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Novel Actuation Methods for High Force Haptics

AdvancesThe application of robots to provide sensory-motor physiotherapy is a flagship applicationunique to this emerging area The ultimate goal is to promote, enhance and acceleratery after anthat affects motor behavior Commones include strokecerebral vascular accident)(Volpe et al, 2009)and cerebral palsy (Krebs et al, 2009)Scientific and clinical evidence has shown that movement of the affected limbs is a key processompromised ability to move that immediately followspheral neural, muscular and skeletalthat hasTaub and Uswatte, 2006: Wolf et al, 2006) In thecerebral palsy, unaddressed motor deficits also interfere with a childs development, leadinsevere, permanent motor disability In contrast, studies(Nudo, 2007)ctivity-dependent neural plasticity can offset these degenerative trends and, incases,en reverse themThe process of recovery resembleslearning(Hogan et al, 2006) though there aresuch as abnormal muscle tonent experIrepetitionnot enough: voluntary part ent conventional physiotherapypetitions)is one of the ways robotic tools may au2004)ure voluntary participation, the machine must assist only as needed Etimportant, the machine must not suppress any productive movements a patientvements while gently resistinimportant than assistance(Krebs et al, 2003)Theging“gooddiscouraging bad" movements-is perhaps the most important distinction betwetherapyboticassistive technologies such as amputation prostheses, poweredorthoses, etc The latter compensate for a motor deficit; the former attempt to ameliorateThis may account for the contrasting results to date with upper-extremity and lowbotic treatment of upper-extremity stroke-related motorakkel et al

, 2007; Prange et al, 2006) It has even proveneneficialrs in the "chronic phase"md apparently ceased In contrast, clinical studies to date have shown that robottreatment of lower-extremity motor disorders is about half as effective as conventionalapproaches (Hidler et al, 2009: Hornby et al, 2008) Thistherabots were designedpose motion rather than proviedance(Neckel et al, 2008; Israel et al, 2006) More recent designs for locomotor therapyhave begun to address the formidable challenge of providing highly"back-drivable"(lownpedance) interaction(Roy et al, 2009: Veneman et al, 2007)while supporting substantialkelet, examples of high forceditionalaptic applicationsnclude hal devices (Guizzo Goldsooni Guo, 1993), physicallycooperative man-machine systems(Peshkin et al, 2001)and similar applications Like thesentechopen

Novel Actuation Methods for high Force haptic32 Interaction Controlrategies that differ significaon or velocity servo problems Because of the unique characteristicsraction described above theapproachThe most straightforward er)of interaction, eg by using impedance controldynamic behavior at the poembodiment of this theory, termed simple impedance controlmotoforce-producing actuators to implement virtualelocity feedback (or derivative povirtual viscous damping, If implemented ideally with positiveand actuators, the result is passive port impedance(Hogan Buerger, 2005) This approachis powerful, robust and easily implemented, and has been applied successfully( Krebs et alntrol can do nothing to corfriction in the physical system

Thus whilemple impedance control can efftabilize interaction by guaranteeingdo little to address the limitations of actuator technology discussed in the previoustion, providing significant motivation for the alternative techniques discussed hea class of control methods has been developed that uses6) at theted Thispotential to mask the physical properties of thehardware, presenting a desired dynamic response at the port of interaction that closeltracks target dynamics derived independent of the physical hareFor instance theapparent inertia and frictinactuators to drive the device in the direction of applied force When the target impedancethis is termed force control Unfortunately this approach seriously threatens couplct passivity is lost whenever the apparent inertia is reduced by more thafactor of two below the physical inertia( Colgate Hogan, 1988, Nomittance control exploits the fact that loss of passivefrom reducing the apparentf theoretically ensuringpassivity while aggressively reducing the apparent friction well below the physical level bykeeping the inertia at a level that ensures passivity(Newman, 1992) This approach candramatically improve feel by virtually eliminating static friction, but cannot mitigate higlthat passivity, though sufficstability when coupled to a widge of environments including large inertial loads, kinematic constraints, highly nonlinearfrictional contact, etc, On the other hand, the dynamic characteristics of human limbs areconsiderablimitedstability can be positedtive bounding valuesused for operator dynamic properties, and robust control methods can be used to shape thedynamics of the force feed back control loop to maximize performance (by minimizing)while guaranteeing coupled stability(Buerger Hogan, 200ntechopen

Advances33 Advanced actuatorscharof high force haptic dedparticularly for complex and high-DOF devicesdevelopment offer promising future alternatives for the highmproves energy density andHowever, force andto be fundcompressed-air systems Inid changes of stiffness (to simulate contactingDramatic thermal changes would alsoendpoint impedance In the authors opinion, this approach seems quite promising, thougheries elastic actuators, which include compliant members placed between high-impedanceactuators and the environment and use force feedback control, can achieve highpedance(Pratt Williamson, 1995) The elastic element piseveral advantages for certain applications, but does not guarantee passivity, and a carefulgenerally requiredtability This is problematic whendictableAn alternative doethod thatincludes carefully controlled physical damping in coniwith natural admittanceheoretically guarantee passivity (Dohring ne2002) Generally,theCfter the compliant element must be This limits the utility of this approach by limitingachievable stiffness

Still, carefully designed series dynamicstresses These musclelike materials couldday produce effective high force hapticactuators, but have not yet been shown to scale up to the forces needed ( Bar-Cohen, 2004)To the best of our knowledge, no existing actuator technology or control strategy provides astability An alternativeof evaluating the potential of major human-scale actuatortechnologies is by available stress, which is strongly related to force density The fetput of electromagnetic actuators is limited by the shear stress in the air gap betweh is typically tens of pounds per square inch(psi)reds of pelevated, due to high levels of stored energy By contrast, hydraulic actuators routineusands of psi (McBean Breazeal, 2004) This fundamed look at hydraulics to see if the underlying high impedance of servovalvesbeoided, and if the tradeoffs between the six criteria listed in section I can be improvedntechopen

Novel Actuation Methods for high Force haptic4 Hybrid hydraulic actuators for high force hapticsfering high force density, high stiffness, and flexible connectivity bed the interaction port Their main drawback is high impedance, wlprimarilyand because of this they have been little-used forinterfaces Bntrast, electromagnetieely used for haptics due to their favorabnd impedance behaviorsuffer from dramatically inferior force density A hydraulrvovalve would bedevelopment We have investigated a hybrid architecturfor actuators that exploits the benefits of both hydraulic and electromagnetic actuation whilecircumventing the weaknesses of each In this design, sketched in Fig 4, a hydraulic elemeris used purely as a transmission, while a remotely-located source actuatorn,and dictates the representation of the virtual environment The hydraulicmotion of thepled fromthee actuator and theremain stationary

Critically, this architecture obviates the need for aalve, eliminating thef high impedance The hydraulictransmission is analogous to a mechanical transmission but, unlike cables, tapes or rods,This architecture also enables the use of effective source actuators, particularly direct-driveelectromagneticvide favorable force, motion and impedanceproperties The source actuator can have large mass, because it need not moveMotorFlexibleFluid LinePistonFig, 4 Schematic of linear actuation scheme with fluid trarWhile this proposed architecture can dramatically reduce endpointed to using only direct drivennected directly to the endpoint ) Total mass is critically important for someapplications (eg fully mobile exoskeletons), and this approach may not be suitmportance thanotal mass Therapeutic robots,ce,may tolerate being tethered to a stationary org for power(Roberts, 2004) On theother hand the absence of amay lead to a lower system mass than a purentechopen

Advanceshydraulic system This passive hydraulic architectureof the drivetrainfrom the mobile interaction port and conducts energy tohydraulic, not electrical, for41 Design Model and tradeoffsone embodiment of this architecture that uses a linearectromagnetic motor as aactuator and a passive hydraulic system as a powerission The hydraulic system consists of a piston/cylinder on each end for conversionmotor, and the other acts as an actuator Unlike sehydraulics, the mechanical piston-cylinders, each of which acts as bothfor the hydraulics, and the tubing that joins them need not include small orificesed to have relatively low intrinsic impedancIf thecapable of providing the desired force and impedance, then an idealenf In this context, transparency (previously used todescribe an objective for bilateral teleoperation systemshat theforce, motion, and energy exchanged between a load and the transmission is equal to thatctuator behavior to a remote endpoint package that weighs less than theguredepicts a generic transmission architecture If the transmission is perfectly transparent, thethe force exchanged at port 2that exchanged at port 1, and the impedancnterface to the environmenttly equals the actuator impedance

That is,alossless and has the following propertiesx2(D)=x()F2(n)=F(t)(10)XFig 5 Schematic depiction of a transmission between a source actuator and environmentgy and will therparent Furtherdynamics To approach ideal behavior, the transmission should be designed to minimizeinertia, compliance, and friction (although transmission dynamicpe the port impedance; see 43) While transparency is an importajective, an effective transmission must also be fexible A perfectly flexiblallow infinite separation (in all spatial def freedom) of theendpoint package from the source actuator with(torques) A pratransmission must provide sufficient freedom of motion from thentechopen

Novel Actuation Methods for high Force hapticworkspace Forces and torquests of fe quired to bend and twist the fluid line should beWhether a transmisstended to be transparent or to shape impedance, itsdesign specifications focus on how it impacts endpoint impedance This distinguishes higo problems Belowbles the prediction of the transmissions transparency and its impedance First several issues must be addressed to ensure that useful actuatorsbilateralFrom Figure 4 it is straightforward to envision the hydraulic components transmitting force,and porpression However most highstsometimes actuate bilaterally (pulling as well as pushing) If tensile forces are applied topressure drops below ambient and the(cavitates)

If the seals are imperfect, air leaks in, Two simple options enable bilateralactuation: a bias pressure that exceeds the pressure needed to transmit tensile fortroduced, or actuator pairs can be used together The latter is doaperedas oM Aq paulo! A oM aues au I ur!M is!Xe sypned sua, 10y auo'saum pinythe other for"compression This configuSeals where the pistons exit the cylinders are particularly problematic, as any liquid thatleaks there leaves the constant-volume system and must be replacedT6 Bilaterally actuated transmissioth two fluid pathsler method of tensile force transmission that uses a single fluid path requireswithout force applied by thetor or environment Thisapplying a constante force to each piston When the systemon each side cancel, but the fluid in the chamber is at an elevated presTensile forcere, but if the force does not exceed the bias force level, the fluid pressureabove ambient and cavitation and gas leakage into the system are avoided Thisthe applied load, and increasesperating fluid pressure, but reqonly two moving seals rather than fourUanicalpproach, the trapurposes as the simple straight-pipe system shown in Fig 7 This model, used as theimpedance, includes eahe piston- cvlinderiameters DI and D2 and length Li)and approximates the flexible line that connects tntechopen

Advancestraight, smooth and rigid cylindrical pipe (with diameter D and length L) The forcesand F2, and the piston velocities are D and v2 The bulkfluid velocity in the line is v, The transition from piston diameter to hose diameter must alsoof the fluid in the system, and the inertia due to fluid acceleration Calculations based orummarized below to illustrate thethis hydraulic) amplificationreduction, without adding mechanical parts that might contribute backlashlis case, the gear ratio is equal to the ratio of the pistonD2 Azg 7

Straight-pipe, dual piston model for a linear passive hydraulic transmissionecture musttroducing a significant separation between theor and the endpoint whereehavior is controlled, with accompanying transmission dynamics, the structure of thestem poses a potential challenge for effective and highly stable control Because stability are paramount, one way to represent target impedance is to feed back motiononly at the source actuator, closing a simple impedance control loop around only the welharacterized electromagnetic source actuator, yielding a robustly stable implementationThis arrangement depends on the transmission to reliably (and nearly transparently)transmit impedance between the source actuator and operator, but without usingthe interaction port, it may be vulnerable to small and accumulating position errorsFortunately, although humans excel at gathering information from physical contact, theygenerally sensitive to small changes in position Provided that physical contact isbe tolerated withif the device is usedbehavior of the working fluid, and in fact the dynamics of the transmission may betentionally sculptedrove both interaction stability and perfoping, as discussed briefly belontechopen

Novel Actuation Methods for High Force HapticsFTo illustrate the key design issues for this architecture designesented by applying the model in Fig 7 to the specifications for an actuator for an uppelimb physicaot deThistendeaddition to the planar MIT-MANUS robot, and has previously been addressed with twoesigns, one using a rotary electric motor and a low-friction roller soand the otherdirect-drive linear electromagnetic motor( Buerger et al, 2001, Kreld challg target specifications for this application include af at least 65 nf less than 2 kf at least 3 m betwactuator and the mobile endpointthan 2 ke Coulomb friction less than 2N, and linear damioefficient offour In this section the design model is developed to predict frictional and inertial dynamicsof the transmissionpliance is discussed

a prototype actuator(Fig 8)wasfabricated and its measured propertiesmping: A major advantage of this configbilitoid or minimize theses that arise in conventional hydraulics frtransmission line contributesmping due to viscous drag, Assuming the fluid in Fig 7 is incompressible, steadflow between any two points in the pipe is governed by the following expression, deriveheP(11)ntechopen

Novel Actuation Methods for high Force hapticother high force haptic devices, successful therapy robots must simultaneously embody1)The capacity to delivforces, sufficientlimbs activelsubject (eg due to abnormal tone), and in someg balance &e locomotion) to support substantial fractions of body wei2) The ability to represent controlled, virtual environments(eg virtual walls or springsin order to provide physical guidance, assistance(but only as neede

d), protection fromfor strength training), and3) The ability to be backdriven, to avoid inhibiting a patient or operators attemptshese efforts4) Large workspaces, up to a cubicale human6)Gd stability and safety while exchanging significant force and power withon-expert, impaired and unpredictable human subjectstrast, most existing haptic and robotic systems embody some subset of this list oft not all More specifically, most existing robotic devices haveAchieving this full set of features is a formidable engineeringthat isexisting actuator and control technologiespter we proof the tools available tohallenge by summarizing and critiquing available techniques, discussing several advancedpproaches that show promise, and presenting a novel actuator architecture thatprovide a superior solution for certain high force haptic applications In the next sectionand stability considerations for high fhigh force haptics

Section 4 introduces a novel hybrid actuator architecture thattal limitations plaguing actuators for high force haptics Analysisand experimental validation of a simple example are included Coprovided in Section 5 The prior and novel work presented here provides the foundation ofnascent toolkit of methods to design and build effective high force haptic machines2 Perforce and stability of High Force Haptic Systemsn between an engineered mechanicalice) and a htperator While haptic devices and robots bothTs,nsors,control software, and mechanisms designed todiffer from most common robots because the physicasubject has a strong influence, by design, on theunderstood For a traditionalon-controlled roboticem,perforeasured by the systems ability to track trajectories or move to locations in space Stabilitydetermined by the robot and its controller, possibleration of static payloadsntechopen

Advances()81 Phyeraction betwend humanport funtion B)Block diagram representationderations are quite different Rather than control motion, haptictransition between apparent free motion and apparent conta that they must convincinglydevices are intended to reprephysical propeerformance is best understood as the quality of the virtualhe"feel" presented to the operator by theFurthermore theynamic system that is physically coupled to the haptic device, A criticaldistinction between typical robots and haptic devicesIn robotic systd stability areforce hatiperformance is solely a property of the haptic device, while stabiliperator and the hapticmethods of analyzing the perfoand stability of robotic systems are not ideally suitedBue8y flow betweenphysical poports(Hogan2005define the behavior of each system in terms of the relationshibetween conjugate"effort"and"flow power variables, depending on causality ImpedanZ) provides the effort output in response to a flow input, while admittance (Y) is theIn the mechanical domain, force (or torque)is the effort variable while velocity (stem representedce(Ye) In this2:二the magnitude of either the impedance or admittance port functionsloosely thought of as dynamic stiffneonlinear, and includes stiffnessinertia, friction and other dynamic behaviors, e

gtended feel at the interface can be represented by some virtual environmetified bedance function, which may be linear or nonlinear andnd time performann thenfied bthe target impedance (or the target virtual environment)and that achieved in harddetract from this performanenclude unwanted inertial as unhelpful or distracting vibrations This is consistent withthe definitions of"fidelity"found in the haptics literature A related performance metric,ansparencybilityminimize or disguise parasitic dynamics that are not part of the software-generated virtualonment( Carignan &x Cleary, 2000) Specific high force haptic applicmay benefitntechopen

Novel Actuation Methods for high Force hapticPinction C that consists of a frequency-weightedbetween theagnitudes of the actual (Z) and target (Ztarg) mpedamake the argument of the log dimensionless), yielding a singlemInimizefeatures such as precise resonances, and o can be replaced withfrequency weighting In othersight may be gained by quantifyingin terms of intuitively familiar physical quantities such as the apparent inertiafriction etc, metricscomplex whenntend thaperformance of a high force haptic system derives from the port behavor ctified by the mechanical impeIn contrast, theofnteractive systemdynamic propered ports If both port functiolinear, the characteristiclynomial of thFig 1BThe stability of theed system, termed coupled stability( Colgate &x Hogan, 1988)determined by the real part of the roots of this quantity Clearly, the dynamics of the humanperator contribute fundamentally to total system stability This fact, taken with theprevious paragraph, highlights an important distinction between physically interactivelinearontrolled systems, the sation determines closed-loop stabilityetc )In linear interactiis dictated by the port function of the haptic system alone(Zn)while stabilityerminedby equation 2, which includes properties of the operator as well Buerger Hogan,Because the dynamic properties of thetor cannot be controlled by thstemdesigner, guaranteeing coupled stability poses a challenge

One valuable concept forunderstanding coupled system stability is passivity a power port with a passive punction cannot release more energy than has been put into it For the linear time-invariase,a system defined by the linear 1-port impedance function Z(s)is passive iff1 Zp(s) has no poles in the right half planeary poles of Zp(s)are simple, and have positive real residuesthat when two pport functions are coupled together as in Fig 1, the total open-loopphase must be between-180 and +180 at all frequencies, and the Nyquist stability criterioncannot be violated, so the coupled pair is guaranteed to be stable(Colgate Hogan, 1988)ntechopen

Advances in Hapticsenergy propeTpassive ports, If two passive pgenerate energy indefinitely, and therefore stability is guarantee(perhaps with fine tuning) to all physical domains T Wyay sultBecause it is energy based, this extraordinarily powerful rerks for linear andystems(for nonlinTo the extent thstems at theirprovides a powerful stability metric for high force haptics While this has not beempirical resulttheory strongly suggest that this is1989)Unfortunately, making high force haptic systems passiveCertain simple control laws can preserve passivity, but given the limitations of availabthe haptic system port These ple controllers often can not achieve adequate performanceactuator hardware these siviewed in the next section3 Actuator and Control Technology for High Force Haptic SystemsIdeal high force haptic systems would achieve high forces while representing portr infirupled stability Actuators for these idealized systems wouldrequire similar properties,ne additional properties(e g low maf actuateffective at human scales(tens to hundreds of n, cm to m motions, frequenHz), then by exploring the benefits of available advanced control method31 Classical Actuator Technologies for High Force Hapticsfidelity whenused in direct drive configurations

Friction can be extraordinarilyially at the lowfrequencies typical of interaction with humans(atcurrent or rpassivity The main drawback is limited fornsity(Hollerbach et al, 1992)ning thatgh forces lead to large, heavy actuators Electromagnetic actuators are easy to use, and inystems can be successfully designed to meet certain limited requirements inpite of force density limitations An example is the MIT-MANUS robot for upper-limbsical theratfreedom) planar closed-chain configuratKrebs et2004) Other devicesery small translational workspacesBerkelman et al, 1996) The force density limitation is far more difficult to ovfoen-chain serial systems If the actuator for doF #1 is carried by doF #2, asserial robot arms, then the mass of the actuator not only increto the endpoint inertimechanisms, and is thereforen, as fcarrying the full weight of direct drive actuators rapidly becomes prohibitive When rotarymotors cannot be used, largens pose an additional problem, as the highforce increases nearly linearly with range of motionntechopen

Novel Actuation Methods for high Force hapticAn obvious way to improve the force density of electromagnetic or other actuators is to addgearing This approach makesg actuators in a serial mechanism feasible and is usedextensively in robots, Unfortuapparent inertia and friction due to edbserved ant, by the square of the gear ratio Coulomb friction and stiction inthe actuatored linearly by the gear ratio Furthermore, the gear train adds itswn trictionand backlash as a result, eveWhilplble to modest gear ratios(typically less than about 5: 1)rger gear ratios rapidly lead to unacceptable levels of reflected inertia and friction Theof gearing to solve the underlying force density problem in high force hapticsistinguishes this problem from most robotics, where gearing is generally very successfulignificant problem with using direct-drive electronfor highre used Mechanical transmissions such as cables, belts, tapes and rods offer a poterpportunity to keep the actuators stationaryconfigurations, while transmitting their force, motion and impedance properesigned to achied impedance capabilities in high-DOF serialg the WAM arm(Townsend Guertin, 1999) The complexity of the mechanisms thatthe WAM underscore the fact that routing of mechanical transmission members canbe extremely challenging When actuators for multiple DOFs of a serial mechanism areDOFs must pass througaround other joint(s) This presents an extreme packaging challenge as the number of DOFsgrows, and this challenge is compounded by the fact that fixed separatnerally bemaintained between transmissbetween pulleys in a cable system)

Cablequiring tight, deterministic couplingthe adand the intermediate and terminal joints that they actuate, even as thedependently actuated THembers also tend to(a" guitar-string effect) and can severely limitlumping challenge, as the gears that mate adiacent rods must be kept in tightly controlledtheir limitations are insurmountable, and other options must be sov e 3,ontact In certain configurations, mechanical transmissionsforce haptic solution, and thus represent an important tool Hfor other applicateastbetter than ungeared electromagnetic motors(Hollerbach et al, 1992) Because the workingfluidhumans Pand valves can be located remotely, with force and motionupled to the interaction port through flexible tubing, which can be routed with greaterdvantagesKazerooni &e Guo, 1993, Lee Ryu, 2008)) This is because the operation of conventionaators to have high intrinsicdance, and in facgenerally to be non-backdrivable Hydraulic actuators rely on nonzero valve impedance tontechopen

AdvancesPsPaFig 2 Schematic of flapper servovalve, with resistor model of left halfregulate output, placing a lower limit on the output impedance The fundamentalbe demonstrated by considering a typictrolled tooduce nominally constant pressure Ps, and a servovalve connected to a control system thatmeters the flepressure, depending on the valve designontrol structure to thenpedance A common valve architecture felargelysimilar tradeoffs) The flapperration is used, foe, as the first stage of theMoog series 15Pdifferential pressure(PrPu) Two streams of fluid from the high-pressure source Ps push inainst the fllich is attached to the rotor both fluid streamsn drip to the return at pressure Pr The flapper rotates to partially restrict one side andraise the fluid pressure in that branch For the change in fluid resistance at the flapper tompact on Pa and Pa, each side of the(oa and ow

Unfortunately, any fluid supplied to the load must pass through one of theseorificesg the impedance and degrading the valve s quality asof fluid resistorsbelow the schematic, Theorifice is modeled as the resistor Ron, and the flapperopening is modeled as the resistor Rin(e), which creates a pressure drop between Preturn pressure P, and depends on the rotor angular position 6 If Ror=O, then the outprper has no effect on output If a single fixeposition 0@, is considered, Rla"(0) Deriving the output impedance Z,"P/Qo where QR。Rwould have Z 0 If Ror is too small, then changes in Ri(e) have littleeffect on the output pressure Pa, and the valve will not function Zu can be made small byminimizing Ria However, the total valve output impedance isntechopen

Novel Actuation Methods for high Force hapticZ=2z。+Zwhere Zs is the port impedance for the other side of the valve, and has the4) But Ro(e inRia(e) decreases, so the only way for the total outpuwould significantly reduce the output pressuramplification in age(as in the mwith this amplifier are twofold: first,if it operates perfectly, itplifies the impedance of the first stage at the endpoint by acting as a gear mechanismogousrough which the fluid must flow Enlarging the orimply produces a leaky valve, increasing power consumption and reducing efficiencytoth substantialleakage flow, which increases compressor size, Given the stringent impedance requirementsof high force haptics, the leaky valve approach is generally impractical High impedance inthe valve is directly related to the ability generate output pressure, and cannot beliding cylinder seals represent anotherwantedhbe challenid, particularlyibute viscous damping and inertia Another disaddraulics is thatodest forces(by hydraulic standards)required for human interaction mitigate this hazardrefore problematic for close proximity to human subjects

In section 4 of this chapthat in spite of these limitations, the forcety advantage of hydraulicsfurther consideration in different configurations for high force haptics, and wearchitecture that cirents the high-impedance servovalve challengPreside iehactiato rs are e so cap blct at br ge bore des wieh: e reteratahs th at con 2o)flow restriction, much like hydraulic servovalves, low impedance is readilorking fluid, Indeehe enclosedoflehirequires high pressure, and transitioning from low to high stiffness (e ga virtual wall) requires rapid pressure changes This can be understood bng the simple example of a closed cylinder in compression due to force fromdiabatic conditions yield similar conclusions Behavior at the port of interactionh thetor is characterized by the applied force F and displacement x Thelinder is at the absolute pressure P, and the specific gas constant R and temperature Tfixed, while the volume V varies with x Pamb denotes ambient pm of an idealass M, is contained in the cylinder The ideal gas law for this volume isRTntechopen

AdvancesP mR TFig 3 Schematic of an ideal gas under isothermal compressioPressure consists of ambient plus thated forceSubstituting VAx and eq (7)into eq(6)and rearranging producRT8)roduces the stiffnedF rT mFor fixed (orfixed )x, for example when traversing a virtual wall, stiffness isonal to the enclosedTo simulate a virtual wall with stiffness 100 timesthe enclosedby a factor of 100 within the period of simulatedfluid recntactwall From eq(6), this means that the pressure also must increase 100-fold( For a realinst the other face of the piston)

Thus discrete virtual environment featuresch as virtual wallsxtremely difficult and inefficient to implement in this wayAnother problem shown by eq(9) is that stiffness is highressure must also be varied to mlinear stiffness, if that is desired An alternaoperate at high pressures, keeping the transmission stiff, andg impedancepedance challescribed in detail above for hydraulics, pneumatic actuatoe notoriously difficult to control, and the additional challenges of high force hapticsexacerbate the problems The fluid dynamics of pneumatic actuators are also forbidding formplementing closed-loop control using a regulator to respond to measured endpoint forcesenting can be used to eliminate resistance from the gas, but this can be quite inefficientFinally, compressed gas stores orders of magnitude more energy than liquids at the sameand thrallsIn spite of their challenges, pneumactuators have beenosed forhaptic and high force haptic applicattheir intrinsic compliance can be beneficial, including exoskeletal devices(Tressler et al2002)and other devintechopen