Haptic Interface Transparency Achieved Through Viscous ...haptic/pub/AMO-ET-AL-IJRR-12.pdf · Haptic Interface Transparency Achieved Through Viscous Coupling Abdenbi Mohand-Ousaid,

Haptic Interface Transparency Achieved Through Viscous Coupling∗

Abdenbi Mohand-Ousaid, Guillaume Millet, Stephane Regnier,Sinan Haliyo, and Vincent Hayward

upmc Univ Paris 06, umr 7222, Institut des Systemes Intelligents et de Robotique, Paris, France.

E-mail: [email protected]

Abstract

Electromagnetic drives are subjected to an inher-ent inertia-torque tradeoff that fundamentally limitstransparency: the higher the torque, the higher theinertia. We describe a dual-stage design that is notsubjected to this tradeoff and that is able to approachperfect transparency for human users. It comprises alarge, proximal motor and a small, distal motor toreproduce the transients. The two stages are coupledby a viscous clutch based on eddy-currents that, with-out contact, accurately transforms slip velocity intotorque. Such a system can, in general, be controlledto achieve a variety of objectives. Here, we showthat an advanced, discrete-time, rst polynomial pole-placement controller can achieve near-perfect trans-parency. Experimental validation evaluated the hu-man ability to detect small haptic details when usingthis drive and compared it to when using a conven-tional, single-motor interface.

KEY WORDS—Electromagnetic drives, discrete-domain pole placement, haptic interfaces

1 Introduction

The ideal haptic device has no mass, infinite band-width and can supply unlimited force or torque. Inhaptic device design, the actuator, or ‘prime mover’,is often a limiting element, followed by mechanicaltransmissions and structural elements which all re-strict the range of signals that can be transmittedto a user (Morrell and Salisbury, 1997; Hayward andAstley, 1996).

Given a particular actuator, no matter how welltransmissions and linkages are designed, these ele-ments can only degrade key aspects of performancethat include the dynamic range, i.e. the ratio of thelargest to the smallest specifiable force, the stiffnesslinking the prime mover to the manipulandum, or theend-point inertia. In order to cope with these practi-

∗The final, definitive version of this paper published bySAGE Publications Ltd, All rights reserved. c©V. Hayward

cal limitations, human sensorimotor performance canbe used as a factor to bound the desired performance.

One aspect of human performance that is relevantto device design is the smallest detectable force, since,ideally, this quantity should match the smallest forcethan can be commanded by the device. At the up-per end of the range, the largest force should matchthe motoric output of the hand. Ideally, the dy-namic range of the device should be achievable overthe whole frequency range available to touch, that is,from dc to, say, 1 kHz.

While actuator saturation (short and long term)is the factor that determines the upper limit of therange, the lower limit merits discussion. When a ma-nipulandum interacts with a hand, it is subject toseveral forces.1 Neglecting the effect of internal elas-tic forces, that is, if the device operates below its firstresonant mode, these forces are:

a, the actuating force, typically a Laplace force de-veloped in the motor windings;

b, forces due to induced currents which oppose mo-tion;

c, forces due to mechanical losses: viscosity, friction;

d, inertial forces to which moving parts are sub-jected;

e, the force applied by the hand which include atleast an inertial component, a viscous compo-nent, and an elastic component, due to the move-ment of tissues.

According to Newton’s second law, all these forcesmust balance. In the above list, it is well known tohaptic device designers that all these factors play asignificant role in the total result. To illustrate thetradeoffs involved, direct-drive, friction-free floaterdesigns pay the price for nearly absent losses by largeend-point inertias due to necessity to actuate againstgravity (Berkelman and Hollis, 2000).

1for brevity, no distinction is made between forces andtorques.

Authors’ submitted copy, published in the International Journal of Robotics Research, 31(3):319–329, 2012.


We therefore desire a transducer able to commanda desired force at the interface between a manipulan-dum and the soft load represented by a finger thatcan minimize all parasitic forces. Informally, an ide-ally transparent device should be such that a ≈ e andthat b, c, and d in the above list can be neglected.An estimate, developed further later, shows that theend-point inertia should be on the order of grams, nothundreds of grams, which is the standard in today’sdevices. We also desire that this force be accuratelyproduced, not only at dc, but over a wide frequencyrange, up to one kilohertz.

In this article, we first develop target performancefigures that result from the above considerations, andpropose a dual-stage drive architecture that has thepotential to meet these targets and we describe thedesign of its key elements. We then describe a con-trol design performed in the sampled-data domain inorder to maximize accuracy. Lastly, we tested humanperformance gained when using this device. To thisend, we asked participants to perform a foreground-background signal detection task and compare the re-sults with those obtained with a single-stage design.

2 Haptic Transparency

Achieving haptic transparency depends on reduc-ing the parasitic forces under the smallest human-detectable force under all desired operating condi-tions. Seen from the viewpoint of the hand, we desirethe device to have a mechanical impedance (the ra-tio of force over displacement and derivatives) that issignificantly smaller than that of the fingertips sincethen, the deformation of the tissues would not bethe result of parasitic forces, but predominantly fromcommanded forces.

Some target values were suggested by Millet et al.(2009) to specify the characteristics of a haptic inter-face that can operate at the limits of human perfor-mance, see also (Baud-Bovy and Gatti, 2010). Thesenumbers, reported in Table 1, are arrived at by con-sidering that when the hand actively interacts withthe handle, parasitic forces should be at threshold,thus not interfering with the Laplace force producedby the motors.

It is worth noting that the dynamic range from thelowest to the highest specifiable force covers four or-ders of magnitude and that the achievable dynamicrange of a high-quality dc motor is only about twoorders of magnitude. It is clear that a single standardelectric motor, the actuator of choice when buildingimpedance-based haptic devices, cannot meet our ob-jectives.

Table 1: Target performance figures with a 70 mm diam-eter handle (Millet et al., 2009).

Quantity Value Equiv. angular Value

Massa 0.5 10−2 kg 6.1 10−6 kg·m2

Viscosityb 0.5 10−1 N·s/m 6.1 10−5 N·m·s/radFrictionc 1.0 10−3 N 3.5 10−5 N·mMax. forced 5.0 N 1.8 10−1 N·mRise-timee 1.0 10−3 sa from largest acceleration and lowest statically detectable forceb from largest velocity and lowest statically detectable forcec from lowest dynamically detectable force (reversal transients)d obtained from common sensee obtained from vibrotactile performance

2.1 Related Approaches

Perhaps the oldest motivation for dual-motor designsis the desire to modulate the intrinsic dynamics ofan actuated joint to imitate the antagonist action ofskeletal muscles. Sugano et al. (1992); English andRussell (1999); Stramigioli and Duindam (2001) de-scribe efforts aimed at modulating elasticity with elec-tric motors, and Boulet (1990) describes the modula-tion of viscosity with hydraulic motors. These ideashave evolved to be included in the design of robotsthat can interact with people, see (Bicchi et al., 2008).

In the symbolism of Fig. 1, a rectangular box rep-resents an inertia, two parallel lines represent a con-trollable source of force, typically a Laplace force, acoil represents a spring, a piston represents a damper,a small circle represents the load, and a mechanicalconnection represents a common velocity on each side.Lack of space prevents us from commenting on thevarious control options afforded by each design ar-rangement.

a

b

c

d

f

g

h

je

i

Figure 1: Several ways one or two motors can beencoupled to a load. See text for discussion. Combi-nation j is adopted for the device described in thepresent article.


The first case, a, is important because it mod-els most actual haptic devices, since the preferredmethod of construction calls for grounding the actu-ators. There is an elastic element between the motorand the handle. If elasticity is built-in by design, wehave the so-called “series elastic actuators” intendedto be employed in closed-loop (Pratt and Williamson,1995; Lauria et al., 2008). In haptics, one wouldrather make the transmission as stiff as possible toraise the system’s natural frequency.

The next configuration, b, corresponds to the stan-dard, variously called coarse-fine or mini-macro ma-nipulator design (Sharon and Hardt, 1984; Sharonet al., 1988; Salcudean and An, 1989; Khatib, 1990;Hollis et al., 1991). Here, a large motor ‘carries’ asmaller one, but both share the same load since theyare on the same load path. Such a scheme has beenadvocated for haptic devices (Stocco and Salcudean,1996; Wall and Harwin, 2001). With proper control,this configuration can reduce the apparent inertia ofthe whole system but the small motor must be ableto bear the whole brunt of the load. Addressing thislimitation naturally leads to an arrangement, c, de-scribed by Morrell and Salisbury (1997), and appliedto making human-friendly robots and force feedbackdevices (Zinn et al., 2004, 2008).

The large motor supplies the largest portion of theforce and the small motor “fills-in” during transients.With proper control, the user is exposed to the inertiaof the small motor but not that of the large. A variantdesign is proposed in (Conti et al., 2007), where thelarge motor is replaced by a passive brake.

More generally speaking, the haptic designer coulduse all three types of mechanical coupling: elastic, dis-sipative, and inertial, suggesting configuration d. Infact, it is by inertial coupling that portable phones,gaming pads or more advanced transducers oper-ate (Yao and Hayward, 2010).

Option e can achieve an effect similar to that ofarrangement c but introduces another tradeoff if thedisplacement of the distal motor is limited, since iner-tial coupling establishes a quadratic dependency be-tween this displacement and the lowest frequency atwhich is can operate.

Dissipative forces can also be used to achieve de-sirable couplings. The counterpart of case a, case f,is described by Chew et al. (2004) for robotic appli-cations. It is not appealing for haptics since coupledto elastic load like a hand, this coupling will intro-duce an attenuation of 6 dB/octave in addition to the12 dB/octave attenuation due to the motor inertia.

We could then think of yet another option, g, to‘take up’ the response in the high-frequency, but sim-ilarly to b, this configuration would solve this problemby creating another. Option h is worth mentioning

since it can be used to generate distortion-free hap-tic information up to 100 Hz but does not operateat dc (Campion et al., 2008). Arrangement i wouldsuffer from the same difficulties as e.

This enumeration naturally leads us to the last de-sign, j, that could compete with the elastic couplingof configuration c. A comparison between the twooptions is carried out in the next section.

2.2 Discussion

Elastic couplings have the property of storing energy.This property is an advantage in applications whereenergy storage and restitution is a desirable property,such as in a walking machine, but in haptics, energystorage is inconvenient, even hazardous.

An elastically coupled drive system must be wound-up to output a torque. If the output torque needs tobe brought to zero abruptly, for instance when break-ing contact with a virtual wall or when letting go ofthe handle during interaction, the limited speed ofcoupler unwinding forces a delay in the regulation ofthe output torque since this torque is two integralsaway from the displacement of the motor. Moreover,the stored elastic energy could be uncontrollably con-verted to output kinetic energy, causing a hazard.

With viscous coupling the proximal stage mustspin, also storing energy but in kinetic form. This en-ergy cannot be transferred at the output transientlysince the coupling naturally dissipates energy in it-self, rather than in the user, without any need foractive control. In contrast with the elastic couplingcase, the energy storing quantity—velocity—is onlyone integral away from the output torque.

The basic servo mechanism that must govern theproximal stage is velocity control, which is easier tosynthesize than a position servo since the system hasone fewer order. The proximal stage can react morequickly than in the case of an elastic coupling, re-ducing the reliance on the distal stage to produce anaccurate output torque.

There are other advantages of the viscous couplingover the elastic coupling, chiefly among them is ac-curacy. Dual-stage designs produce accurate outputtorques because, in essence, they are force-feedbacksystems. In the elastically coupled case, the feedbackcontrol system must regulate the spring deflection. Ifthe elastic element is not of stringent quality, therecould be hysteresis and high-frequency modes. Moregenerally speaking, viscous coupling enjoys the gen-eral advantage of precluding the occurrence of struc-tural dynamics present in any mechanical system hav-ing elastic elements.

With viscous coupling the onus is also on the cou-pler to provide an accurate relationship between dis-


placement and torque. Due to the absence of con-tact, the main source of the injurious properties ofmechanical systems, couplers based on eddy-currentinduction create resistive torques that are exactly pro-portional to the relative slip velocity. At very highvelocities, the viscous coefficient decays, see the dis-cussion in Section 3.2.1.

3 Prototype Drive

We now describe the system depicted in Fig. 2. Theobjective was to prototype a haptic interface that issuch that, seen from the handle, the system’s appar-ent mechanical impedance is small, but the torquethat it can deliver is large. The result is a very high-performance system that closely meets the goals listedin Table 1 and thus is close to achieve perfect trans-parency.

proximal position encoder

distal position encoder

Ø35 mm motor

Ø16 mm motor

eddy-current viscous coupler

handle

Figure 2: Prototype realized according to strategy j.

3.1 Design Parameters

The quantities that participate in the performanceare:

J1: the inertia connected to the proximal shaft thatincludes the proximal rotor and the clutch induc-tor;

J2: the inertia related to the distal axis that includesthe rotor of the distal motor, the clutch arma-ture, and the handle;

b: the coefficient of viscosity of the clutch.

Rapid changes in torque benefit from a short timeconstant for the proximal stage. This stage can berepresented by a first-order system with a time con-stant equal to the ratio of its inertia to the viscosity ofthe clutch. Reducing inertia and increasing viscosityimproves the capacity of the proximal stage to effectrapid torque changes without the help of the distalstage.

Achieving precise output torque requires the per-turbing torque caused by friction to be minimized.In open loop, the inertias of both stages should beminimized. In closed loop, however, the inertia of theproximal axis can be hidden, since the energy neededto back-drive the system is supplied by an externalsource—the electronic amplifier, and not by the load.

The control is based on the estimation of the rela-tive speed of the two shafts and can suffer from quan-tization effects. For a given torque transmitted by theclutch and a given quantization resolution, a higherviscosity decreases relative speed and thus the sig-nal/noise ratio. These conflicting requirements re-quire the use of high-resolution encoders or of a stateobserver.

In all cases, a design generally benefits from min-imizing the inertia of the distal stage, J2, as well asminimizing the time constant of the proximal stage,J1/b.

3.2 Analysis

3.2.1 Design Criteria Approximations

The quantities J2 and J1/b are affected by the me-chanical and magnetic characteristics of the cou-pler. An eddy-current coupler has more parametersto optimize than a brake. There are two rotors: apermanent-magnet inductor and a disc armature. Amultiple-loop magnetic circuit was designed accord-ing to the guidelines found in (Gosline and Hayward,2008) and from the results of the prototype describedin (Millet et al., 2009). Figures 3a and 3b illustratethe adopted geometry. As seen in Fig. 3b, a multiplic-ity of closed magnetic circuits create a periodic mag-netic flux that crosses the annular armature mostlyorthogonally. As a result, relative movement induceseddy-current loops as represented in Fig. 3c.

The analysis of the two optimization criteria, J2and J1/b, provided insight regarding the critical de-sign parameters. The geometric parameters are de-fined in Fig. 3b and 3c. The first criterion, J2, isthe sum of the inertias of the armature, the rotor ofthe distal motor, and the handle. Provided that thewidth of the armature wa is much smaller than itsmean radius r, to good approximation,

J2 ≈ 2πρatawar3 + Jr2, (1)

where ρa is the mass density of the armature, ta isits thickness, and Jr2 is the inertia of the distal ro-tor plus that of the handle. The mean radius of theclutch cubically scales the inertia of the armature, soit should be kept small. In our prototype, the handleaccounts for about two thirds of J2 and the armaturefor one third.


a b

c

J

Bv

r

ta

tf

wa

tm

wm

iron annulus

magnets

armature

lm = wf

g/2

Figure 3: Eddy-current viscous coupler. a, Cutawayview of the coupler. b, Magnetic flux density stream-lines generated by the magnets. c, Current densitystreamlines in the mid-plane of the armature duringrelative movement.

The second criteria to minimize is the time constantof the proximal stage J1/b where 2n magnets, twoiron annuli, the rotor of the proximal motor, and themagnet holder participate in the moment of inertia.Considering that the width of the annuli, wf , and thelength of the magnets, lm, are much smaller than themean radius, r, the inertia is approximated by

J1 ≈ 2nlmwmtmr2ρm + 4πwftfr

3ρf + Jr1 (2)

where ρm and ρf represent the mass densities of themagnets and of the annuli, tm and tf their thicknesses,respectively, and Jr1 is the inertia of the proximalrotor plus that of the magnet support.

The modeling of the magnetic field and induction incomplex geometries is difficult because it involves sev-eral nonlinear phenomena (Balakrishnan et al., 1997;Heald, 1988; Srivastava and Kumar, 2009). Never-theless, several simplifying assumptions can be madeto find a closed-form expression that estimates theviscosity of the clutch. When the armature rotatesrelatively to the magnets, the magnetic field, B, in-duces an electrical field, E = v × B, orthogonal toB and to the linear velocity v. Following the reason-ing of Wouterse (1991), an approach to estimate thecurrent density induced in the armature is to supposethat the return path around the magnet is of negli-gible resistance. The current density induced undermagnets is then J = σav × B, where σa is the ar-mature’s conductivity. Assuming that B is uniformthrough the volume of the armature covered by mag-nets and is sufficiently greater than the magnetic fieldinduced by the eddy currents, the power dissipatedby the eddy currents can be computed by integratingthe currents over the volume of the armature that is

covered by magnets,

Pdiss =1

σa

∫|J |2 dV ≈ nσatalmwmr

2B2mω

2, (3)

where n is the number of magnetic loops and Bm

the magnetic field produced by the magnets throughthe armature. The coefficient of viscosity, b, is thenapproximated by

b ≈ nσatalmwmr2B2

m. (4)

That the viscosity coefficient is independent of the ve-locity follows from the assumption than the magneticfield induced by eddy current can be neglected com-pared to Bm, which is borne out at low speeds (An-war, 2004). For the present prototype, this assump-tion breaks down at high torques, that is, at speedshigher that 2 000 rpm where b would probably no-ticeably begin to decrease. This effect, however, is ofno consequence to our main objective. We can nowevaluate the proximal stage time constant

J1b≈ 2nlmwmtmr

2ρm + 4πlmtfr3ρf + Jr1

nσalmwmtar2B2m

. (5)

From this expression, it follows that stronger mag-nets, higher conductivity, and a lower mass density inthe armature all enhance performance, which is ob-vious. Finding the optimal number of magnets andtheir geometry, however, is not trivial.

Similar issues have been discussed for the designof magnetic undulators used in free-electron lasersand synchrotron radiation facilities. Literature fromthis topic provides some insight (Quimby and Pin-droh, 1987; Elleaume et al., 2000), but the tradeoffwith inertia is not considered. These considerationsjustify a multi-physics numerical design optimizationapproach.

3.2.2 Numerical Simulation and Optimiza-tion

A 3D simulation was set up with a multiphysics sim-ulation package (comsol ab, Stockholm, Sweden),a finite element analysis simulator suitable to simu-late eddy currents induced in a moving conductor.The two symmetries (mid-plane and n angular anti-periodicity) in the problem were used to reduce com-putation time. By establishing anti-periodic bound-ary conditions at the mid-planes of two consecutivemagnets, the simulation of one of the 2n anti-periodicsectors was sufficient.

The mesh resolution was set to 0.3 mm for the re-gions of the armature shadowed by the magnets andcoarser elsewhere. An important criterion for select-ing the mesh resolution was to mesh the boundary of


the annulus with element sizes sufficiently small to ac-count for the skin effect. An ungauged potential for-mulation was used to solve the electromagnetic prob-lem. Typically, convergence was achieved in 15 stepsfor a relative precision of 10−6.

The skin depth was about 12 mm for a relativespeed of 21 rad/s, hence invading the whole armatureat higher speeds. This effect is visible in Figure 4that shows the current density induced in the arma-ture. Density is slightly smaller in the mid-plane ofthe armature. Figure 4c shows the results of the sim-ulation for a relative speed of 21 rad/s, generating abraking torque of 50 mN·m.

a b

currentdensity(A/mm2)

1.0

3.0

5.0

7.0

9.0

current density streamlines

armature sector

half

magnet

iron return sector

magnetic�uxdensity (T)

currentdensity(A/mm2)

1.0

0.5

0

-0.5

-1.0 1.0

3.0

5.0

7.0

magnetic �ux density streamlines

c

Figure 4: a, Current density induced in a 32 mag-net pair armature rotating at 21 rad/s. b, Zoom onone sector. c, Electromagnetic simulation of a halfmagnetic loop.

The influence of the thickness and width of the ar-mature, ta and wa, the number of pairs of magnetsn, and the gap, g, between the armature and mag-nets were studied. Other parameters were fixed. Themean radius was r = 20 mm, the magnet dimensions2×2×10 mm, their remanent field Bm = 1.37 T. Thegeometry of the iron annuli was constrained by themagnets and the need to prevent magnetic satura-tion.

Figure 5 shows that increasing the number of mag-nets increases the total torque until a certain limitwhere magnets become too close, causing magneticleakage. The reduction of the inertia of the proximalstage J1 conflicts with the optimal number of mag-

nets. The best tradeoff for the present design corre-sponds to a number of magnets pairs between 32 and36 and an armature thickness of 1.0–1.5 mm.

0.5 1.0 1.5 2.0 2.51.2

1.6

2.0

2.4

visc

osity

(mN

•m•s

/rad

)

12.0

14.0

16.0

18.0

20.0

22.0

time

cons

tant

(s)

0.5 1.0 1.5 2.0 2.5

24

24

28

28

3236

32404036

number ofmagnets

armature thickness (mm) armature width (mm)

Figure 5: Viscosity coefficient and time constant ofthe proximal stage axis according to the armaturethickness and the number of magnets. Other param-eters were fixed, wa = 10 mm and g = 1 mm.

Figure 6 shows that selecting the width of the ar-mature to be slightly longer than the length of mag-nets significantly increase the viscosity coefficient,while not affecting the inertia of the distal axis sig-nificantly. This result agrees with experimental ob-servations found in (Gosline and Hayward, 2008).Lastly, Figure 6 shows that the viscosity coefficient isstrongly influenced by the gap which should be keptas small as possible, within the limits of manufactur-ing feasibility.

0.4 0.6 0.8 1.0 1.41.21.0

2.0

3.0

4.0

visc

osity

(mN

•m•s

/rad

)

9.0 10.0gap (mm) armature width (mm)

1.0

2.0

3.0

4.0

visc

osity

(mN

•m•s

/rad

)

11.0 12.0 13.0 14.0

Figure 6: Influence of the gap and the width of thearmature on the viscosity coefficient.

3.3 Resulting Prototype

The system seen in Figure 2 was manufactured using acombination of conventional machining and rapid pro-totyping (abs plastic), which was effective for thoseparts which had to be lightweight. Some structuralengineering was carried out to ensure that all theparts had the required rigidity.

The motors were a 35 mm core-less dc motor(model re-35, 273754, graphite brushes, Maxon Mo-tors AG, Sachseln, Switzerland) for the proximalstage and a small 16 mm motor (model re-16,118698, precious metal brushes) with a peak torqueapproximatively 20 times smaller than the larger


motor. The motors were powered by two analogcurrent/voltage amplifiers (model lcam, Quanser,Markham, on, Canada). The two shafts were fit-ted with high-resolution digital encoders (MercuryM1800, MicroE Systems, Bedford, ma, usa) giv-ing 1,638,400 counts per turn. The clutch had 60neodymium magnets, and the armature parameterswere ta = 1 mm, r = 20 mm, wa = 12 mm.

It is of paramount importance to have accurate esti-mates of the system parameters. They were measuredas described in Millet et al. (2009) and the results col-lected in Table 2. The viscosity coefficient was a bitlower than expected from the simulation because ofthe lack of dimensional accuracy of the rapid proto-typing manufacturing process forcing us to increasethe gap.

Table 2: Measured system parameters.

Quantity Value

distal torque constant k2 7.9 10−3 N·m/Aviscous coefficient b 8.7 10−4 N·m·s/radproximal inertia J1 2.6 10−5 kg·m2

distal inertia J2 6.4 10−6 kg·m2

distal dry friction C2fric 1.3 10−4 N·mmax torque C1max 2.0 10−1 N·m

With proper control, the system matched closelythe entire range of human sensorimotor performance,or “perfect transparency” as quantified in Section 2.

4 Control System Design

Referring to Fig. 7, the system has two torque com-mands and one torque output, which can potentiallyprovides for a number of control options. Here, theprimary control objective is output torque regulationand tracking. One effect of this particular control ob-jective is to disconnect the effects of the proximal mo-tor dynamics from the experience of the user. Duringactive exploration, when the handle is back-driven,the power required to move the proximal motor isentirely supplied by the power amplifier, not by theuser.

To achieve this objective, the reference torque, τd,is compared to the torque produced by the coupler,which is proportional to relative velocity between theproximal and distal motors. The proximal motor isslaved by the compensator C(z) to the torque error,operating in the sampled-data domain with period h.The distal motor is commanded to reduce the errorwithout compensation since it is needed to transientlycompensate for the slower response of the proximalstage. More complex schemes to achieve a wider range

z−1

z−1

h

hZOH

ZOH

C(z)

τd

τuser

1

s

1

s

b

−bθ1

b

h

τoutτcoupler

θ1

θ21

b+ J2s

1

b+ J1s

θ2 � θ1

Figure 7: Control Scheme.

of objectives could involve compensation of the distalmotor dynamics as well.

The controller has a feedback path to regulate thedifferential velocity of the two shafts (θ1 − θ2). Ifregulation and tracking are sufficiently good, the dy-namics of the proximal stage is eliminated from theuser’s experience. The transparency is limited by thehigh-frequency dynamics of the distal stage only. Inother words, for a null torque set-point, what is feltis only the distal stage. This scheme relies on an ac-curately specified viscous coefficient, b, which eddy-current couplers allow.

4.1 Polynomial Pole-Placement

We adopted a discrete-time polynomial pole place-ment approach because, in contrast with other ap-proaches, this method allows for an exact design (Lan-dau, 1990; Astrom and Wittenmark, 1996; Ostertagand Godoy, 2005). The discrete-time controllers arespecified by three polynomials R(z), S(z), and T (z),as shown in Fig. 8, where y(z) is the measured plantoutput, r(z) the reference set-point, and u(z) the con-trol signal.

H(z)1/S(z)T (z)

R(z)

u(z)r(z) y(z)Hm

Figure 8: Polynomial control structure.

Control synthesis is purely algebraic and bringsabout a solution systematically, once the discretemodel of the plant is known and a closed-loop modeltransfer function, Hm(z), has been specified. Thethree control polynomials can be selected to achievecertain performance objectives, including regulationand tracking. The discrete-time plant, here the sam-


pled continuous-time plant, is

H(z) =B(z)

A(z), (6)

and the control law is

U(z) =T (z)

S(z)r(z)− R(z)

S(z)y(z). (7)

The feedback control, −R(z)/S(z), gives a closed-loop characteristic equation,

A(z)S(z) +B(z)R(z) = P (z), (8)

that takes the form of a Diophantine equation.The design involves first selecting P (z) to deter-

mine the closed-loop regulation behavior through theplacement of the closed-loop poles, taking the con-straints on the degrees of the polynomials into ac-count. The tracking polynomial, T (z), is then se-lected to independently determine the tracking be-havior.

4.2 Design

If we neglect the velocity of the distal stage, thatis, consider it small compared to that of the prox-imal stage, then the compensator acts on the dy-namics of the proximal stage only. The discrete-timetransfer function of the plant results from cascading azero-order hold with an integrator and discrete-timederivation. With a sample period of 0.1 ms, the planttransfer function becomes,

H(z) =0.001671z + 0.001669

z2 − 0.9967z. (9)

The desired closed-loop polynomial was selected tocorrespond to a second order continuous plant withnatural frequency and damping, ω0 = 680 rad/s,ζ = 0.9, respectively. This led to the characteristicpolynomial

P (z) = z2 − 1.8800z + 0.8848. (10)

The solution of the Diophantine equation (8) gave

S(z) = z − 0.98855, R(z) = 1.3240. (11)

Perfect model tracking is achieved when

T (z) =P (z)

B(1), (12)

and the model was

Hm(z) =0.001625z + 0.001569

z2 − 1.898z + 0.9009. (13)

4.3 Control Performance

The control system was implemented on a personalcomputer running rtai real-time Linux kernel andthe sampling rate was set to 10 kHz. The system wastested by holding the handle with a normal grip anddemanding a step of torque. Saturation levels wereset to 5 mN·m for the distal motor and to 200 mN·mfor the proximal motor, because the distal stage mo-tor normally operates only during the transients, itssaturation can be set much higher, viz. by a factorfive, without adverse effects. Figure 9a shows the re-sponse of the system to a step of amplitude 5 mN·m,where the output torque, τout (black line), is the sumof the viscous coupler torque, τcoupler, and of the dis-tal stage motor torque, τ2.

0

0

10.0

20.0

30.0

50.0

0.01 0.020.01time (s)

torq

ue (m

N•m

)

0 0.040.030.02

τcoupler

τout

τ2

τ1

0

-10.0

-20.0

0

10.0

20.0

time (s)

a bτ1

τout

τ2

0.05

40.0

-10.0

τcoupler

Figure 9: Step response time domain performance.a, Case without saturation. b, Case with saturation:the distal motor torque, τ2, is limited to 5 mN·m.

As was expected, see Fig. 9a, the proximal motorreceived a large command, τ1, during a short tran-sient to minimize the reaction time and the torquemissing in τcoupler was taken up by the torque, τ2,produced by the distal stage motor. When satura-tion was not reached for the distal stage motor, as inthe case of Fig. 9a, the mechanical time constant ofthe system was equal to that of the distal motor, thatis about, 1.0 ms. In the cases where the demandedtorque caused saturation of the distal stage, the tran-sient response was imperfect, as in Fig. 9b where thestep magnitude is twice that of the distal motor satu-ration level. The steady-state part, however, remainsunaffected.

5 Validation

The objective was to verify that the high level degreeof transparency of the dual-stage drive had a measur-able effect on human performance when using a hapticinterface. The purpose of the experiment was to test


the device effectiveness, not human performance. Tothis end, we selected a task where participants had toperform as signal detectors using a stimulus that hadtwo components. The first component had a fixedmagnitude and the other was varied from impercep-tible values to easily detectable values. To create anexperimental condition that resembled actual use, weasked the same volunteers to detect the presence ofweak, high-frequency force perturbations superposedonto a slowly varying background force at randomlocations in the workspace. At any given time, how-ever, the participants were not aware of the conditionunder which they were working.

The stimuli were administered through two iden-tical handles, one connected to the proximal motor,and other to the distal motor, see Fig. 10. We testedwhether the subjects could detect smaller details inthe same signal rendered with the dual-stage interface(Condition A) rather than with the large motor alone(Condition B), similar to a conventional interface. Allother parameters remained equal.

Figure 10: Experimental setup. In Condition A, thehandle was connected to the output of the dual-stagedrive. In Condition B, an identical handle was con-nected directly to the shaft of the proximal motorand the coupler was disconnected. The device wasmounted on a heavy steel slab to prevent possiblevibrations arising from the rotation of the proximalmotor to find a path to the hand.

5.1 Methods

5.1.1 Subjects

Six members of the laboratory, five male and one fe-male, volunteered their time. They were aged from23 to 56 with a median age of 28.

5.1.2 Stimulus

The slowly varying signal was produced by simulat-ing dry friction and the fast signal was obtained by

modulating the amplitude of the force according toτC[1− h0 sin

(2πθ

λ

)], when θ0 < θ < θ0 + Θ,

τC, otherwise,

(14)see Figure 11. The friction torque was calculatedaccording to the algorithm described in (Haywardand Armstrong, 2000) and its level, τC, was fixed at5 mN·m (0.14 N at the handle periphery). From trialto trial, the onset of the texture, θ0, changed ran-domly in the range 0–1.57 radian (0–π/2), and itsextent, Θ, was fixed at 0.035 radian (1.22 mm) andits period, λ, at 0.005 radian (0.17 mm).

2h0

Θ

λ

τC

θ0

Figure 11: Stimulus signal. A small burst of oscil-lation of size Θ, amplitude h0, and spatial period λ,was superposed onto a larger friction force, τC.

When turning the handle, it felt as if its motionwas impeded by a brake and it was like trying to de-tect a slight imperfection. For Conditions A and B,preliminary tests enabled us to determine that thethresholds of detection for h0 were below 0.1 and 1.0,respectively (0.014 N and 0.14 N at the handle periph-ery). The period, λ, and amplitudes, h0, simulatedvery fine and very small textures, which was a testfor the device’s capabilities. A better device shouldallow users to perform better.

Rendering a given texture with a given device,however, imposes limits that are not to be ex-ceeded (Campion and Hayward, 2005). The lowestspatial period, λ, that can be reliably synthesized isconstrained by (α/λ)vT < 1 where v is the velocityand α > 2, and T is the sampling period. For a ve-locity of at most 2.9 rad/s (0.1 m/s at the handleperiphery), with T = 10−4 s and α = 10, the small-est spatial period should be 2.9 mrad (0.1 mm). Theother constraints in were easily met by our prototype.The width, Θ, of the texture should also be greaterthan 3λ.

5.1.3 Procedure

We adopted a two-alternative forced choice testingprocedure where h0 was randomly selected in the sets{0.0, 0.01, 0.03, 0.053, 0.08, 0.1} mN·m and {0.0,0.2, 0.4, 0.6, 0.8, 1.0} mN·m, for Condition A and B,


respectively. Each stimulus was presented 10 times,therefore the participants completed 60 trials for eachcondition, which could be done in a few minutes. Inboth conditions, the setup was concealed inside anenclosure having the same visual aspect from bothsides. Only the two handles were visible. To switchfrom Condition A to Condition B, all there was to dowas to turn the set-up around and to disconnect thecoupler from the proximal motor.

The participants were asked if they felt anything atall, in which case they had to respond ‘no’, or a smalltexture, in which case they would answer ‘yes’, andindicate where they had felt it.

5.1.4 Results

We fit the experimental data with cumulative Gaus-sian distributions of the form f(x) = [1 + erf((h0 −µ)/√

2σ)] where µ and σ2 were the detection meanand variance, respectively, using a non-linear least-square procedure. The threshold points were ex-tracted from the amplitude of the stimulus texturethat corresponded to a 50% probability texture de-tection, for each subject, in the two configurations.The average detection threshold across subjects was0.036 when using the dual-stage drive and 0.27 whenusing the standard configuration.

0.10

0.05

0.5

0.10

1.0

prop

ortio

n of

text

ure

dete

ctio

n

0

0.5

1.00

0.5

1.00

0.5

1.00

0.5

1.00

0.5

1.0

00

0.5

0.5

1.0

1.00

0.5

1.00

0.5

1.00

0.5

1.00

0.5

1.00

0.5

1.0

h0 h0

condition A condition B

SA

SB

SC

SD

SE

SF

participants

Figure 12: Results and fits for Conditions A and B.

5.1.5 Discussion

All participants, by-and-large, produced typical psy-chometric curves shown in Fig. 12. Participant SD,who was very cautious when using the improved de-vice, made decisions without hesitation when usingthe standard drive, but the opposite was true for par-ticipant SE. Such differences are not surprising con-sidering that haptic interfaces, no matter how wellthey are constructed, are instruments and that userscan choose to focus on various aspects of their op-eration, even in a simple detection task. They canalso refer to their past experience to various degrees.Whether naive or experienced, their relationship withthe instrument and their skill in using it can vary andthe effects of changing an instrument design can bedifferent from person to person.

Despite these inter-subject variations, it can thenbe concluded that the performance detection of thesubjects was improved by almost an order of magni-tude. It was the case for participants SA, SB, SC,and SF) and to a slightly lesser extend for SD andSE. Lastly, the thresholds corresponded to force vari-ations of 5.2 mN and 38.3 mN for Conditions A and Brespectively, the former figure being in line with thehuman performance threshold (0.5 g experienced dy-namically).

6 Conclusion

Using a dual-stage approach, we designed an elec-tromagnetic drive for use in haptic interfaces andother applications where the maximum torque deliv-ered is decoupled from its effective inertia. In termsof haptic interfacing, this means that transparencyis improved since the ‘tool’ interposed between thesource of torque and its point of delivery causes para-sitic forces originating from inertia and friction to becommensurate with perceptual thresholds. In otherwords, the torque specified is for all practical pur-poses independent from both the movements of thehand and from those of the device.

In sum, the interface achieves two orders of mag-nitude of improvement in transparency over existingdesigns measured in terms of the magnitude of para-sitic forces owing to friction and inertia. The inertialload seen by a finger is only of the order of one or twograms. Yet, the design does not limit the torque mag-nitudes that can be produced, and can operate in itspresent configuration over a bandwidth that exceedsone kilohertz. For the task that we have selected, theimproved transparency allowed users to detect detailsthat were ten times smaller in magnitude than whenusing a conventional design.


Acknowledgments

The authors wish to thank Andrew H. Gosline for ad-vice on magnetic design of viscous couplers and BrunoSauvet for help with prototype manufacturing. Thiswork was supported by the ANR (Agence Nationalede la Recherche, France), project PACMAN “percep-tion haptique des echelles micro et nanoscopiques”.Additional funding was from the European ResearchCouncil, Advanced Grant PATCH, agreement No.247300 (to V.H.).

References

Anwar, S. (2004). A parametric model of an eddycurrent electric machine for automotive braking ap-plications. IEEE Transactions on Control SystemsTechnology, 12(3):422–427.

Astrom, K. and Wittenmark, B. (1996). Computer-controlled systems: theory and design. PrenticeHall, New York.

Balakrishnan, A., Joines, W., and Wilson, T. (1997).Air-gap reluctance and inductance calculations formagnetic circuits using a schwarz-christoffel trans-formation. IEEE Transactions on Power Electron-ics, 12(4):654–663.

Baud-Bovy, G. and Gatti, E. (2010). Hand-held ob-ject force direction identification thresholds at restand during movement. In Kappers, A., van Erp,J., Tiest, W. B., and van der Helm, F., editors,Haptics: Generating and Perceiving Tangible Sen-sations, volume 6192 of Lecture Notes in ComputerScience, pages 231–236. Springer Berlin / Heidel-berg.

Berkelman, P. J. and Hollis, R. L. (2000). Lorentzmagnetic levitation for haptic interaction: Devicedesign, performance, and integration with physicalsimulations. International Journal of Robotics Re-search, 19(7):644–667.

Bicchi, A., Peshkin, M., and Colgate, J. E. (2008).Safety for physical human-robot interaction. InSpringer Handbook of Robotics, chapter 57, pages1335–1348. Springer-Verlag.

Boulet, B. (1990). Modeling and control of a roboticjoint with inparallel redundant actuators. Mas-ter’s thesis, Deptartment of Electrical Engineering,McGill University, Montreal, Qc, Canada.

Campion, G., Gosline, A. H., and Hayward, V.(2008). Passive viscous haptic textures. In Pro-ceedings of the 16th Symposium on Haptic Inter-

faces For Virtual Environment And TeleoperatorSystems, pages 379–380.

Campion, G. and Hayward, V. (2005). Fundamentallimits in the rendering of virtual haptic textures. InProceedings of the First Joint Eurohaptics Confer-ence and Symposium on Haptic Interfaces for Vir-tual Environment and Teleoperator Systems. WorldHaptics 2005, pages 263–270.

Chew, M., Hong, G.-S., and Zhou, W. (2004). Se-ries damper actuator: a novel force/torque controlactuator. In Proceedings of the 4th IEEE/RAS In-ternational Conference on Humanoid Robots, pages473–478.

Conti, F., Khatib, O., and Baur, C. (2007). A hy-brid actuation approach for haptic devices. In Pro-ceedings of the Second Joint Eurohaptics Confer-ence and Symposium on Haptic Interfaces for Vir-tual Environment and Teleoperator Systems. WorldHaptics 2007, pages 367–372.

Elleaume, P., Chavanne, J., and Faatz, B. (2000). De-sign considerations for a 1A SASE undulator. Nu-clear Instruments and Methods in Physics ResearchSection A: Accelerators, Spectrometers, Detectorsand Associated Equipment, 455(3):503–523.

English, C. and Russell, D. (1999). Implementation ofvariable joint stiffness through antagonist actuationusing rolamite springs. Mechanisms and MachineTheory, 34(1):27–40.

Gosline, A. H. and Hayward, V. (2008). Eddy currentbrakes for haptic interfaces: Design, identification,and control. IEEE/ASME Transactions on Mecha-tronics, 13(6):669–677.

Hayward, V. and Armstrong, B. S. R. (2000). A newcomputational model of friction applied to hapticrendering. In Corke, P. and Trevelyan, J., editors,Experimental Robotics VI, volume 250 of LectureNotes in Control and Information Sciences, pages403–412.

Hayward, V. and Astley, O. R. (1996). Performancemeasures for haptic interfaces. In Giralt, G. andHirzinger, G., editors, Robotics Research: The 7thInternational Symposium, pages 195–207, Heidel-berg. Springer Verlag.

Heald, M. A. (1988). Magnetic braking: Improvedtheory. American Journal of Physics, 56(6):521–522.


Hollis, R. L., Salcudean, S. E., and Allan, A. P.(1991). A six-degree-of-freedom magnetically lev-itated variable compliance fine-motion wrist: De-sign, modeling, and control. IEEE Transactions onRobotics and Automation, 7(3):320–332.

Khatib, O. (1990). Reduced effective inertia in macro-/mini-manipulator systems. In Miura, H. and Ari-moto, S., editors, Robotics Research 5, pages 279–284. MIT Press.

Landau, I. D. (1990). System Identification and Con-trol Design. Prentice Hall, Englewood Cliffs, N.J.

Lauria, M., Legault, M.-A., Lavoie, M.-A., andMichaud, F. (2008). Differential elastic actuator forrobotic interaction tasks. In Proceedings of IEEEInternational Conference on Robotics and Automa-tion, pages 3606–3611.

Millet, G., Haliyo, S., Regnier, S., and Hayward, V.(2009). The ultimate haptic device: First step. InProceedings of the Third Joint Eurohaptics Confer-ence and Symposium on Haptic Interfaces for Vir-tual Environment and Teleoperator Systems. WorldHaptics 2009, pages 273–278.

Morrell, J. B. and Salisbury, J. K. (1997). In pursuitof dynamic range: Using parallel coupled actua-tors to overcome hardware limitations. In Experi-mental Robotics IV: the 4th International Sympo-sium, 1995, volume 223 of Lecture Notes in Controland Information Sciences, pages 263–273. Springer-Verlag.

Ostertag, E. and Godoy, E. (2005). RST-controllerdesign for sinewave references by means of an aux-iliary diophantine equation. In Proceedings of the44th IEEE Conference on Decision and Controland the European Control Conference (CDC-ECC’05), pages 6905–6910.

Pratt, G. A. and Williamson, M. M. (1995). Serieselastic actuators. In Proceedings of the IEEE/RSJInternational Conference on Intelligent Robots andSystems, pages 399–406.

Quimby, D. C. and Pindroh, A. L. (1987). High fieldstrength wedged-pole hybrid undulator. Review ofScientific Instruments, 58(3):339–345.

Salcudean, S. E. and An, C. (1989). On the control ofredundant coarse-fine manipulators. In Proceedingsof the IEEE International Conference on Roboticsand Automation, pages 1834–1840.

Sharon, A. and Hardt, D. E. (1984). Enhancementof robot accuracy using endpoint feedback and amacro-micro manipulator system. In ProceedingsAmerican Control Conference, pages 1836–1842.

Sharon, A., Hogan, N., and Hardt, D. E. (1988). Highbandwidth force regulation and inertia reductionusing a macro/micro manipulator system. In Pro-ceedings of the IEEE International Conference onRobotics and Automation, pages 126–132.

Srivastava, R. and Kumar, S. (2009). An alterna-tive approach for calculation of braking force of aneddy-current brake. IEEE Transactions on Mag-netics, 45(1):150–154.

Stocco, L. and Salcudean, S. E. (1996). A coarse-fineapproach to force-reflecting hand controller design.In Proceedings of the IEEE International Confer-ence on Robotics and Automation, pages 404–410.

Stramigioli, S. and Duindam, V. (2001). Variablespatial springs for robot control applications. InProceedings of the IEEE/RSJ International Con-ference on Intelligent Robots and Systems, pages1906–1911.

Sugano, S., Tsuto, S., and Kato, I. (1992). Forcecontrol of the robot finger joint equipped with me-chanical compliance adjuster. In Proceedings of theIEEE/RSJ International Conference on IntelligentRobots and Systems, pages 2005–2013.

Wall, S. A. and Harwin, W. (2001). A high bandwidthinterface for haptic human computer interaction.Mechatronics, 11(4):371–387.

Wouterse, J. H. (1991). Critical torque and speed ofeddy current brake with widely separated soft ironpoles. Electric Power Applications, IEE Proceed-ings B, 138(4):153–158.

Yao, H.-Y. and Hayward, V. (2010). Design and anal-ysis of a recoil-type vibrotactile transducer. Journalof The Acoustical Society of America, 128(2):619–627.

Zinn, M., Khatib, O., Roth, B., and Salisbury, J. K.(2008). Large workspace haptic devices – a new ac-tuation approach. In Symposium on Haptic inter-faces for virtual environment and teleoperator sys-tems, pages 185–192.

Zinn, M., Roth, B., Khatib, O., and Salisbury, J. K.(2004). A new actuation approach for humanfriendly robot design. International Journal ofRobotics Research, 23(4):379–398.

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