor representation,the following augmented state vector xt is considered:

xt(k) =[st(k) a1(k) · · · aNt (k) b1(k) · · · bNt (k) ω(k)

]T,

where tremor, xt,1(k), is given by Eq. (2), a static nonlin-ear model, and the other states, representing the time-varying model parameters, are modeled as random walks.Both tremor and its parameters have been explicitlyincluded in the filter augmented state vector due to theinterest in representing individually the uncertainties ofeach model.

Concerning the ARMA model that describes voluntarymotion, in order to reproduce Eq. (3) Nv auxiliary vari-ables αn were used. The filter states related to voluntarymotion, xv, are

xv(k) =[α1(k) · · · αNv (k)

]T,

where xv(k) is given byc1 1 0 · · · 0c2 0 1 · · · 0...

.... . .

...cNv−1 0 0 · · · 1cNv 0 0 · · · 0

xv(k−1) +

d0d1...

dNv−2dNv−1

νsv (k). (4)and xv,1(k) = sv(k). Using this state space representation,process and measurement noises are not correlated. Thisis particularly suitable to the current problem, sincemeasurement noise corresponds to sensor noise only.

To obtain the full state vector, we combine the statesregarding tremor and voluntary motion:

x(k) =

[xt(k)xv(k)

], (5)

from which the total number of states is defined by Nx =1 + (2Nt + 1) + Nv. The respective process covariancematrix, Q, is composed by the individual variances.

Finally, the measurement model is simply given byEqs. (1). Hence, the model presents a linear relation withrespect to the state vector, and its variance r is directlyrelated to sensor noise.

The optimal estimator for linear systems with additiveGaussian noise is the KF. Since the obtained systemis nonlinear, a modification of the Kalman filter forsuch class of problems has been used, the EKF. In theEKF, the Kalman equations are applied to the first-orderlinearization of the nonlinear system around the currentstate estimate [12]. All the parameters and initial esti-mates used to configure the proposed recursive algorithmare available in [11].

Once the tremor model parameters are estimated forevery time-instant, tremor power or intensity may becomputed directly from the coefficients of truncatedFourier series:

Pt(k) =1

4

Nt∑n=1

‖bn − ian‖2, (6)

B. Closed-loop tremor compensation

Here we describe an uncomplicated closed-loop tremorcompensation system which is based on the conceptthat higher FES-induced joint impedance may reducethe effects of more severe tremors. One of the majoraspects within the design of such system is that thecontroller closely interacts with the subject. Due to thatimportant feature, the final goal is not to completelysuppress tremor (the case in which maximum joint activeimpedance would always be the best control action), butinstead to provide the greater functional benefit, whileminimizing total discomfort.

With respect to the control problem itself, the practicaldifficulties that appear when controlling musculoskeletalsystems using FES must be pointed out. Indeed, control-ling such systems using invasive technologies is already adifficult task due to the complexities of muscle action, butseveral other practical issues arise when using superficialelectrodes. For instance, small differences in the elec-trodes positions highly affect the response obtained. It iseven a greater issue if we consider electrical stimulationdiffusion to other muscles. Together, these effects preventthe application of same model parameters on differentexperimental sections. Other time-varying effects mayinterfere also within a single trial, like changes in skin-electrode interface, muscle fatigue induced by FES. Dueto those reasons, FES control and identification remaina challenging domain [13].

6500

Further difficulties arise when FES is applied on sub-jects that have full control of the muscle, such as tremorpatients, since involuntary contractions in reaction tothe stimulation may greatly disturb the output. Unfortu-nately, these effects are hardly absent both for subjectswho are already familiar with FES and those who havenot yet experienced it.

Based on this context, the controller evaluated in thispaper may be seen as a regulator designed to rejectan estimated disturbance (the tremor). However, dueto the issues described above, we have chosen a simplemethod to validate this new closed-loop approach: wehave designed a simple PI controller with anti-windup,while this last feature is due to the actuator saturationwith respect to physiological limits and subject comfort.The controller error is Pt, the tremor severity estimatedby the online tremor tracking algorithm. The control lawis implemented for a particular controlled muscle and thecorresponding antagonist muscle input is given by

ue =MfMe

uf , (7)

to ensure no residual torque will be applied. In the equa-tion, ue and uf refers to the stimulation levels appliedto extensor and flexor muscles, respectively. The ratioMf/Me is related to the maximum torques delivered bythe antagonist muscles and is chosen based on the subjectevaluation of the subjects with respect to the stimulationlimits.

One of the particularities of such a controller is that itmust be able to handle the following situation: since thecontroller error is always positive (there is no Pt < 0), apure PI regulator will wrongly provide additional jointimpedance even if tremor amplitude is within accept-able limits. The solution to avoid this problem is tosuspend the stimulation if tremor severity drops below athreshold. If a measurement of the trembling muscle ac-tivity was available (from surface electromyography, forinstance), a separate estimate of tremor intensity couldbe computed and such routine would be unnecessary.

IV. Experimental evaluation

A. Subjects and FES normalization

In preliminary trials, tests were conducted on 4 sub-jects with no neurological impairment, and tremor on thetarget joint was induced by an independent stimulator.Next, the performance of the proposed closed-loop strat-egy was evaluated on 1 female tremor patient.

Concerning the healthy subjects, 1 female and 3 malesubjects took part in the study. The target joint wasthe wrist, particularly the dorsi/palmar flexion. FES-induced tremor was produced either by stimulating flexormuscles, such as the Flexor Carpi Radialis (FCR) orthe Palmaris Longus (PL), or extensor muscles, such asthe Extensor Digitorum Communis (EDC). Antagonistmuscles chosen to attenuate tremor, such as the Flexor

Fig. 2. General diagram illustrating the experimental setup usedin this work.

Carpi Ulnaris (FCU) and the Extensor Carpi Ulnaris(ECU).

Due to inter and intra-subjects variations concerningelectrically controlled muscles, every experimental ses-sion was preceded by a procedure to identify the ap-propriate stimulation parameters for each muscle. Con-sidering that the stimulator applied in this work allowsonline update of all three traditional FES parameters,the following rules were applied:

• Frequency was fixed for every experiment (30 Hz).• Amplitude was also fixed and its value was chosen

by the subject based on the discomfort produced.Typical values ranged from 15 to 25 mA.

• General stimulation level was controlled by thestimulation pulse-width (PW). Minimum (PWmin)and maximum (PWmax) values obtained accordingto the person’s subjective evaluation were used tonormalize FES control:

PW = (PWmax − PWmin)u+ PWmin, (8)

where u, 0 < u < 1, is the control variable.

B. Setup

The experimental setup may be represented by the Fig.2. The main components are the stimulating, sensing andprocessing units. The stimulator is an 8-channel stimu-lator, the Prostim, designed jointly by the LIRMM andNeuromedics. The main sensor used in the control loopis the IDG-300, an angular rate sensor from Invensense.Both tremor tracking and tremor attenuation algorithmsare executed in a 50 Hz-loop. The whole system iselectrically isolated to ensure the subject’s safety. As anadditional hardware used on the trials involving healthysubjects, a commercial stimulator from CEFAR, thePhysio 4, was used. It produces biphasic square pulses,opposed to the biphasic pulses with capacitive dischargegenerated by Prostim.

6501

0 5 10 15 20 25 30 35 40 45 50 55 60−10

0

10G

yro

[ra

d/s

]

0 5 10 15 20 25 30 35 40−10

0

10

Time [s]

Gyro

[ra

d/s

]

FES attenuation off

FES attenuation on

Fig. 3. Subject A. The top figure illustrates the effects of FES-induced tremor only (starts at 5 s). The bottom figure illustratesanother trial, where FES-induced was kept at the same level, butthe closed-loop FES compensation was activated.

10 20 30 40 50 60 70 80 90 100−4

−2

0

2

4

Time [s]

Gyro

[ra

d/s

]

Tremor off Tremor on

Fig. 4. Subject B. Progressive reduction on tremor intensity withclosed-loop FES compensation. FES-induced tremor starts at 22 s.

C. Results

The proposed tremor compensation strategy was eval-uated using two different methods. Either we have com-pared tremor severity with and without the FES compen-sation system in distinct moments, or the attenuationstrategy was turned on for a brief period during atrembling motion.

Concerning the experiments involving subjects with noneurological impairment, illustrated in Figs. 3, 4, 5, and6, FES-induced tremor frequency was constant duringthe tests. Variations in tremor amplitude have occurreddue to variations throughout time of the subjects’ in-voluntary resistance to the FES-induced motion. Theillustrated data (one for each subject) was chosen tosupport the discussion that is presented in the followingsubsection.

After validation of the closed-loop strategy on healthy

0 5 10 15 20 25 30 35 40−2

−1

0

1

Time [s]

Gyro

[ra

d/s

]

FES onFES off FES off

Fig. 5. Subject C. FES-induced tremor is highly variable,but mean amplitude clearly reduces when the closed-loop FEScompensation system is active (between 10 and 25 s).

0 5 10 15 20 25 30 35 40 45−3

−2

−1

0

1

2

Time [s]

Gyro

[ra

d/s

]

FES onFES off FES off

Fig. 6. Subject D. The closed-loop FES compensation system(active between 10 and 25 s) produces a reduction on tremoramplitude and, once it is stopped, tremor reestablishes.

−0.5

0

0.5

Gyro

[ra

d/s

]

0 5 10 15 20 25 30

50

100

150

200

250

Time [s]

PW

M [us]

FES off FES on FES off

Fig. 7. Patient 1. Effect of the closed-loop FES compensationsystem on a mild tremor at the thumb. The lower figure illustratesthe stimulation level applied to the concerned muscle.

subjects, the same tremor patient whose open-loop re-sults are illustrated on Fig. 1 has participated in onepreliminary experiment. The results are shown in Fig.7. The satisfactory performance of the method was alsovalidated, even considering that the patient presents amild postural tremor.

D. Discussion

In other studies [5], we have already conducted prelimi-nary validation using a quantitative evaluation of averageresults recorded in different trials. Then, here we focuson a qualitative analysis of the approach, consideringmore experimental data is now available. Based on thisanalysis, the first aspect that has to be pointed out isthat the possibility of using this closed-loop strategy toattenuate tremor has been validated, since a reduction ontremor amplitude was observed in every subject. How-ever, a satisfactory performance with respect to tremorintensity requires that all parts of the solution work prop-erly. Indeed, the tremor characterization algorithm hasbeen already evaluated independently [11]. Hence, thediscussion concentrates on the advantages and drawbacksof the tremor compensation approach based on FES-induced joint modulation.

One important issue refers to the transient responseof the controller. For instance, based on Fig. 3 wemay conclude that tremor amplitude is reduced to anappropriate level with a satisfactory response time. Onthe other hand, that would not be the conclusion whenanalyzing the data in Fig. 4. In this case, the performancewas highly affected by the fact that subject B had no

6502

prior experience with FES, and thus the FES limits setsubjectively in the initialization procedure prevented abetter performance. On tests involving other subjectswith previous experience with FES, such as subjectC, this effect may also be observed. In this case, theresults indicate that the joint impedance provided bythe FES system was enough for compensating the weakercomponents of tremor, while faster peaks on tremor werebarely attenuated.

In other trials, particularly the one illustrated in Fig.7, but also in Figs. 5 and 6, another issue is that anoverall reduction on tremor amplitude may be observedeven after the compensation system is turned off. One ofthe possible explanations for this fact is that the subjectsinvoluntarily mimic the behavior of the compensatoryFES system once its effects stops. The reason for suchphenomena may be also related to fatigue or similareffects, since the trembling muscles are often also stim-ulated by the attenuation system. Either way, subjectshave not particularly complained about pain or fatigueduring or after the experiments.

We may also highlight some problems related to theuse of FES-induced tremor. For instance, since only onemuscle is stimulated, a strong stimulation level may causethe limb to deviate from its resting position. Indeed, insome experiments with healthy subjects, tremor had tobe kept in low amplitudes, since increasing the stimula-tion level would naturally reduce tremor intensity due towrist overextension. Another key issue is the diffusion ofthe stimulation to different muscles, which is intensifiedwhen using FES-induced tremor.

Considering specifically the trial with the tremor pa-tient, the behavior of the controller was affected by acombination of the PI gains (which have been chosenpreviously targeting stronger tremors), the FES limits setsubjectively by the patient, and the low tremor intensitypresented in that case. Due to those facts, there was alack of range of possible stimulation levels, causing thesystem to be reduced in practice to an on/off schemetriggered by the detection of tremor. Even in this case,however, the benefit of the compensation system wasevident.

V. Conclusions and Future Works

The design of a tremor compensation system based onelectrical stimulation is a complicated task. Pathologicaltremor often presents great inter-subject variation andtime-varying intra-subject dynamics. Furthermore, mus-cle command using FES is complex, particularly withsurface electrodes. More important, the system must bedesigned to provide functional support for the patient,with unconditional safety and reasonable comfort.

In this paper, we have described the design of asystem capable of providing tremor attenuation usingFES to co-contract a pair of antagonist muscles, thusincreasing the impedance of the target joint. Such asystem is currently able to estimate tremor features in

real-time, while filtering the components from voluntarymotion, and compute the appropriate FES parametersthat modulate joint impedance, while minimizing theresidual torque delivered to the joint. The approach,which had been already validated on open-loop on tremorpatients, has been validated in closed-loop on 4 healthysubjects and 1 tremor patient.

Our future efforts include further development of thedescribed strategy, particularly the design of more so-phisticated experimental protocols and controllers thatmay minimize the drawbacks of the current compensa-tion system. Additionally, we intend to persist in theevaluation of the proposed tremor attenuation systemon tremor patients, focusing also on the choice of thosetremor types and muscular groups that could be moreindicated for the proposed solution.

VI. Acknowledgments

The authors would like to thank the subjects thatparticipated in the research and also the French NationalResearch Agency.

References

[1] K. E. Lyons and R. Pahwa, Eds., Handbook of EssentialTremor and Other Tremor Disorders. Taylor & Francis, 2005.

[2] S. Pledgie, K. E. Barner, S. K. Agrawal, and T. Rah-man, “Tremor suppression through impedance control,” IEEETransactions on Rehabilitation Engineering, vol. 8, no. 1, pp.53–59, Mar. 2000.

[3] E. Rocon, J. M. Belda-Lois, A. F. Ruiz, M. Manto, J. C.Moreno, and J. L. Pons, “Design and validation of a re-habilitation robotic exoskeleton for tremor assessment andsuppression,” IEEE Transactions on Neural Systems and Re-habilitation Engineering, vol. 15, no. 3, pp. 367–378, Sep. 2007.

[4] A. Prochazka, J. Elek, and M. Javidan,“Attenuation of patho-logical tremors by functional electrical stimulation I: Method,”Annals of Biomedical Engineering, vol. 20, no. 2, pp. 205–224,1992.

[5] A. P. L. Bó and P. Poignet, “Tremor attenuation using FES-based joint stiffness control,” in 2010 IEEE InternationalConference on Robotics and Automation (ICRA 2010), 2010,pp. 2928 – 2933.

[6] E. R. Kandel, J. H. Schwartz, and T. M. Jessell, Principles ofNeural Science. McGraw-Hill, 2000.

[7] J. M. Winters and P. E. Crago, Biomechanics and NeuralControl of Posture and Movement. Springer-Verlag, 2000.

[8] A. P. L. Bó, P. Poignet, D. Zhang, and W. T. Ang, “FES-controlled co-contraction strategies for pathological tremorcompensation,” in 2009 IEEE/RSJ International Conferenceon Intelligent Robots and Systems (IROS 2009), 2009, pp.1633–1638.

[9] C. N. Riviere, R. S. Rader, and N. V. Thakor, “Adaptivecanceling of physiological tremor for improved precision inmicrosurgery,”IEEE Transactions on Biomedical Engineering,vol. 45, no. 7, pp. 839–846, Jul. 1998.

[10] A. P. L. Bó, P. Poignet, and C. Geny, “Filtering volun-tary motion for pathological tremor compensation,” in 2009IEEE/RSJ International Conference on Intelligent Robots andSystems (IROS 2009), 2009, pp. 55 –60.

[11] ——, “Pathological tremor and voluntary motion modelingand online estimation for active compensation,” IEEE Trans-actions on Neural Systems and Rehabilitation Engineering,vol. 19, no. 2, pp. 177–185, 2011.

[12] D. Simon, Optimal State Estimation: Kalman, H Infinity andNonlinear Approaches. John Wiley & Sons, Inc., 2006.

[13] C. L. Lynch and M. R. Popovic, “Functional electrical stim-ulation,” IEEE Control Systems Magazine, vol. 28, no. 2, pp.40–50, Apr. 2008.

6503