Friction Compensation in Energy-Based Bilateral Telemanipulation

Michel Franken, Sarthak Misra, and Stefano StramigioliUniversity of Twente, Enschede, The Netherlands

Abstract— In bilateral telemanipulation algorithms based ontime-domain passivity, internal friction in the devices poses anadditional energy drain. Based on a model of the friction, thedissipated energy can be estimated and reclaimed inside theenergy balance of the control algorithm. As long as the estimateis conservative, passivity of the entire system is maintained. Inthis paper we consider two types of friction and discuss theinfluence of two types of measurement noise. Without noisecompensation the dissipated energy is largely overestimated. Acompensation method based on the probability density of thenoise is proposed. This leads to an energy estimate which isalways conservative even in the presence of measurement noiseand does not require additional filtering. Simulation results areprovided that show the increase in obtained transparency whenthis energy compensation technique is applied.

I. INTRODUCTION

A bilateral telemanipulation system, Fig. 1, presents theuser with haptic feedback about the interaction with theremote environment. Such a system is said to be transparentwhen the user has the perception of direct interaction withthe remote environment [8]. This means that the user shouldnot be able to discern the dynamic behavior of the devicesand the controllers themselves during operation. When leftuncompensated internal mechanical device friction at boththe master and slave side can decrease the obtained trans-parency.

Several model-based friction compensation techniqueshave been proposed to decrease the negative influence ofinternal friction on the transparency of the system. Basedon a model of the friction an additional force is computed,which is added to the force computed by the controller. Thisadditional force ”cancels out” the friction force. Examplesconsidering different friction sources and using differentmodels are the work of Bernstein et al. [2], Hayward etal. [7], and Ferretti et al. [4]. Mahvash et al. [10] presentthat such techniques can overcompensate the device friction,which is dangerous as this may lead to stability problems.They introduce a compensation technique for tendon-drivenjoints based on single-state elastic friction models which isguaranteed to be passive and thus overcompensation cannottake place.

The concept of passivity is also used as a design tool forthe entire control structure. Passivity is an elegant solutionto deal with the destabilizing influence of time delays inthe communication channel connecting the master and slavedevice and hard contacts on bilateral control algorithms.

Michel Franken, Sarthak Misra and Stefano Stramigioli are affiliated withthe Institute for Biomedical Technology and Technical Medicine (MIRA).{m.c.j.franken, s.misra, s.stramigioli}@utwente.nl

Communication

Channel

UserMaster

Device

Master

Controller

qu(t)

τu(t)

EnvironmentSlave

Device

Slave

Controller

τrm(k)qrm(k) qrs(k)τrs(k)

τe(t)

qe(t)

Fig. 1. Schematic overview of all the components of a bilateraltelemanipulation system: τ∗ and q∗ represent forces/torques and velocities,respectively. The subscripts u, rm, rs and e represent the user, mastercontroller, slave controller, and environment, respectively.

Time-domain passivity architectures have been proposed inliterature for impedance-type devices (force as an outputcausality) which ensure that the telemanipulation systemremains passive and thus stable. Two examples are the workby Ryu et al. [11] and Franken et al. [5]. Time-domainpassivity of a telemanipulation system implies that all theenergy which is extracted from one side, was injected at theother side. These architectures are usually defined on theinterconnection of the continuous and discrete domain as atthat point the energy exchange can precisely be determined[14]. However, this implies that all the energy which isdissipated due to internal friction in the slave device needsto be injected by the user, irrespective of the chosen controlstructure. This can severely decrease the level of transparencythat can be obtained.

In this paper, we will consider the situation in which theslave device contains a high amount of friction. We willextend the two-layered framework introduced by Franken etal. [5] with a dissipated energy compensation component atthe slave side. This energy compensation will increase thetransparency of the telemanipulation system as the energydissipated internally in the slave device no longer has to beinjected by the user.

The paper is organized as follows: Section II introducesthe two-layered approach to bilateral telemanipulation. Sec-tion III presents the used friction model and the compensa-tion strategy. Section IV discusses the noise sensitivity of thecompensation strategy described in Section III and introducesadequate measures based on the stochastic properties of themeasurement noise to prevent overcompensation. Simulationresults showing the improved transparency with this frictioncompensation technique are presented in Section V. Thepaper concludes and provides direction for future work inSection VI.

II. TWO-LAYERED APPROACH

In this section we will briefly treat the working of thetwo-layered framework proposed by Franken et al. [5]. Theyshowed that it is possible to implement a direct energy

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coupling between the interaction port at the master andthe slave side which is passive irrespective of the timedelays present in the communication channel. This energycoupling can be combined with any control strategy to obtaintransparency of the system. For a full treatise of the theorybehind this framework please refer to [5]1.

The framework consists of two control layers in a hier-archical structure, the Transparency Layer and the PassivityLayer, see Fig. 2. The Transparency Layer can contain anycontrol algorithm that delivers the desired transparency, aslong as it results in a desired torque/force to be appliedto the devices at both sides. These desired torques are theinputs to the Passivity Layer. The Passivity Layer is centeredaround the concept of communicating energy tanks. Anenergy tank is defined at both the master and the slave side.From these tanks motions by the master and the slave devicecan be powered and when the available energy is low, theforces which can be exerted by the devices are restricted. Amodulated damper is defined at the master side to regulatethe energy level in the system. It is activated in order toextract an initial amount of energy, and further additionallyrequired energy, from the user to maintain passivity.

An energy requirement can be detected as the energy levelin the tank available during sample period k + 1, Hm(k + 1),will drop below the desired level of the tank, Hd. Such arequirement can be detect at both sides. The additional force,τTLC , exerted by this modulated damper, d(k), will be

τTLC(k) = −d(k)qm(k) (1)

d(k) =

{α(Hd −Hm(k + 1)) if Hm(k + 1) < Hd

0 otherwise

where qm(k) is the velocity of the master device at sampleinstant k and α is a tuning parameter for the rate at whichthe additional required energy is extracted from the user.

The energy exchange, ∆HI(k), between the continuousand discrete domain for impedance type displays can beexactly computed a posteriori as

∆HI(k) =∫ kT

(k−1)T

τrm(k)qrm(t)dt

= τrm(k)∆qrm(k) (2)

where τrm(k) is the force applied by the actuators duringsample period k, qrm(t) is the velocity at which the actuatorsare moving, and ∆qrm(k) is the change in position of theactuators measured at sample instant k. .

The Passivity Layer contains an algorithm which monitorsand enforces the neutral energy balance of the system:

∆HT (k) = ∆HIm(k) + ∆HIs(k) (3)

where ∆HIm(k) and ∆HIs(k) are the amounts of energyexchanged between the continuous and discrete domain at the

1With respect to the mathematical notation used in this paper we wouldlike to point out the following. The index k is used to indicate instantaneousvalues at the sampling instant k and the index k is used to indicate variablesrelated to an interval between sampling instants k − 1 and k.

EnvironmentMasterDevice

SlaveDevice

User

Passivity

Layer

Passivity

Layer

Transparency

Layer

Transparency

Layer

τTLs(k− 1)τTLm(k− 1)

τrs(k)τrm(k) qs(k)qm(k)

Measurementsslave

Measurementsmaster

Fig. 2. Two layer algorithm for bilateral telemanipulation. The doubleconnections indicate an energy exchange interaction.

master and slave side during sample period k, respectively.∆HT (k) is the change at sampling instant k of the energypresent in the Passivity Layer, HT (k). In [5] the algorithmis explained that allows (3) to be enforced when a commu-nication delay separates the master and slave system so thatsimultaneous information about ∆HIm(k) and ∆HIs(k) isunavailable.

As mentioned in Section I the user should not be ableto discern the dynamic behavior of the devices and thecontrollers during operation. This means that with respectto the energy exchange interaction, the following is desired

Hu = −He∫ t1

t0

τu(t)qu(t)dt = −∫ t1

t0

τe(t)qe(t)dt (4)

where the subscript u and e refer to the interaction pointbetween the user and the master device and between the slaveand the remote environment, respectively. Hu and He are theenergy exchanged between the user and the master deviceand between the slave device and the remote environment.This means that with respect to the desired energy balanceof (4), the device dynamics are still present in the energybalance which the Passivity Layer maintains (3), irrespectiveof the controller in the Transparency Layer.

The exchanged energy, ∆HIs(k) can be divided into threecategories:• Energy injected directly into the environment.• Energy stored as potential/kinetic energy in the device.• Energy dissipated due to friction in the device.

Of these three categories the third poses a problem withrespect to the energy balances of (3) and (4). The dissipatedenergy vanishes from the system and is lost. This means thatwhen the slave device is moving a continuous drain of energyat the slave side occurs, forcing the modulated damper atthe master side to be activated. Even if the slave is movingin free space, the user will experience the force generatedby the modulated damper. Therefore, the activation of themodulated damper decreases the transparency of the systemand the decrease in transparency is related to the amount offriction present in the slave device.

III. FRICTION COMPENSATION

In the previous section we have discussed that frictiondecreases the transparency of the system in the two-layeredapproach as it poses an additional energy drain. However,as the device is known and does not change much duringnormal operation, an estimate of this energy, ∆Hr(k), can

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RemoteEnvironment

NetworkStructure

EnergyDissipation

EnergyStorage

Actuators

τrs(k)

Dissipated EnergyEstimation

H(k)

Hd

∆Hr(k)

∆HIs(k)∆Hms(k)

Passivity Layer

Control Framework Device

Transparency Layer

τT Ls(k − 1)

Fig. 3. Dissipated energy compensation in the Passivity Layer:∆Hms(k) represents the two-way energy exchange interaction betweenthe master and slave system. For clarity only the energy flows are depictedin the Passivity Layer.

be computed. As long as this estimation is guaranteed to beconservative with respect to the physically dissipated energyit can be reclaimed into the energy tank, Fig. 3. Note thatthis procedure only works unconditionally for the slave side.When applied to the master side it should be noted that abuild-up of energy can occur when the slave is moving infree space.

In order to compensate for the energy lost due to internalfriction in the slave system, a model which accuratelydescribes this friction is needed. In literature several frictionmodels have been proposed suitable for various joints and/ormaterials. Here we will assume that the physical frictioncan be represented by a model consisting of both coulomband viscous friction. We furthermore assume that based on agood device characterization the parameters which describethe physical friction are known, or at least a conservativeestimate is available. Although the results presented here arespecific for the chosen friction model, the procedure of Fig.3 can contain any number of friction models.

The friction model containing both coulomb and viscousfriction is given by

Fr(t) = −bcsgn(q(t))− bv q(t) (5)

where bc and bv are the coulomb and viscous frictioncoefficients, respectively.

Using the friction model of (5), the energy dissipated,∆Hr(k), during a sample period, k, can be computed aposteriori at sample instant k. The input for this computationis the displacement of the slave device that has occurredduring the sample period, k. As this computed energy isadded to the energy tank in the Passivity layer it needs to bea conservative estimate. Overestimating the dissipated energywould lead to a breakdown of the passivity ensured by thePassivity Layer, as “virtual” energy is produced in the energyfeedback.

First we will look at the coulomb friction compensation.The power, Pc(t), dissipated due to coulomb friction is

Pc(t) = bc|q(t)| (6)

The integral of (6) during a sample period gives the dissi-pated energy. However, it is not possible to detect a change ofdirection during a sample period. Therefore we must assumethat the sample frequency of the control loop is fast enoughto capture all the dynamic behavior of the slave device. In

that case the energy dissipated by coulomb friction duringthe previous sample period , ∆Hc(k), follows directly fromthe measured displacement as

∆Hc(k) =∫ kT

(k−1)T

bc|q(t)|dt

= bc|∆q(k)| (7)

The power dissipation due to viscous friction is

Pv(t) = bv q(t)2 (8)

As the velocity is not measured at all times, the integralof (8) cannot be explicitly computed. When the averagevelocity during a sample period is used to compute theviscous friction force, an estimate of the dissipated energyis obtained as

∆Hv(k) =∫ kT

(k−1)T

bv∆q(k)T

q(t)dt

= bv∆q(k)2

T(9)

Using the Cauchy-Schwartz inequality it can be proven that(9) is a lower bound of the integral of (8), as shown byAbbott et al. [1]. This means that estimating the dissipatedenergy, ∆Hv(k), by viscous friction based on the averagevelocity is always a conservative estimate of the physicallydissipated energy, ∆Hv(k). Lee et al. [9] have applied (9) fora similar purpose as in this paper. They apply (9) to computethe energy dissipated inside a damped spring-like positioncontroller, whereas in this paper (9) is used to compute thephysically dissipated energy in the mechanical structure ofthe slave device.

IV. NOISE SENSITIVITY

In the previous section we have shown that the dissipatedenergy by coulomb and viscous friction can be estimatedbased on a model of the physical friction and a positionmeasurement. Every position measurement suffers from dis-tortion due to noise. In this section we will look into theeffects of both Additive White Gaussian Noise (AWGN) andquantization noise on the estimates derived in the previoussection.

A. Quantization Noise

Quantization noise occurs due to finite precision withwhich variables can be transformed from the continuous intothe discrete domain. Examples of quantization processes arethe number of pulses per rotation for optical rotary encodersand the number of bits of analog-to-digital converters. Herewe will assume that all values in a range are mapped ontothe boundary values depending on the direction of the signal.The relation between the measured positions, qm(k), and thephysical position, q(k), assuming forward motion is

qm(k) = q(k)− βk∆SZ (10)

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where β ∈ [0..1) and ∆SZ is the step size of the quantizationprocess. This means that the position difference obtained atsample instant k is

∆qm = ∆q(k)− βk∆SZ + βk−1∆SZ (11)

In order not to overestimate the true displacement we cancompensate for the uncertainty introduced by the quantiza-tion of the measured position by assuming the worst casesituation in which βk = 0 and βk−1 ↑ 1. This means that themeasured displacement is reduced with the step size, ∆SZ ,of the quantization process

∆q(k) = sgn(∆q(k))(|∆q(k)| −∆SZ) (12)

This compensation technique was also used by Secchi etal. [13] and can be applied for the dissipation estimationfunctions of both coulomb and viscous friction, (7) and (9),respectively.

B. Additive White Gaussian Noise

Another type of noise often encountered in measurementsystems is AWGN. This noise has a gaussian probabilitydensity function characterized by a standard deviation, ση ,is unbiased µη = 0, and no correlation between consecutivevalues of the noise. AWGN is often used to represent allkinds of disturbances which cannot precisely be defined,e.g. play, misalignment, thermal effects, finite manufacturingprecision etc. [12]

The difference with quantization noise is that it distorts themeasurement in the continuous domain. Even if the device isperfectly stationary a displacement will be measured due tothis noise vector. Introducing the AWGN noise vector, η(k),to the measured position at sample instant k, the measuredposition difference becomes

∆qm(k) = ∆q + η∆q(k) (13)

whereη∆q(k) = η(k)− η(k − 1) (14)

η∆q(k) is the noise term in the obtained position differenceat sample instant k. Combining (13) with the dissipationestimates of (7) and (9) yields

∆Hc(k) = bc|∆q(k) + η∆q(k)| (15)

for the coulomb friction estimate, and

∆Hv(k) = bv∆q(k)2 + 2η∆q(k)∆q(k) + η∆q(k)2

T(16)

for the viscous friction estimate. It is observed from (15)and (16) that the addition of AWGN yields non-conservativeestimates of the dissipated energy. There is always a positiveindependent contribution of the noise.

As this noise has a high frequency with respect to theexpected physical motions of the device, filtering is an optionto reduce its effect. Filtering however will never removeall of the noise and higher-order filters can introduce asignificant amount of phase-lag which will interfere withthe other processes of the Passivity Layer. However, this

negative noise effect can be compensated without filtering.The major problematic noise additions in (15) and (16) arethe absolute and quadratic terms, which can be regarded asbeing independent of the actual displacement. Even thoughthe instantaneous value of η∆q(k) cannot be determined,the long term contribution to (15) and (16) is determinedby the probability density function, f(x), characterizing theAWGN. Using this probability density function the averagenoise contribution to (15) and (16) can be determined.

The probability density function, f(x), of AWGN [6] is

f(x) =1√

2πσ2η

e−x2

2σ2η (17)

where ση is the standard deviation of the noise. The averagevalue of this distribution when the absolute value of the noiseis considered can be obtained by computing

µ|η| =1√

2πσ2η

∫ ∞0

xe−x2

2σ2η dx

=ση√2π

(18)

The average value can also be computed for the quadraticnoise

µη2 =1√

2πσ2η

∫ ∞−∞

x2e−x2

2σ2η dx

= σ2η (19)

Using (18) and (19) and considering that the average valueof η(k)η(k − 1) is zero it follows that

n∑k=1

|η∆q(k)| ≈n∑k=1

2µ|η|

n∑k=1

η∆q(k)2 ≈n∑k=1

2µη2 (20)

if n is large enough.We can use (20) in (15) and (16) to compensate for the

non-conservative influence of the AWGN.

C. Energy dissipation estimation with noise compensation

In the previous sections the influence of two types of mea-surement noise on the energy dissipation estimation functionsof Section III was discussed and a compensation method wasproposed. Each type of noise was treated independently, butin practice the quantization procedure will also influence theamount of the AWGN that is present in the measurement.Applying the derived solutions when both types of noiseare present will make the estimation conservative. As thisis desired it is considered not to be a problem.

Application of (12) and (20) to the estimation functions(7) and (9) yield the following noise compensated estimationfunctions

∆Hr(k) = ∆Hc(k) + ∆Hv(k) (21)

= bc(|∆q(k)| − 2µ|η|) + bv∆q(k)

2 − 2µη2

∆T

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!2

0

2

Po

sit

ion

(m

)

0

1

2

Ec (

J)

Physical

Noise uncompensated

Noise compensated

0 5 10 15 200

20

40

Ec (

J)

Time (s)

Fig. 4. Energy dissipated by coulomb and viscous friction estimation.The plots show that the energy estimation without noise compensation canlargely differ from the physically dissipated energy. Using the compensationtechnique a conservative estimate is obtained for both types of friction.

where ∆Hr(k) is the combined estimated dissipated energy.As the noise compensation can be too conservative when thedevice is not moving the following lower bound is enforced

n∑k=1

∆Hr(k) ≥ 0 (22)

which means that the estimated dissipated energy is alwaysat least equal to zero.

Fig. 4 shows the estimated dissipated energy for a generalsinusoidal motion applied to a damper with arbitrarily chosenfriction coefficients bc = 0.1 and bv = 2, respectively.The regular estimation technique, given by (7) and (9), andthe noise compensated technique of (21) are implemented.The energy estimation procedures are executed at a samplefrequency of 1 kHz Both AWGN and quantization are appliedto the position measurement. A quantizer with step size9.58 × 10−5m was applied and the AWGN had a standarddeviation ση = 5 × 10−4. It is seen that without thenoise compensation the dissipated energy by both coulomband viscous friction is largely overestimated. The energydissipated by viscous friction is especially susceptible tonoise influence and is overestimated by approximately 100%for this small noise vector. Fig. 4 also shows that the noisecompensated estimation functions are indeed conservative.

V. EXAMPLE

In Section IV the negative influence of two types of mea-surement noise on the dissipated energy estimation functionswas discussed and a compensation algorithm was proposed.In this section we will apply this compensation algorithmat the slave side into a full simulation of the framework ofSection II.

A. Model

We will consider the situation where the user is executinga sinusoidal motion with the master device. The master and

slave devices are modeled by

τu(t) + τrm(t) = mmqm(t) + bvmqm(t) (23)τe(t) + τrs(t) = msqs(t) + bcssgn(qs(t)) + bvsqs(t)

where m∗, bc∗, and bv∗ represent the mass, coulomb frictioncoefficient, and viscous friction coefficient, respectively, ofeither the master or slave device. The force exerted by theuser τu(t) is such that

qm(t) = 0.25sin(t) (24)

The remote environment consists of a soft viscoelasticmaterial located at position qw. The interaction force withthis material, τe(t) is given by

pe(t) = qs(t)− qw (25)

τe(t) =

{−kpepe(t)− kde|pe(t)|pe(t) if pe(t) < 00 otherwise

where pe(t) is the penetration of the slave device into theviscoelastic material and kpe and kde are the stiffness anddamping of the material, respectively.

In the Transparency Layer a position-force controller isimplemented. A PD-controller is implemented at the slaveside to synchronize the motion of the slave device with thatof the master and the measured interaction force at the slaveside is set as desired torque to be applied to the master device

τTLs(k) = kps(qm(k)− qs(k))− kdsqs(k)τTLm(k) = τe(k) (26)

The communication channel connecting the master andslave device in this example is ideal (lossless and zero timedelay). Therefore, the energy tanks at the master and slaveside in the Passivity Layer are combined into a single energytank. For this example no additional limiting functions havebeen implemented in the Passivity Layer. Noise with thesame characteristics as in Section IV-C is added to theposition measurement.

TABLE IPARAMETER VALUES USED IN THE SIMULATION

Parameter Value Parameter Valuemm 0.1 kg ms 0.1 kgbvm 0.1 Ns/m bcs 0.1 Nbvs 2 Ns/m qw -0.2 mkps 100 N/m kds 10 Ns/mHd 0.1 J α 100kpe 20 N/m kde 100 Ns/m

B. Simulation results

The simulations have been carried out with the simulationprogram 20-sim [3]. The two-layered control framework isexecuted at a sample frequency of 1kHz. The parametervalues used in the simulation are listed in Table I. Thephysical meaning of the parameters has been discussed inSection II and V-A

Two simulations have been performed. In the first, thetelemanipulation system is operating without the energydissipation compensation proposed in Section IV. In the

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!0.4

!0.2

0

0.2

0.4

Po

sit

ion

(m

)

Master

Slave

0 5 10 15 20!1

0

1

Fo

rce (

N)

Time (s)

Fig. 5. System response of the bilateral telemanipulation systemwithout friction compensation: The modulated damper is continuouslyactivated to compensate for the energy dissipated by the internal friction ofthe slave device causing the interaction force to be masked.

second simulation the user is executing the same motion,but now with the dissipated energy compensation enabled.

Fig. 5 depicts the response of the telemanipulation systemwithout the energy dissipation compensation. The frictionat the slave side causes a position lag with respect to theposition of the master device. A large difference betweenthe interaction force at the slave side and the feedback forceat the master side is visible. This force difference indicatesthat the modulated damper of (1) is continuously activated tocompensate for the energy dissipated internally in the slavedevice. The peak of the interaction force at the slave sidecan be seen in the feedback force at the master system, butit is unlikely that the user will be able to clearly discern thisforce during operation.

Fig. 6 shows the system response when the dissipatedenergy compensation is enabled. The position lag betweenmaster and slave is still present as the controller in theTransparency Layer is not optimized to deal with the frictionforces in the slave system. Now the energy dissipated by thatfriction is reclaimed in the Passivity Layer and no longer hasto be extracted from the user by the modulated damper. Theinteraction forces between the slave device and the remoteenvironment are now much more accurately reflected by themaster device to the user. This indicates a significant increasein obtained transparency. As discussed in Section IV theenergy estimation is conservative and as a result it is notentirely reclaimed. Therefore, the modulated damper is stilllightly activated to compensate for the difference betweenthe estimated and the physically dissipated energy.

VI. CONCLUSIONS AND FUTURE WORK

A compensation technique was proposed for the energydissipated by physical friction in the slave device of a time-domain passive telemanipulation system. By reclaiming thisenergy the transparency of the system is increased. Ananalysis was performed showing that measurement noise,especially AWGN, has an adverse effect on the regular esti-mation functions leading to overestimation of the dissipatedenergy. It is shown that given the probability distribution ofthe noise, a conservative estimate of the dissipated energycan be obtained without filtering.

!0.4

!0.2

0

0.2

0.4

Po

sit

ion

(m

)

Master

Slave

0 5 10 15 20!1

0

1

Fo

rce (

N)

Time (s)

Fig. 6. System response of the bilateral telemanipulation system withfriction compensation: The interaction forces are now discernible at themaster side.

A clear increase in obtained transparency is obtained ina simulation of a time-domain passive bilateral controller.However, the introduced compensation technique is not lim-ited to the used two-layered framework and can be appliedin any time-domain passivity based algorithm.

Future work will focus on implementing this compensa-tion technique on a physical telemanipulation system withhigh internal friction to investigate the increase in obtainedtransparency.

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[13] C. Secchi, S. Stramigioli, and C. Fantuzzi, Control of interactiverobotic interfaces, ser. Springer Tracts in Advanced Robotics vol. 29.New York: Springer-Verlag, 2006.

[14] S. Stramigioli, C. Secchi, A. van der Schaft, and C. Fantuzzi, “A noveltheory for sampled data system passivity,” Proc. IEEE/RSJ Int. Conf.Intelligent Robots and Systems, pp. 1936–1941, 2002.

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