Event-Based Haptics with Grip Force Compensation

Jonathan Fiene Katherine J. Kuchenbecker Gunter NiemeyerStanford University Telerobotics Lab

Stanford, CA 94305-4021jfiene, katherine.kuchenbecker, gunter.niemeyer@stanford.edu

Abstract

Previous work in event-based haptics has demonstratedthat augmenting position-based force feedback with high-frequency impact transients significantly improves the real-ism of virtual contact. Transients can be portrayed moreaccurately by accounting for the dynamic relationship be-tween actuator force and hand acceleration, a technique wecall acceleration matching. This work extends the methodof acceleration matching by analyzing how changes in usergrasp dynamics affect the transients produced when tappingon real and virtual objects. We use this understanding toupdate the event-based paradigm, measuring grip force inreal time and adjusting transient output accordingly. Whenimplemented on a system that can provide high-bandwidth,high-magnitude transient current, this new approach suc-cessfully compensates for changes in user dynamics, signif-icantly improving the robustness of the event-based hapticsparadigm.

1 Introduction

When interacting with real objects, humans judge ma-terial stiffness more accurately by tapping with a stylusthan by pressing with one [13]. Tapping on a surface elic-its short-duration, high-frequency transients that provide anidentifying signature of the underlying material by stimulat-ing the Pacinian corpuscles in the fingertips [20]. The hu-man sensory system uses these haptic clues to form a richperception from tapping, whereas the quasi-static responseelicited by pressing provides significantly less information.The dynamic acuity of human touch can be traced to the1 kHz bandwidth of fingertip mechanoreceptors, which ex-hibit peak response around 300 Hz [1]. This sensitivity tohigh-frequency vibrations coincides well with the frequen-cies of the transients produced during tapping, which spanfrom the 10’s to 1000’s of Hz, depending on mechanicalproperties of the object and stylus, the velocity of the im-pact, and the way in which the human holds the stylus.

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0 10 20 300

1

2

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ce F

orce

(N)

Time (ms)

Soft Grip - 0.86NFirm Grip - 4.74N

Figure 1. Tapping at a given velocity with dif-ferent grip levels yields identical stylus accel-erations and different surface forces.

Haptic simulations attempt to re-create the feeling ofinteracting with real objects in a virtual environment, us-ing a lightweight robotic arm and a variety of feedbackalgorithms. Numerous haptics researchers have shownthat augmenting standard proportional feedback with high-frequency signals at contact can significantly improve hap-tic realism, as will be discussed in Section 2. Buildingupon this foundation, we have developed the paradigm ofevent-based haptics and the approach of transient accelera-tion matching. This approach honors the user’s sensitivityto high-frequency accelerations and adds such signals to vir-tual objects via an understanding of human-device dynam-ics. Supported by our findings in two previous user studies,we believe that haptic simulations will feel most real whenthe hand accelerations produced by virtual contact are wellmatched to those of contact with real objects [10, 11].

While our previous work focused on cases in which userdynamics remained approximately constant, we recognizethat changes in these dynamics have significant effects onthe performance of the system. Indeed, Fig. 1 shows theresult of varying grip force in a two-finger stylus graspwhile tapping on a real surface at a given incoming velocity.

Changing grip force does not alter the acceleration transient,but it does change the force that produces that acceleration,hinting at differences in the underlying dynamics. Usinga measurement of grip force, we have characterized thesechanges in user dynamics and developed an event-basedhaptic controller that adjusts accordingly, thereby increas-ing the robustness of this promising paradigm.

To enable these improvements, Section 3 examines theforces and accelerations produced by tapping on real ob-jects and begins developing a grip-based model of thehand/stylus dynamics. Section 4 then describes a methodfor overdriving motor current to produce the high force tran-sients necessary for rendering hard surfaces under high gripforce and/or high incoming velocity. Section 5 developsa frequency-domain model relating motor current to stylusacceleration for a wide range of grip forces. Building uponthe three previous sections, Section 6 updates the acceler-ation matching approach to account for user configurationchanges via grip force measurement, and Section 7 presentsresults from preliminary testing. Concluding remarks andsuggestions for future work appear in Section 8.

2 Evolution of Event-Based Haptics

Originally developed to let users of telerobotic systemsfeel remote interactions, haptic feedback has been shown toreduce error incidence, task completion time and cognitiveload [6, 15, 19]. Over the past two decades, similar meth-ods have been employed in virtual reality to allow users tofeel simulated environments with many of the same bene-fits. When portraying contact with a virtual environment,the rendering algorithms employed by the majority of to-day’s haptic systems supply the user with feedback forcesthat are proportional to penetration depth [21]. Though suchsystems can adeptly represent the forces of relatively softobjects, limited sensor resolution and computational speedrestrict the closed loop stiffness of these virtual springs tolevels far below those found in everyday rigid objects suchas wood, plastic or metal [3]. Additionally, the thermal dis-sipation properties of a haptic device’s motors govern themaximum current, and thus the maximum force, that it cancontinuously apply to the user; this thermal saturation limitis typically far lower than the forces that a human hand canexert, leaving simulations feeling weak and unnatural.

Many attempts have been made to overcome the limi-tations of closed-loop haptic feedback, including the useof high-fidelity hardware, modified control techniques, andsensory substitution via visual or auditory channels. Thefirst researchers to augment low-frequency force feedbackwith high-frequency transients were Kontarinis and Howe,who added vibratory feedback to a teleoperator; high-frequency accelerations were measured at the slave robot’send effector and played back on the master device using a

Proportional

Transient

Posit

ion

Forc

e

Time

Figure 2. Event-based transients are overlaidwith standard proportional feedback.

secondary actuator [9]. From this initial investigation on thebenefits of transient feedback, Okamura et al. studied theusefulness of overlaying transient forces with proportionalfeedback in virtual environments [16, 17]. This work useddecaying sinusoids scaled by contact velocity; transient pa-rameters were tuned for realism via human subject testing,and follow-on experiments demonstrated a significant im-provement in virtual material discrimination.

Continuing exploration of this field, Lawrence et al. rec-ognized the importance of contact transients and defineda corresponding new performance metric for virtual sur-faces [14]. Rate-hardness, the initial force rate of changeover the initial penetration velocity, was shown to be a bet-ter indicator of perceptual hardness than stiffness, strength-ening the case for superimposing high-frequency forces atcontact. Constantinescu, Salcudean, and Croft applied thisprinciple to multi-rigid-body virtual worlds, combining im-pulsive forces on impact with penalty and friction forcesduring sustained contact [2]. Their passive algorithms al-low users to experience large hand accelerations during col-lisions without requiring high underlying stiffness. Hwang,Williams, and Niemeyer also investigated the use of short-duration contact transients, contributing the perspective ofmomentum cancellation [8]. By varying the parametersof open-loop pulses, this work sought to bring the mastermechanism to rest as quickly as possible, creating strongacceleration transients and minimizing initial penetration.

Together, these previous investigations form the basis ofevent-based haptics; short-duration, high-frequency forcetransients are used to instill realism into contact with hardvirtual objects [10, 11]. As illustrated in Fig. 2, the surfaceof the virtual object is used as a discrete event trigger, ini-tiating playback of a pre-computed transient profile. Theamplitude of the transient signal correlates with the user’sincoming momentum, as stronger transients are required tosimulate impacts at higher velocity or with more effectivemass. When executed well, an event-based transient can

create an acceleration profile that is indistinguishable fromreal contact, naturally conveying a rich array of material andgeometric properties to the user.

The acceleration felt at the stylus is determined togetherby the chosen force signal and the dynamics of the user andthe mechanism. In earlier work we developed the method ofacceleration matching for determining the transient shapenecessary to produce a desired tip acceleration [10, 11].The motor-current-to-tip-acceleration dynamics of the user-device system are characterized via standard system identi-fication techniques, and the accelerations produced by tap-ping on a specific real object are recorded. These acceler-ations are then applied to the inverse system model to esti-mate the current profile needed to create them in a virtualenvironment. A transient library created via accelerationmatching was rated by human subjects as feeling similarto a real specimen mounted on a foam substrate, exceedingthe realism of pulse and decaying sinusoid transients as wellas that of proportional feedback alone. The success of ouroriginal techniques in acceleration matching strengthenedour belief in the event-based haptics paradigm; we now seekto develop this approach further, making it even more real-istic and robust.

3 Tapping Dynamics

During our previous work on event-based accelerationmatching, we found that natural variations in the user’shold on the stylus, such as a decrease in grip force, sig-nificantly changed the feel of virtual contact because thesystem could neither sense nor adjust to these changes. Inaddition, limited current output restricted users from con-tacting the surface with high velocity and also preventedthe accurate portrayal of very high frequency transients. Tomitigate these factors, subjects were asked to use moderatevelocities and maintain a consistent grip on the stylus. Ourcurrent work aims to fully understand how changes in userconfiguration affect the dynamics of the system, as well asto develop a strategy for safely applying higher current tran-sients, thereby overcoming these limitations.

To analyze the effects of grip force and higher current,we selected a simple one-degree-of-freedom device thatuses a Maxon RE025 motor with an optical encoder andprovides approximately the same motor-torque-to-stylus-force ratio as a Sensable R© Phantom, as shown in Fig. 3.The stylus was instrumented with an Analog Devices R©

ADXL321 ±18g accelerometer mounted to a custom cir-cuit board, used for both transient recording and valida-tion. In addition, a Flexi-force R© force-sensitive resistor wasmounted on the stylus to measure grip force in a two-fingergrasp configuration. The system was controlled by a 10kHzservo loop on a desktop computer running RTAI linux.

As was illustrated in Fig. 1, changes in user grip force

Figure 3. One-DOF haptic device with accel-eration and grip force sensors.

have little effect on the acceleration transient produced dur-ing tapping; however, changing grip force does affect thesurface reaction force corresponding to that acceleration.To more fully understand this phenomenon, we placed anATI R© mini-40 force sensor beneath a real object within theworkspace of the device to measure the surface reactionforces during tapping. The object used in the tests was athin piece of wood mounted on a foam substrate. We believethis arrangement is an ecologically valid analogy to the ca-pabilities of our system because it presents high-frequencyimpact transients with low steady-state stiffness, much likeour device.

As a first approximation of the underlying dynamics, weintroduced the second-order hand model shown in Fig. 4(a),which has been examined by a number of researchers overthe past decade [5,7,18]. The surface exerts a contact force,F , on the lumped hand/stylus mass, m, while the user fol-lows a desired trajectory, xd, with stiffness, k, and damping,b. Tapping on a hard surface yields little deflection, mak-ing estimation of stiffness difficult; however, it allows for a

Figure 4. Simple hand/stylus models.

Figure 5. Model parameter estimates.

wide range of incoming velocities, making the estimate ofthe damping parameter relatively robust.

Using the accelerometer and encoder to measure xs andxs respectively, and estimating velocity from these two sig-nals, we can express the model shown in Fig. 4(a) as

F = m xs − b (xd − xs)− k (xd − xs) (1)

Assuming the user’s desired velocity, xd, remains constantover the first 30ms after impact [20], we can use leastsquares techniques to estimate the parameters m, b and kfrom recorded data of force and acceleration during tapping.Expressing (1) as:

F0

F1...

Fn

=

x0 (x0 − vin) (x0 − 0)x1 (x1 − vin) (x1 − vinT )...

......

xn (xn − vin) (xn − vinnT )

mbk

(2)

where vin is the user’s incoming velocity and T is the sam-ple period. Using the pseudoinverse to solve for [m b k]T

produces an estimate of the three parameters for a giventrial. The results for various levels of incoming velocity andgrip force over eighty-one separate trials are plotted againstincoming grip force in Fig. 5.

Our model parameter estimates show a definite correla-tion between grip force and the underlying dynamics of thehand and stylus during tapping on real surfaces, though theamount of scatter (possibly due to non-zero incoming accel-eration, among other factors) merits further investigation.Linear fits for each parameter give

m = 0.215 kg− 0.00328 kg/N · Fgrip (3)b = 6.713 Ns/m + 0.369 s/m · Fgrip (4)k = 75.65 N/m + 14.72 1/m · Fgrip (5)

The increase in both the stiffness and damping withincreased grip force matches intuition, as well as the

findings of Hajian and Howe [5], and Kuchenbecker, etal. [12]. Interestingly, our results echo those of Hasser andCutkosky [7] in showing a decrease in the estimated masswith increasing grip force, indicating that a second-ordermodel cannot correctly capture these changing dynamics.As mentioned by Hasser, a fourth-order model incorporat-ing skin stiffness and damping might be necessary to accu-rately represent the dynamics of the hand/stylus system, asshown in Fig. 4(b). Unfortunately, the unmeasured state,xh, of the hand mass makes the least squares solution forthe fourth-order model significantly more difficult.

Even from the simple, three-parameter hand model, wecan see that grip force measurements are an indicator ofchanges in the underlying dynamics of the hand/stylus sys-tem. To interpret these results, we can represent the environ-ment by a simple linear spring of stiffness kenv " k, wherewe then see that the acceleration of the system is largely afunction of the hand/stylus mass bouncing against the en-vironment stiffness. The increase in hand damping withincreased grip force will require additional reaction forceto traverse the same change in velocity, as was shown inFig. 1. To accurately re-create these higher-force transients,we developed a method to overdrive our device for shortdurations, as will be described in the next Section. We willthen turn to frequency-domain and non-parametric identifi-cation techniques in Section 5 to fully capture the effects ofthese changing hand dynamics.

4 Improving Transient Capabilities

To recreate the sensation of real tapping in a virtual sys-tem, a haptic system’s actuator must be able to generateforces that match or exceed the bandwidth and amplitudeof recorded forces for the materials we wish to represent.This requirement necessitates a brief investigation of am-plifier and motor dynamics.

4.1 Amplifier Dynamics and Prefiltering

To meet the necessity of higher peak current, we used aCopley 303 pulse-width modulation (PWM) amplifier tunedto provide a maximum current of 6 Amps, switching at22.5 kHz. While such amplifiers are commonly assumedto behave as ideal current sources, they often have signifi-cant high-frequency dynamics that affect the generated mo-tor current.

To evaluate the dynamics of the amplifier, experimentaltransfer-function estimate (ETFE) analysis was performedfrom commanded to actual current using a swept sinu-soid input from 10 to 4000 Hz. Initial findings showedthat this type of amplifier is influenced by load dynamics,with higher inductance motors resulting in somewhat re-duced bandwidth. We also observed a significant amount

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Figure 6. Current amplifier dynamics beforeand after prefilter.

of crossover distortion when the amplifier switched polar-ity. Figure 6 shows tests of 0.75A swept sinsoids, alongwith a simple first-order model approximation with a poleat 1.05 kHz and a constant time delay of 68µs. While themodel does not match any of the tests exactly, it serves as asimple, easy-to-implement compromise. Using the inverseof this first-order model as a prefilter for the amplifier com-mand, we were able to effect a significant increase in band-width, as shown to the right in Fig. 6. Note that the phaselag in the ETFE for the prefiltered amplifier is due solely totime delay.

4.2 Motor Temperature and Current Saturation

Motor torque amplitude is ultimately limited by thermalheating of the motor. Fortunately, the length of an event-based transient is far shorter than the thermal time constantof most motors, making short-duration heating permissi-ble. To support transient force overdriving, we constructeda simple thermal model to estimate motor coil temperature.Using datasheet values and formulae from Maxon Motor,the following discrete-time equation was used to estimatethe above-ambient temperature of the coil:

Tn =[Rt Rc (1 + αcu Tn−1) i2n

](1 + e−∆t/τ )

+ Tn−1 e−∆t/τ (6)

where Rt is the lumped thermal resistance of the coil andhousing, Rc is the nominal coil resistance, αcu is the ther-mal resistance coefficient of copper, in is the motor currentand τ is the thermal time constant of the coil.

The pulse-width modulation of the Copley 303 amplifiereffectively adds a high-frequency oscillation about the de-sired current, creating additional motor heating, especiallyif the electrical time constant of the load is small. Becausethe switching frequency of the amplifiers was over twicethe servo rate of our system, we created a detailed simu-lation of the motor and amplifier to distill out the macro-scopic effect of the PWM switching on the inter-cycle tem-

perature of the motor coil. The simulated system included amodified motor model to account for a jump-phenomenonin the current response to step changes in motor voltage,as presented in [4]. The amplifier/motor model showedthat resultant motor coil temperature was highly dependentupon both the motor inductance and switching frequency,where lower inductance and slower switching increase thecoil temperature significantly. The standard RE025-118743motor, which has an inductance of 240µH and an electricaltime constant of 0.11ms, experiences heating equivalent toan effective current of:

ieff = iavg + (0.02A) · sign(iavg) (7)

This adjustment accounts for the PWM’s additional heating,guarding against thermal damage to the motor.

While a thermal monitor could be used as a simple emer-gency stop, such a system would reach it’s thermal limitsvery easily during unrestricted operation. Instead, we choseto keep the standard current-based limit for steady-state re-sponse, ilimit, ss, focusing the system’s overdriving capabil-ities on event-based transients. While many methods couldbe used to integrate the thermal model into a controller, wechose a straightforward strategy of fixing the transient cur-rent limit:

ilimit, tr = β ilimit, ss (8)

where β is tuned to allow repeated taps at relatively highvelocity. The thermal model works in conjunction with thisfixed limit, disabling the transient if the temperature climbsto within a threshold of its maximum. A second, more adap-tive algorithm that monitors temperature and dynamicallysets β based on a safety margin is also under development.

Combining the amplifier prefilter with the temperatureestimator in the real-time controller, we have achieved high-bandwidth output with significant short-duration currentoverdriving capability. These improvements allow our sys-tem to output the force transients necessary to re-create re-alistic tapping interactions at a range of velocities and gripforces.

5 Modeling System Dynamics

To faithfully render real impacts using a virtual system,we must understand how forces produced by the device’smotors translate to accelerations of the stylus. As discussedin Section 3, we know that changes in grip force affect thetransfer function from surface force to stylus accelerationduring real tapping. In addition, we need to know the dy-namics of the device transmission, including the motor iner-tia, cable stiffness and any dissipative or other effects. Us-ing the aforementioned prefilter to generate motor currentsover a broad frequency range, we can turn to frequency-domain techniques to create an accurate model of our de-

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0 101 102 103

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090

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Figure 7. Grip-dependent ETFE results andrepresentative dynamic models.

vice dynamics from motor current to tip acceleration undervarying grip force.

The system’s multi-element transmission and complexhand dynamics make it particularly well suited to non-parametric identification. Experimental transfer-functionestimate (ETFE) techniques were used to analyze the grip-dependent dynamics between motor current and stylus ac-celeration with a user holding the stylus in a neutral posi-tion. Each solid curve shown in Fig. 7 is the result of acomplex-domain average of four independent, two-secondlong, swept sinusoid trials from 1 to 2000 Hz. The ampli-tude of the input sinusoid was fixed at 0.75A, with the start-ing polarity reversed for two of the four trials. Grip forcefor each curve was maintained at a constant value through-out each test using a real-time graphical display for userfeedback. The zero-Newton grip force case represents thenatural dynamics of the device and must also be character-ized.

The five dashed-line models shown in Fig. 7 were hand-tuned to match the observed dynamics closely withoutadding complexity [11, 12]. Because the models are all lin-ear, it is possible to linearly interpolate between the transferfunctions to generate models for grip force levels betweenthe representative values chosen. A basic approximation ofthe dynamics below 100 Hz shows that when the user isdisconnected from the stylus (i.e. - zero grip force), the lowfrequency dynamics are dominated by the inertia of the sty-lus and mechanical linkage. When the user holds on, we seethe addition of a low-frequency spring and a mid-frequencydamper. These additional elements cause the frequency re-sponse to have an approximate slope of +40 dB/decade be-low 5 Hz and +20 dB/decade between 5 Hz and 80 Hz. Itappears that changes in the stiffness of this spring and dissi-pation in the damper are the major effects of changing gripforce, where a decrease in ETFE magnitude corresponds toan increase in the respective parameter value. Looking backto the least squares analysis of Fig. 5 shows that the same

trend of increasing damping and stiffness with increasinggrip force is generally supported by the ETFE results. Aseries of time-domain tests was used to validate this model,comparing the actual and simulated acceleration responsefor a variety of transient current commands.

6 Implementation

Figures 8 and 9 provide an overview of grip-modulatedevent-based haptic feedback with acceleration matching.Recorded acceleration transients are used to create a libraryof motor current waveforms. This library is then used todetermine the correct motor command in the virtual render-ing of the surface. Building upon the process outlined inour previous study of acceleration matching [11], we havedeveloped a technique for generating the transient signalsthat incorporates knowledge of changing grip force. Wehave chosen to split the task into an offline portion, whichprocesses the desired acceleration transients and generatesthe current waveform library, and a real-time portion whichinterpolates the transient from the library based on incom-ing velocity and grip force. With adequate computationalpower, the signal processing could also be done in real-time.

Figure 8 illustrates the process of generating a two-dimensional library of transient current waveforms. Ac-celeration transients are recorded during tapping on a realobject for a variety of incoming velocities, seeking to ade-quately cover the range of expected values. Each recordedacceleration transient is first zero-padded and smoothed to

Figure 8. Transient library generation.

Figure 9. Transients are selected and addedto proportional feedback at impact.

remove high-frequency noise. The clean signal is thenpassed through the model family H(s) to determine the ar-ray of current transients necessary to produce that accelera-tion for all characterized levels of grip force.

Examining the controller diagram shown in Fig. 9, wecan see that the transient force signal is summed with thestandard position feedback. Although its contribution issmall immediately following contact, it is important to ac-count for this virtual stiffness in the generation of the forcetransient. Because the spring force is inherently low fre-quency, we can safely assume that the position measured bythe encoder, x, can be represented as the second integral ofthe stylus tip acceleration, x. We can thus invert the sys-tem’s closed-loop dynamics to determine the form for theinverse model:

H(s) =s2 − k G(s)

s2 G(s)(9)

where G(s) is the grip-dependent family of models.Following inversion, each resulting current waveform is

high-pass filtered at approximately 8 Hz to compensate foruser intention. The zero padding is subsequently removedand the tail of the signals are tapered to zero to smoothlytransfer forces from the open-loop transient to the propor-tional controller. As a validation step, the forward modelis simulated using the current waveforms as input, and theoutputs from the model are compared with the desired ac-celeration transient for each grip force to ensure that theinversion process did not distort the signals significantly.

Fig. 9 illustrates how the real-time controller uses mea-surements of incoming velocity and grip force to interpolatethe appropriate transient from the two-dimensional library.This open-loop waveform is then displayed to the user incombination with the standard proportional controller.

7 Results and Discussion

Figure 10 shows measured acceleration transients for vir-tual taps using grip-modulated event-based haptic feedback.The black dashed traces are the measured accelerationsfrom real taps that were used to create the transient library.The correspondence to the desired signals and the unifor-mity across grip force for each incoming velocity demon-strate that the changing user/stylus dynamics are accuratelyaccounted for by the system. For comparison, if the systemwere to blindly apply the medium grip current transient re-gardless of grip force, the acceleration would be too largefor softer grips and too weak for firmer grip forces.

The right-hand column of Fig. 10 shows the motor cur-rent corresponding to each tap. For higher incoming ve-locities, we see that the current was saturating at the maxi-mum transient limit of four Amps, causing some distortion

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Time (ms) Time (ms) Time (ms) Time (ms)(~

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Inco

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Figure 10. Virtual transients match the de-sired accelerations over a wide range of ve-locities and grip forces.

and excitation of higher-frequency modes in the accelera-tion signals. This transient limit, as discussed in Section 4,was chosen conservatively and could be increased to pro-vide a larger range of operation. More striking is a com-parison of the current signals with the original steady-statecurrent limit of 1.25A, which would have clipped almostevery signal in the test to well below the level necessary toachieve accurate acceleration matching.

8 Conclusion

In conclusion, we have shown that changes in user dy-namics can be estimated via grip force measurements, andthat compensation for these changes significantly improvesthe performance of event-based haptic rendering.

From analysis of the forces and accelerations producedduring tapping on real objects, we saw that the transient ac-celeration produced is predominantly a function of the mo-mentum of the object and the stiffness of the surface. Incontrast, the forces corresponding to the acceleration tran-sient are highly correlated to the dynamics of the impactingobject. We have seen that when a user holding a stylus in-creases his or her grip force, the stiffness and damping of thehand increase, creating higher resistance to motion. This in-creased resistance to motion in turn requires higher impactforces to effect the same transient acceleration.

Realizing that the dynamics of the interaction are more

complex than a simple second-order system, we employedfrequency-domain techniques to analyze the effect of gripforce on the dynamics from motor current to stylus tip ac-celeration; grip force significant changes the system’s dy-namic response from DC to approximately 100 Hz. Non-parametric models were fit for various levels of grip force,and these models were then used to compute the currentnecessary to produce a desired acceleration given measure-ments of incoming velocity and grip force.

Using an amplifier prefilter and a thermal model ofthe motor, we were able to achieve high-bandwidth, high-current transients on our single-DOF testbed. Implementinggrip-modulated open-loop transient acceleration matchingon this device yielded very promising results that providesignificant encouragement for the future of the event-basedhaptics paradigm.

Further work will include an investigation of how grip-force compensation is affected by changing users, followedby a thorough user study to achieve a qualitative measureof the improvements made through this work. We also planto test this methodology by building libraries for other ma-terials and extending the paradigm to multiple-degrees-of-freedom.

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