Elan Microelectronics Corporation v. Apple, Inc.

Filing 293

Declaration of Jennifer Liu in Support of Plaintiff Elan Microelectronics Corporation's Reply to Apple, Inc.'s Opposition to Elan's Motion for Partial Summary Judgment of Infringement filed byElan Microelectronics Corporation. (Attachments: # 1 Exhibit A, # 2 Exhibit B, # 3 Exhibit C, # 4 Exhibit D, # 5 Exhibit E, # 6 Exhibit F, # 7 Exhibit G, # 8 Exhibit H, # 9 Exhibit N, # 10 Exhibit O)(Liu, Jennifer) (Filed on 6/16/2011)

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EXHIBIT H The nternationtf Journal of tnt of robot SE Cur ic reerch Shel UNIVERSITV SN DIEGO Received VoL 1982- Cur 7\ f\L /\/ OF on no CALIFORNIA LI8RRIES Q627-9Q Cprinq Editor The Michael Brady Oxford Paul University of Pennsylvania Richard Number Volume Editorial ISSN 0278-3649 Research review June April December and August October bimonthly is published February London Offices changes and mailing Tactile Sensing Journals to 55 $140.00 $17.00 Single of copies missing issues issues free claims 617 Department tocopy Adaptive Chung and Gary the clients is for Robotic directly MA Salem of the fee $5.00 that have with license been CCC 1990 Sadegh and Roberto Horowitz fee code Reporting For Dataflow Steve pro 74 Multiprocessor Gef/in System for Robot Arm Control 93 and Borko Furht those granted BOOK REVIEW is per copy Street for users Advanced Service Research in VLSL Proceedings of the 1989 Decennial is Caltech organiza Conference 104 photocopy system of Institute separate payment has been Controllers with the 27 Congress The Transactional 0278-3649/90 tions CCC to Class of Adaptive pho to copy- Service of $5.00 01970 Analysis of Manipulators CCC Center Transactional Reporting the the by registered Copyright Clearance paid 63 Leininger or personal granted for users and Robustness Stability issue 253-2889 or personal use of internal that Hybrid Manipulator Control for Permission for internal articles use or vided to an Assembly Task 49 Task-Level Nader owner Applied must be made immediately Copyright Information Lght Dexterity Sturges Jack air for $28.00 of the next published receipt of Machine Subscribers current To be honored Circulation Street for individuals postage $25.00 24 and Canada add States for surface Paul Depart Hayward for institutions the with Sliding Contacts Manipulation and Quantification United outside Dexterous Trinkle 02 Rates $70.00 Subscription for Planning correspondence list Press MA Cambridge specific Mechanisms Fearing address Subscriptions be addressed ment The MIT upon MIT and England Business should the by Cambridge Massachusetts Press mail 1990 Contents Journal of Robotics International and June Assistant Batten Jennet The Journal of Robotics Research Editor Founding International University of arranged The Massachusetts Technology Postmaster Send 55 Research Cambridge paid at Advertising 55 changes to Street and Journals Street Second class at additional Advertising Press Hayward 617 Hayward 02142 MA Boston The MIT address Journal of Robotics International The post postage offices Manager Department Cambridge MA 02142 253-2866 APE L0007542 Fearing of Electrical Department Tactile Sensing and Computer Engineering Mechanisms Science of California University California 94720 Berkeley Abstract from orientation Cameron in This tactile sensor and has been depth made between been dimensional and sensor with implemented Jbr are sensitivity contact and has simple one The 1985 has an contact have sensors been element tactile of for dextrous trol for dextrous mine contact with Some point it nice to to sensors to finger the finger at 1984 It is necessary to contact on the finger for know accurate This article addresses tactile finger transduction mechanism tact and magnitude using location niques paper Fearing 987b iffTnverse force of the linear of to con tech based on curvature and hemispherical ing elements and International Vol 1990 No June Journal of Robotics Research 1990 Massachusetts Institute of Technology 12 for total 133-element and The is is rubber in is finger Figure on the cy the underneath 12 sens capacitive on cylinder connected externally to now work adequate cylindrical in Fearing for local finger the in sensor density has been Other 256-element roll tactile tactels of device described main goal shown for better subset The and gauges but an manipulation are elements from previously reported determination 1985 1988 as elements Only an aliasing for molded hand tactile gives Strain of force shapes in and electronics reduce tact tip point Fearing 1986 under the tip creased to The 12 portion contacts describing surfaces fingers are the object if sensor that single Round the Stanford/JPL and single multiple quantities for hands about ing objects interface recover surface better fool sensors are not very useful dextrous lindrical discusses filtering is Object other as well as the object at measuring objects measure using type addition and can mea difficult is It contact each force There the filtering 1988 with In touch tip for application and determination for surface explore single one to simultaneous the object sensor array was packaged design issues Fearing and Binford nor con Fearing the location good flat to parameters example are array sensor tips surface common only the resultant deter to and type of curvature see for are quite con fingers with with the fingers have determine where the impor force shown the need of the most useful plane line is multifingered angle and magnitude of force are mals location of contact tact open-loop hand have types and location Fearing 1986 recover with manipulation Experiments for advantage However sensors must remain grasped hands al et measurement equivalent while being manipulated time consuming fingers be sensor can over the whole finger ment tant Hillis Siegel single measurements tactile surement at each from the from shape In one sense and force Introduction information 1987 and transducers 1984 Chun and Wise motion makes contact structure and Dario Bicchi of deflection location gives gauge Preliminary total move Local strain in contact obtaining array sensor approach 1985 discussed are also sensor that using uses arrays Boie two- to finger-tip force Brock and Chiu 1985 that measurements and Speeter1987 approaches are resultant 1981 contact line formation and of strain set 1988 et different determining analyzed normal deflection only of of skin thickness effects location infor localization comparison sensor model The basic of appropriate analysis accurate the cylindrical on force An allow Two cylindrical planar linear elas spatial aliasing methods for determining tangential to of for determining contact stress-strain depth using analysis used and reduced contacts design analysis signal mation about the applied sensor themes mechanical models ticity main has three paper static and inversion methods Transduction 987a con tips are Allen and Bajczy fiber-optic device Begej the use of this finger as an ex APE Fearing LJOO7543 Tactile Fig sensing Fig finger hand Stanford/JPL for sensor Capacitive block Drive diagram 100 Ki-Ix ultiplexor Multiplexer Output Detector device perimental The search and It in is not intended not robust probably however is sensory and manipulation for is finger rather as enough final re prototype and reasonably sensitive use for industrial durable laboratory use output improve Hz to been speed were tip good so that many designing and low sensitivity designs could be quickly and the success with Siegel arrays Bole and Miller from capacitors oped here of other workers al 1985 Boie 1984 devel the sensor analysis the most part mechanism transduction evaluated us to build tactile arrays led However for is 1985 et described as and ease of fabrica These considerations capacitor the tactile finger aliasing 1985 and Hollerbach by Fearing tion in used of the independent by having the was not intersection As in tance in but it was This since only forces the has not was an issue thus the remotely shielded cables driving from the sensor distance at built of about into 30 the finger of installing cost The are large is tip it enough inter thus lost in of this capacitance Two cable capacitance significant cm electronics of the signal fraction required to reduce at improved significantly the sensor design was stable one coupling the array and one for sensing the array output Improvements used the rate constraints could be in sensitivity and reduced accomplished embedded in by wir custom the core of the finger Design Figure of rows the method at for static capacitance sensor allows for but be increased electronics significant the shielding 2.2 As shown hand that felt hybrid circuit Electrical done the considerable nally ing 2.1 could While performance would be for Hz 15 to potential The improved noise performance are mounted the base of the criteria at Simplicity of construction Criteria ground to cross-talk limitation electronics primary scanned for has been analysis The and reduce array was originally reduced Construction/Design row and column Unused selected shielding low scanning Finger for voltage and columns are switched rows junction capacitors are formed at and columns of conductive used is by Siegel measured 1986 by the the strips capaci amplitude Measurement the of the Using an amplifier with input impedance voltage output of the tactile sensor is RL given the by APE L0007544 The International Journal of Robotics Research in Capacitor Fig elastic model strip of width mm and 2.5 0.5 tric constant From 00 surface mm The of separation pF about is the dielec for of about in the arguments given 1985 bach mm and 5.1 capacitance normal the an important beneath strain measuring the subsurface the surface is To approximate we use measure to quantity and Holler- Fearing strain Ad where Ad is capacitor CSRLo CSRLW CL2 of the top is small and Ad d0 d0 the bottom since VI displacement long very has no effect the percent WRLCL C5 jVdI C50 VSVCL__CL_1 _M d0 d0 V5 where Vd the drive is tances between for and columns CL and columns rows thus the cable capacitance dominate The will significantly CL C5 larger and shows Figure eq large is simple model capacitor plate the sensor capacitance plates that can be assumed are the fractional cell at the same twisting for thin well-behaved each and given RL and CL parameters independent of these to is The fractional force deflection depends elasticity for that depth Percent strain to directly for if cell will all be par cells are used throughout the normal con order only first to deflection to approximation and compared paper for measured with the same wiring and deflection parameters first-order valid capacitance is V5 and that amplifier and the same ticular as undeflected measurements cell it particular stant to the without compression as this strain is C5K00 where K0 ty Since on the modulus of The for to valid sumes capacitor formula made capacitance frequency the nominal function with than the sensor capacitance sufficiently in approximation capacitances from the sensor the amplifier and the amplifier input is This ratio of voltage change be C0 where cable are should With the cable capacitance d0Ad CL ca sensor of stray capaci effects rows the load capacitance into the unselected pressure to unselected the is and amplifier input capacitance capacitance lumped The one junction at pacitance and C5 voltage deflec by obtained is signal is plate of the plate Ignoring tilting of of the plates parallel translation plates tion the of free separation is the dielectric space and is 2.3 Mechanical Design d0Ad constant the plate Ad is the plate actual capacitance fields because pared to the separation may the plate is The d0 is the permittivi nominal as not result very plate The displacement be larger area is area of fringing large com sensor has conductors The finger Curved size surfaces and shape are the fingers Fearing can occur anywhere palmar surface finger is Fearing 1986 chosen are needed on the finger not The good grasping objects In these operations thus complete necessary for for rolling finger just tip made of contact on the sensor coverage is about of the cylin APE L007545 Fig Finger construc tip dielectric Outer Electrodes Inner Electrode JSA of molded Structure Fig tion layer STRIP ON CORE RUBBER drical mm long 25 section with hemisphere with coverage For improved design versions use 3.3 free should design parameter be twice But response overall finger mm width as compliant copper rings DPR In the is inversely sen ap ring for measured is incompressible to very sensory mm covering as Poissons on 10 force is the rigid coverage strips by which transmis molded modulus which Nm2 The rubber ratio 0.5 was veri reduced obtain tric section spatial The im without sensitivity for as case sensor of the wider discussion of soft the and the dielectric to struc foam the skin layer give Fig of the with solid layer had only of the molded Siegel 1986 This some it mm thickness 0.7 some Thus test finger the sensitivity 1985 to spaces foam of about al et hollow as dielectric in as in cells of some strength and homogeneity one-fourth tabs molding during was changed from includes Siegel rubber from the same rubber sensitivity using because the sensitivity decreasing increased about entire improved See foam absorbed structure rubber be move to issues molded same softer In the limiting wide as the to increasing aliasing places initially The foundation the elastic as is be can for rubber This rub separate sample response pulse response The Nm2 modulus deforming on an plate skin depth layer was the harder rubber for without layer ture disc i0 at dielectric rubber helps to widen the sensor response also the dielectric of thickness For low tensile 2.5 design from the Hardman Inc its be about experimentally 0.5 the finger 4280-LV chosen give layer Figure mm and 3.3 separated of about in rings outer whole of the surrounding of the tendency aliasing diameter pro in dielectric foam sensitivity than measured impulse is was chosen newest at to open-cell rubber is fled strain shown is mm 17.7 spaced are sion and protection ber was structure the seven are dielectric molded that compromise between core integrity the eighth the tip The with strain The needed tip lDelrin electrodes connected is subsurface equal to the sensor spacing lightweight at alias ratio softer cause for negligible and aliasing the sensor depth vides structural 2.5 From the sensor depth signal-to-noise also is For increased much used the sensor depth is 1985 depth As to proximately driven along of the continuous good sensitivity proportional The and 180 the length the sensor spacing ing from sampling sitivity and initial the latest performance spatial mm spacing and Hollerbach Fearing good the around the circumference spacing The for UPPER RING to along the length spacing spacing around the circumference 450 diameter of complete goal array on the cylinder led mm center-to-center 3.8 mm in and 25.4 end The the at dielec describe increase compress to ibility Unwrapped the linear around the circumference mm which would cause separation for 450 lot of the elements spacing of aliasing is about Since AP The International Journal of Robotics Research the L0007546 Percent Fig load applied vs deflection to one celL 50-gm load LLneorlty Fearing in sured strain C20 contact pressure area can mate method 15 for to for is almost reduce the force in 40 20 80 100 80 gnoms toad is 3.2-mm does orders of magnitude is copper not stretch beam like the sensor but can This much beam-like better might he obtained rings the length around localization tion Fearing the tactcl straight load 0.5-N rubber relation is The resolution along important circumference for than manipula 1986 of the in true of spond sample is important tion cell AID The for for of each in cells diameter element tactile the finger units gives seven 7.8-mm2 voltage pressure sensitivity meaning because figure of about The 0.5 real gm is of of 0.06 the response for cell 1t change pressure distribution sensitivity output of signal of this 6% sensor 6% table relation medium but capacitor the parallel can estimate an this wasnt would be sensed linear The truly function vernier and found to in for force-deflection make to the for very large even force-strain as than less the strain of load was have similar the sensor appears of plate capacitor raw sensitivity if deflec to re eq area probe is 6% deflection 0.06 A/D gm mm2 unit function also of merit AID units Calibration is for More important The little of the force than measurement capabilities is how of the sensor that is performance of 2000 gm mm2 has figure 100 l/ 3.1 deflec 50-gram load on voltage bits pressure sensitivity sensed is the strain that of rubber with counterbal is The tactel array give hemisphere with an undeflected tactile evaluating 50-gram weight on for 3.2-mm is one at between Evaluation parameter the sensitivity least sensitive as the in to friction instrument placed nonlinear medium were the sensor and relation The An look-up strain needed here This tion This expected used measured Performance and thus is by of the pivot point through origin of 10% strain material easily be more from the This trials halfway There side 1-N load to response line than conductor improved is aliasing degree greater of the finger which The caused probe it of the rings gives and reduces compliant for the rubber approximately property to with on the outside are bend overlap around the circumference than stiffer only cell output of seven with weights diameter on the opposite weight tactel application and the weight the pivot point ance beam balance the force of one deflections be may that The device simply end and The of the large small variations larger approxi in section from the average was generated plot of from the capacitor eq using in spite An response as determined output linear applied described is to the load from the strain determining sizes mea the frequencies peak strain larger increasing weight sensor voltage -o force shows the monotonic Figure 10 give contact varying of the spatial The same As probe 1985 and Hollerbach function is the applied -I- with this particular specified described Sensor 25 probe with 50-gm load at the cylinder elements for while the voltage are recorded location for row each cell tip is increments equal time to each deflection of hemispherical 0.6-mm the pressure vary from element ments and with the sensor geometry ter the spatial to ele 3-mm diame with applied along the length outputs The is of from seven The probe applied maximum the gain parameter is percent stored APE L0007547 Fearing Fig Responses along cylinder Fig moving length for variation Sensitivity among els tact probe .4 Cain Tocteis of 7xSi Gytnder on 40 30 in o20 18 10 010 0.2 0.4 0.8 bit 0.8 sensitivity grams .._ c4 $8 01 7.8-mm2 area probe Five cells were very sensitive with threshold of only 0.2 grams ments are 10 25 mm position finger is which 20 iS in each and used table There by is some variations to normalize variation in around the core during ferent dielectric Figure calibration which ing elements Note the There elastic set is as tactel the right side elements tactel at the the probe tip for within rubber 5% about Figure tactile finger The change in mean the A/D probe first of the calibrated elements on sensitivity converter at sensitiv enough hand is Superposition row the tip to of deflection at the base month but then stabilize to many that theory response can is be all portion of the 1-unit 0.4 grams with the the linear used to analyze and obeys the space probes applied the individual invariant independently strain strain valid assumption profile space profiles invariant from techniques shows interpolated joint for as powerful linear the linear Figure as gain value cylindrical the sensor behaves tion The molding after If there are which can be seen threshold for is 3.2 between sens of the sensitivities the up more than caused giving dif moves from cures further histogram is the hand 400 grams to wrapped interpolation as residual for the gains change the isoprene when is responses along important of Figure may have exerts at different good overlap is it be fabrication the base left to right in the figure at as and thickness shows the cells after dielectric finger stiffness finger has usable.The use with the Stanford/JPL our configuration We is still the sensor output gain which can the rubber in for designed gram which 0.8 with this tactile sensor for this ity in and the worst element functional threshold of about the array ele All it If of superposi assumption profiles least two sum and jointly The corresponds with forces less hold will for well Thus superposition seems at system the sensor principle strain system linear to be to than of the 100 grams or so Sensor two ways hysteresis The interferes first is that with superposition the sensor will not be in time APEL000754S The International Journal of Robotics Research Fig Superposition loads two of 10 Sensor Fig on finger for repeat Superposition 25 --probe Loads of output jitter ed force Probe Repeoted probe 18al.ement oprobe 20 F0.SN AppLicotior 12 41 16 probe botb 15 -.-- 014 probes 12 10 C- 010 4-ci eLements 51 31 s- -5 toctot 0- position 20 40 60 80 100 scrnpLe The invariant tions second relation Because will of the offset for the if that byfp some 2fp described 2fp is zero the sensor not are if input strain initial not condi linear have errors the sensor output load then f2p are the finger friction offset on only sources can Noise With be Limitations mum from the detectable eq Vo tion The step about size 0.3 force AJJ applications is of the signal weight and is applied jitter in Figure 11 The under the probe This error balance beam is is when tactel tactels The location of deviation to 1-gram errors The by quantization force experiments these error all tactel ac calibration Finger errors Behavior application be removed 12 response it force makes be may more how the temporal see strain long it of creep and the useful indicate force removed What how much but elastic remains is when takes to decay strain which delayed elastic is re 1985 The creep strain causes prob can make the sensor output appear as Johnson much exhibit loop to force flow of material lems because to of the sensor to arrows in the figure sensor shows the effects sponse compliant polymers undergoing expected indicate not just is is be hysteresis The and dots continued too can steps of Figure of creep important Soft time response the traditional in high sensitivity hysteresis The force 50-gm if for pay and creep The 100 histogram equivalent so they will affect simultaneously deformations large the force directly for may sensor applied standard caused since limited by these to price than 50- the same at for measurement be neglected Viscoelastic The set of 0.5 grams higher and two adjacent shown 3.4 effects is of the 50-gram weight variation several to shown cells deviation of the sensitivity variation repeatedly the probe jitter quantiza quantization 10 shows the output beneath larger 0.14 grams sensor output gram weight Figure step the standard pivot made Most voltage implying sensitive is on and varying sen 0.05% corresponds of most for the output f/ the deflection larger deflection Figure The the grams implies that the smaller the voltage the in the balance of loca friction surface to mini The converter of the capacitor deflection separation plate in AID depends on the nominal capacitor sor is curacy no load the dominant sensor noise was found quantization combination of contact as single measurements 3.3 in velocities impact rely result probably wobble of the probe varying tion is it is being applied The hard to determine delayed elastic whether contact APE L0007549 Fearing 11 Probe Fig noise histo Fig gram 12 Viscoelastic re of sensor sponse around 13 Response Fig for circumference moving probe Force on F0.SN tI 40 eement 41 mean std IS.9t dev 1.0 gin j30 20 etement 10 31 meon 4.7t std dev 0.4 10 groin 12 iS 14 10 18 defLection has been broken If mined one ual method setting strain contact is is it 0.1 residual the delayed sor output 3.5 error or for an 13 good shows normally reduced as is three this 5% sensor 10% of to is left of the peak or so rate 25% sen represent will to hard to deter be measurements from are Circumference cells with 30 sufficient spacing to and Binford limit remnant around the circumference 450 1989 overlap length to 3.6 is Tip Behavior The tip around the circumfer response 180 probe spacing as intervals along the finger this may It deflection at For to decay 25-Hz scan more uniform along the length Fearing after and the response of about response phantom ence There as the upper scanned be or greater earlier finger applied the resid point practical Beyond Response Around Figure set deflection elastic mine whether contact deflection deflection deflection fractional 35 30 be deter with dealing the response for fractional peak with can elasticity takes about the new zero the sensor should fast for 25 20 see broken Delayed how removal can contact possible 15 time The make but newest it is the responses and circumference consider around the cylinder circumference in not finger the response more detail portion extensively has been analyzed of the finger than the cylindrical portion The less core ex tends slightly into the tip area to improve sensitivity and to prevent hemisphere dead spot at and the cylinder the junction From the top between the of the APE L0007550 I9 The international Journal of Robotics Research 14 Responses Fig normal probe ing mov for to 15 Fig plane tip geometry for Finger assumption stress Pressure The thick normal tact to for response the surface has been analysis The used is for space invariant the tip because not constant above sphere underneath done because the thickness hemi This to is and the medium eter of the cylinder in with position hemi tip This was not of forming thickness Fearing instead length The will Model for Of Half Plane course linear two-dimensional used in Phillips Hollerbach strain on the finger in the and stress-strain and Johnson 1985 will fractional surface of coordinate direction der Consider with the applied 1981 be used capacitor half slice here to predict plane Figure 15 reasonable between Goodier defines is plane strain finger closer so that materials rubber makes first-order are not dielectric sensor nonisotropic is only valid up to 30% approximation For isotropic and the theory elasticity the stresses as here of three that and diam show medium strains are for but this linear the relations Timoshenko and 1951 the for stresses deflection sensor at the top vc5 the defined oJ va ar of the cylin of elastic material in the x-z plane force tion and the stresses to and Fearing deflection axes Capacitor for similar analysis used the they assumed infinite but which ours three-dimensional to the responses of Figure definitely small strains is be inclusion and copper Elastic way 1985 used the plane stress response to sumption corresponds crude and Hollerbach However slab of the finger portion of the slab of plane stress agreement nondevelopable surface Linear the cylindrical to corresponds The the plane stress assumption be sensors on on plates impulse cannot of the of the added complexity capacitor con 14 be yet the varies it mount to tip strain assumption the hemispherical strips for copper the applied point Figure beneath the sensors would be reasonable It for in mm 10 force done on the of analyzing responses of the sensing elements sphere the would be used as of the difficulty cause about is the tip with given for two elements is grasping Not much base the rubber its to hemisphere on top constant on the face in the of the slab direc va equal c4 APEL0007551 Fearing 11 Fig 16 Plane and experimental stress model data lv 1.2 2Pz1v vx 0.8 the relation of plane stress to the following tuting 1980 from Gladwell substitution useful 0.6 shows substi By plane strain eq into 0.4 11 10 0.2 where is lence can be mm position 0.5 shown For example corresponds 4.1 Impulse The strains The each in stresses rameter is are direction Poissons our finger The is for Nm2 for 0.6-mm one crude cell cr where and mation a1 per unit thickness z2 For x2 r2 az rr4 the force is Nm at 2Pzx2 Thus for 2Pz3 of the slab in the plane stress line fit mm and for most of the retical with no free fitting az2 curve Poissons vx2 Eirr4 tactile solid an strain ible infinitely half space approximation corresponding long line of force on an elastic to all 3.8 ay va in results parameters to It is equal The compressibility mm thick estimate mm depth layer acts which The is predicted 0.5 gives for the layer is capacitor postulated Fig by 0.4 best data to rubber top theo in not an arbitrary but this thickness it The mm and 3.8 is the experimental ratio is of depth compared are pa consistent the array the figure in was eq ratio are an incompress material like rubber but the dielectric depth 3.2 elements curve space for expansion For the plane normalization 0.4 These parameters plane stress model with the sin amplitude the plane stress model of and experimental ure 16 The 2P to an is of the previous assumption after from which corre done by adjusting the depth and Poissons The best fitting parameters were rameters approxi load and indentation stress Accordingly 3.8 var cos the plane least-squares from normal angle to section the finger to load at the surface at length the output while recording line with load along the finger approximation with slab line approximates normally increments elastic 1985 which was applied 0.5 load normal to the sur Fearing and Hollerbach are 33 Response Along Length edge Youngs is 10 2.5 knife sponds face plane 0.33 and given by approximately stresses with strain with stress plane by material like rubber an incompressible modulus which are The pa cy and which is equal to 0.5 for ratio given to ratio the equiva Poissons the equivalent that finger layer over above the core coincidental plate is at out to is the about the softer to spread the strain response has some dielectric more giv APE L0007552 12 The International Journal of Robotics Research ing an effective greater The square of mean root scale which full of 0.5 made that tional jitter tion in is model plane stress flection with for It of the region is this sonable the contact diameter finger rigid tion in very The much was done shown the overall rubber Linear Elastic Model an stress plane pacitor plates to are very the sensor depth rate Because model would be an tion in two dimensions fects of the finite The the the impulse given should plate response depth be Figure each strip layer and V24 u2 to YW1XW2YW3t has three displacement The vj Youngs 12 and Poissons modulus com shear modulus is by ratio M2lv 13 the The deflections for the two dimensional from case 1980 Gladwell strips 14 2pu4l vyIiJ-x911zyar3 The 2uw4l might vw3xwi zw34 15 and V3 are plane harmonic functions 16 the capacitor and important is strip and rubber be in is strains are obtained 8w respect rigid founda where medium on question whether strain will rigidly shear strain The obtained from the 2vc2p consider attached are the stresses strains by ow\ Iou for 17 plane via vvc 2va2ji vvE for there the capacitor We is j- from the displacements ca models the ef for The more accu with model to the that other with of the elastic hard or soft foundation the dielectric Vw move indepen of the core and separation shows the plane and the effect stiffness This section An modulus vector displacement ponents next sec in the to that extent to elastic thickness 11 for Strip of infinite close potential stiffness model assumes medium elastic shear the where Wi The as very well to the rubber dently of the copper Thus the copper not increase to by the copper which would allow the rubber skin in the impulse affect do not have much not be bonded may copper is 4u rxIy9z2 de Com the capacitors to caused inhomogeneities the sensor apparently given of the the small theory small compared be as will is scalar the sensor matches why backing ji and potential model may not be unrea is vector with related slab length vector Papko the Using Gladwell 1980 with no 2pd2lvyVr4 where data of the sensor would rigid core of the finger does not response is model The by the experiment speculate The methods potential force the displacement body sensor to interesting the model so well the experimental elasticity the nonlinearity potential elastic can be solved plates by sensor varia of violating spite elastostatic using and posi friction of the capacitor deflections vich-Neuber by cell The function of assumption the ideal behavior to of linear help for larger loads linear close in assumption pensation in explained statistically sensor performs by than the constant above caused rather variance is little not is 1.3% just that with output scale The full beam the sensitivity is error fitting applied 2.0% of variance this There that is losing good considering tactel repeatedly beam balance RMS quite deviation of standard force is without depth 18 19 to 20 the core Fearing APEL07553 where is the For an Fourier transform other potentials are W3 W2 is 1980 representation Gladwell the F_s_h Bse Dsesz 22 and frequency is 2ve Ds where indentation frictionless the strip the surface at adhesion for perfect cosine transform can are To 24 wxzh0 PsHs determine tact solution tion directly the deflec necessary to is beneath The The applied normal stress at the center previous the surface contact px is the contact four equations The gain for the capacitor and normal to with d0 the nominal the four unknowns the system of equations deflection the surface can be solved The FFsHs 27 after kernel Hs matching boundary conditions is the is In the gain Finally plate taken is Crsz KB szB De5t 28 to capacitor medium The zero even so this case when boundary layer Although The terms in the above are expanded as the actual more _Ke2w 2w KC2 2w 29 signal to In the second 3.8 mm depth work case 3.8 plate shows gain plate pre Figure is mm width and the of the top is fixed at the function as gain does gets close the gain in mm thick d0 The value capacitance is as pressure in the of the depth also the top shown is bottom separation plate 36 of the probe function plotted as given by is separation plate surface parabola of the capacitor foundation obtained szA 35 w0zd hd where the as case the first of nominal Hs depth gain for plane stress two cases for given by plane 2iwx The viously 17 is certain at 26 pressure for zds is must equal the Az With to FsHs 25 con for frictionless p4 where wx of pressure simplifies equation so pressure at deflection know it 25 the foundation here the adhesive at found 34 cos 2xsxds sensor gain the percent depth 2jiwO the gives func to Jo bottom of the layer ux 1980 used 07 certain Gladwell be real deflection 23 the and even 2iwx at and of the layer are assuming rx and Hs Fs Because the inverse determine for 33 the thickness sh with tions boundary conditions 2ve 32 CsDl2vAB the inverse Fourier transform The 31 AscxBs 21 Fr2 spatial 30 2w in given 4v where ea 2w e_t0c4c po appropriate are w1x Bs the gives 1980 Gladweil choose to ap stress v/ strip of thickness elastic functions tential vt substitution stresses corresponding For the plane shear stress the proximation to slightly not go the reduced gets larger so there is with the capacitor and the plate bottom separation d0 plate is is fixed at at APE L0007554 14 The International Journal of Robotics Research 17 Gain Fig vs and separation Fig capacitor thick strip half 18 Impulse response plane and strip for ness Coin For E2.5x105 Modet Strip 20 F20 N/m2 ImpuLse N/rn --hotf vs gain s.depthC g15 thickness For Responses ond Strip Hoif PLone ptcne strip cadet 00.8 .4- 008 ID mm 3.3 3.8 .4- mm mm 3.5 ZJ////11//d/.//fJJ//J//t z77z j//////77///////////// -15 0.5 mm The beneath layer now gain has the soft the increased adequate is It above does apparently foundation 10% about predicts 3.8 mm the capacitor approach the infinite Because gain changes thickness plane strip half in is agrees quite similar in more closely is layer to The soft backing no strip it loss model does not The than should be of along the length analysis for layer it can be to much rigid important for and prob The simpler The for pressure from sis for is the length is useful of the cylindrical much than better good position get of peak deflection is also on the estimating load magnitudes describes to of the coarse to to important recovery section recovering an interpolation method location and magnitude of the center discrete restricted measurements contact type is in better Fearing of analy and Bin- 1989 Assume concluded plate spacing it signal Because of the finger localization finger This data measurements strain continuous information ford of sensitivity yield the here it Reconstruction spacing of sensors along the tactel response elastic recover section the skin above multiple discrete portion half plane the bottom capacitor fabrication From simpler for response the impulse can be attached significant makes for much of the previous the plane strip analysis not required dation experimental Strain Signal Fig with increasing with experimental softer lem has not been considered with plane the half plane assumption value As the use the and width shape cause this effect From to little 18 the impulse Figure plane dielectric that half plane Nm1 200 the model thicker so half plane analysis stress As shown may to re impulse stress the finger half plane of the previous seems reasonable it Ft and gets section The that for adequate enough similar assumption the the for calibration with the experimental should model have is sponse but the calculated response obtain to deflection used in the finger as well agrees layer beneath the increase substantially not necessary to compliant mm 0.5 plane the capacitor so seen from the plot be not the impulse of the 15 err tion p051 sensitivity same parameters which As can thickness model This increases capacitor backing the sensor gain capacitor plotted as the thickness is 10 -5 mm thi ok ness ond depth -10 discrete sensors at spacing then seven sensors of one row along the cylinder give is foundation rigid The foun hx plane closed form expression nb rect 37 for APE L0007555 Fearing is Fig Hs As 19 Frequency response and aliased response maximum The assume I.8 that the low-pass is energy The but continuous 1/b03 0.4 is the normal eq strain impulse we filtering Ers version filtered low-pass recovered Ers and the for length is 38 vx2 xEr4 defined now have 42 2bs rect has both As .tAs As and the desired 2bs rect 43 39 The relative from the 38 neglecting spectrum higher by leads error Hs sinc is caused by aliasing an Assuming ideal obtained signal low-pass error E0 filter the by given 40 6xbs is 44 of energy in the reconstruction the energy in the original to 1978 Pratt to error ratio ER E0 domain eq aliased AsH4sHsQ ifIxI In the frequency the is order terms given by rectxl ifx rII2b Hs2ds IHsI2ds ijim with spatial frequency Fourier transform is which is frequency in of periodic in frequency widened Because of Ess of sampling and the frequency of having response and cycles/mm by the convolution result ex finite components from response 2z function Ess by low- by hx rect aliasing be principle limited by aliasing is Es where The in Ignoring the finite finger 0.5 The defined The in practice filtering of the periodic spectrum of the aliased hx may improve slightly cyctes/mm fncquency where we along the occurs reduced can signal with ideal low-pass 0.2 is If pressure distributions but this process 0.1 Hs Figure mm 3.8 sensor width finite significant by low-pass tent of deflection properties of pass contact a.1 the 1/3md ford response integration plate capacitor cC occurs at response shows the frequency 19 with only seven hx eq the plane stress assumption the sinc is 39 given at Ers response is 6irbs term samples The depth with This cluded are by the effects e211 we 41 for localization lated function eq 45 The will effects errors caused Hs Not low-pass and amplitude Fs is an upper bound of aliasing on in the sufficiently and 3.8to 20% interpo bandlimited on the expected localization in filtering 0.20 which implies up If be of the sensor depth for get error 2ird reconstruction of nonideal numerically mm spacing 3xdsI includes expression by the cutoff of the high frequencies Evaluated Hs2irdIsllv 45 the error and amplitude APE L0007556 16 The International Journal of Robotics Research 20 Fig Reconstruction Fig 21 Interpolated error caused by aliasing 3.8 lion mm nterpototion 30 Error continuous ci terpoo in 25 ted somptes 20 tocotizotion 15 1- error offiptitude ci -t- dejiec surface 10 ci toctel postion in force estimation now will be shown row on the finger The along windowed using sinc the seven for strain sensors estimate response angle of force strain be principle when there 1985 no is and the applied pressure hx0 function nh __________ 46 This to is find with window Oppenheim the Hanning 1975 which is makes the ringing the total amplitude point force to the 20 error in filter of samples The finite extent in flection function N-IN-I and when compared Here are response tion forces accurately for Small location can certain finger errors example lead to configurations location to force Localization accurate be but can tool processing the tactels all zj where The is 11 the de interpolated is srnirxisrnnyj 48 wx zwyj are in tactel 21 shows with spacing units where plot of the deflection soft object large useful apply contours contours distances by dividing by the sensor spacing normalized tool The of height than is surface another plot conditions plot onto for of equal percent for where finger unwrapped the surface for plane analyz deflec equal deflection are 1986 Fearing large maximum single by interpolation strain of element ing the sensor output the contact ap the surface fl more know at array formed from the simul of the cylinder and the tip are to an even real-time 10 Localization important force to contact is in fxy window Figure It from the used mainly for sensor evalua be an deflection and reduces the interpolated response strain 47 forjnIN2l the plane stress model continuous 11 response percent shows the peak displacement for 41 is relatively is than as rather taneous number low-pass Figure tion Let is wn4 and and Schafer is and loca for more general tangential the peak scheme simple time consuming force sensors as was proposed and Hollerbach Fearing done by solving and magnitude of at three equations proach is interpolation could tion of errors in xy line x_ APE L0007557 Fearing 17 22 Fig Fig 23 Measured contours Deflection on probe location array Contours Strain interpolated for IS iN degrees III Probe interpoLated Location 6.5---ideaL -I- 6- position esensed Cs Experiment position --5.5- -0 1CA ID35 -0 around tactel The of constant direction on the height 4.5 3.5 circumference surface given is The 5.5 toctot position probe maximum conditions for of are surface by 4tan1f .feee0 Ox 50 The contours found are from iteratively slopes are Oy search Using Newton-Raphson where the zero we Ax\ \AJ Thomas 1968 where Ar is the step size The locationfx Ax and to locations is for contact sor spacing The the deflection with finger low-pass surface is profile decreases spacing 45 has out at about tion on the cylinder rings This to 45 is behaved zero at just 90 may Fig by 3.8-mm sen one as spacing loca by the cop caused of the as find the maximum deflection an unknown pressure iterative and its techniques location spaced are are needed Fig steps location and of the portion 50-gm load will strips is be the The higher is probe if moved along the strip the tactile ele mm along the row the figures are given in tactile element The abscissas tactel spac ing units The ripple on amplitude caused for error between the copper 3.8 three of probe effects The strip by aliasing plitude as well rubber To in is from the max two or along the central boundary 250-jim increments ments unit Note how the cyl by the incompressibility probe above starting recovery deflection avoid cylinder to at the tactel 0y2 in typically and 24 show centered ensures that 45 32f to 0.01 tactel observed is peak percent from the contact be tactel the finger The Ox OxOy 32f Convergence ures 23 not sufficient around the circumference inder bulges per to new tracking algo characteristic well the adjust on the contour rod at around the circumference strain to find new the at error of this contour where the cylinder axis used ensure staying ure 22 shows the output rithm height Ox2 OyOx 51 \ArsinJ to have a2ff 02 arcos4\ 52 and Ox are sensed ing error These of results 0.5 and peak location The position of the probe 12% of within mm along imply that ideal the length aliasing is less is mainly and for am position of the finger severe than APE L0007558 18 ..The.Jmernational JQzirjial of Robotics Research 24 Measured Fig 25 Fig peak around amplitude Poa Interpolated Localization errors circumference Strain 30 4.5 ideaL position sensed 25 position circumFerence around Q20 ci 15 a2 10 .5 1.5 3.5 probe is that the error aliasing above directly polation tactel when zero is because the is the nonuniform 10 probe line An 60 100 60 120 degrees positior HstHOdE the sinc the sample points passes through source of errors tional plane stress model with by the simple load Note 20 6.5 toictet position probe predicted 5.5 inter addi Then normal force for of positioning the sensor rings from manufacture Localization of the finger ing the probe is tested in the same 25 10 Fig manner The increments at larger about mm error This need good of line contact localization along on the by apply localization determine Fearing l987a The the circumference was too large so improved built with 180 we and and around the length the circumference were HOF Fsdx the cylinder finger around error fingers where Force is is the total force recovered the interpolated different It is useful sensor to This estimate know section this the total normal uses simple force For contacts three times the sensor depth proximated Fs will as tend constant to be 56 HOF1Psdx spacing Total Estimating 55 error 2.3- about is To along the circumference orientation L. FHsFsdx performance around the circumference was force aproximation longer Hs can because bandlimited on the than be to two or crudely the surface finger ap pressure The contact integrals disagreement Aliasing can ing 987b method simple fractional the normal direction lengths contribute errors do not show filter in Fear the integrals more accurate but contact large approximation description of fast for large three for SO-gram load deflection to and shows 26 profile with in spite of the crude has Figure deflection each of fractional using an inverse and in by interpolation the method here is areas APE L0007559 Fearing 19 Fig 26 Contacts and total load contact Strain Interpol.oted car Bar normal Loads Smith and there stress 40 aS run fc2dx A1 21 30 mnff rnmJcdx dx 123 132 115 zOpx crx where Now tan /3 sensor at constant fx 1- for the px we fx where px is of an lution Thus components Force Angle would be useful to get result normal pressure information as well as sensor From eq with be the plane both stress contribute and for contacts where the contact 1985 method is function an even pressure is contacts with type here for the proposed edges vertices it The the convolution angle of force planes normal stress and the function odd function as tangential can be stress The measured and interpolated and odd us even gives fx fx fx corresponds to eq an 57 vx2 cos skew index sin which Note gives is defined Similarly are and odd impulse even responses The assumption at the surface can at be made any point that is the tangential proportional to best be 63 maxJ index In general function plicated might heven stress as maxf an indication the skew that indentation there 62 into 2F vx2 fx strain Ejj 2F function deflection by parts skew Cy 61 for and odd components even 60 ddx0 pxx0h0x0ddx0 and cyl spheres seen by breaking an stress in x0hx0 symmetric an even to corresponds in xc fx inders The results tangential and have known priori case when the contact for example and the convo function normal and by the of two even can Fearing and Hollerbach is by convolution caused respectively ./ stresses strain Methods the strain load line pressure tactile normal surface tangential recovering cylindrical from for for assumption the normal to been proposed line the expression normal and seen that information force tangential the at even 58 hoxo ddx0 px It have and an odd function even odd function Recovering strain by an the strain at functions results in an even Length normal xoEhcvenXo pressure on the surface aLong is Jx fdx Jx0 toctel that z0Jipx caused depth px distribution 020 cAx and 1953 Liu of the relative wili the be force skew index will as com be of the pressure distribution used angle zero for pure normal and means of tracking force angle be simply evaluated for line changes the The skew index can APE L0007560 20 The International Journal of Robotics Research 27 Even Fig and odd Fig 28 Measured strain odd percent model components from 300 and even deflection for contact Knife 40- Experiment Edge at30 CF degrees oeven port odd 0.9 30 port --interpoLated 0.6 --3 -3- 020 0.4 4- 0.2 -D -0.2 mm position toctot indentor tion force 0.5 angles The this the plane for Unfortunately with is stress low-fidelity maximum even signal strain assumpfor Knife Edge at Experiment t30 degrees 40 small occurs at Oandisgivenby 30 2Pcosa max 64 020 The maximum odd strain occurs at 010 _____________ 65 and the maximum odd strain ratio 0.5 2F0.2441 maxec The for of odd to even strain is given by toctet sin 66 is strain even max max Figure knife and Figure edge driven from normal with recovered by along the edge 0.2441 67 tan 67 analytic result 28 gives experimental into the surface 100-gm force The interpolation for line force at strain from the seven of the cylinder Since the at results response tactels maximum esis offer is 0.1 for however and aliasing 300 the maximum and odd functions with this point as the origin The of about zcvee 27 shows the 30 for E0 to corresponds sponse the even the skew 10% also improved signal well agrees can be problem force Strain result with obscured errors gauge angle recovery re strain determined experimental errors Amplitude calibration are ratio are eq by hyster caused methods by may Brock and Chiu 1985 For more general even the line load the force Fearing than pressure distribution angle can also be obtained by APEL907561 inverse using the Taking Fourier transforms of filtering and odd impulse even we responses allows partial 68 neous real is the normal function the frequency of surface component and stress is which for sponse The an is strain Fs frequency component of surface inclusions not an isotropic medium from the theoretical existence Fs of the inverse by filter Es 71 thanks ration be in Rise and sensor design and ment and comments for to This work tried of inverse limitations and Binford Ess Tm filtering 1989 72 by Stanford at DARPA provided K-0002 and F336l5-82K-5 and nition Conclusion elastic Simple tactile it for the is for many 0.2 Perhaps to results tactile finger is forces is ade and Intrinsic is to Robotics Boie for the within to im Stanford improvements required and the delayed elastic are re IEEE sen tactile optical Automat Robot 31 Boie eds Roth Research 1984 Proc Atlanta artificial of the 4th Capacitive and 1985 Miller Chiu ASME Winter Annual Daniel robot hand Meeting and mt Symp Bolles on Press readout and on Robotics Conformable 4526043 1985 Miami Califor In impedance IEEE mt Conf 370378 pp and hands Mass MJT image sensor an articulated Cameron for Cambridge sensor U.S Patent Brock August Santa Cruz sensing tion of the recog Conf on 1137 1131 finger-shaped 1987 tactile Automation sufficient Object mt Joint 9th applications Dario to servo system were available aliasing robotic nia tactile of applied are already for and Planar Los Angeles touch pp Intelligence 1988 and Using interpola reliability greatly the biggest reduce tasks is with of the sensor and pressure estimation initial if cylindrical localization manipulation JPL hand of this sensor and using vision Biechi interpretation feature 1985 Bajczy 45472 484 design the to low-level sensitivity manipulation tactel These data in tip The techniques within need tactile encapsulated hemispherical quate models were used both sensor and to develop strategies prove 108 References sors 20% MDA9O3-86- has not been Artificial tion with University contracts experimentally Begej that was invaluable are discussed in This method Mien 10 whose collabo Gorali fabrication was performed while the author student graduate funding Fearing are discrepancies large guidance insight and encourage Shekhar for helpful Armstrong and and The it response to Binford to was Hts Presently these effects 70 flHs Re ftPs the for the rubber in Acknowledgments Ps the would be account to of copper but do not seem to cause Many solved assuming now hard very more homoge conductors stress real the total pressure and angle can is is which strips re by given Ess Since function the imaginary the tangential is 69 It by imperfect and copper compliant stiff ignored hx analyze of the effects for response to caused interface at their slip sensor using easier may be of the creep between the rubber adhesion have hx which Some sponse tactile Environment using contact percep sensors pp 8996 Durrant-Whyte 1988 APE L0007562 22 The International Journal of Robotics Research Touch Philadelphia and Elect 3271 1984 Fearing 1986 for strategy Robotics San Engineering and for tactile force Implementing on sensor during Some exper perception and and shape Philadelphia determining 1985 partment of Active Electrical 1986 Siegel gence Contact sensors TR-900 hands den in SPIE Conf on sensing Engineering and S.M some chanics thesis Computer De Science Speeter ulation 1953 normal loads on an contact McCammon Biggcrs Fl 1987 Ph.D Thomas Reading ity Intelli based stress 1985 sensor tactile and Computer Stresses due Vision to the solid with elastic problems Me Applied .1 tan applica ASME75l57l66 Trans Analysis thesis 1968 Mass Timoshenko and robotic Artificial Hollerbach Robots Liu neering Case Western touch and capacitive Intelligent and tion to the Classical for dextrous Mass MIT Cambridge Garabieta me Rijn Netherlands New York Laboratory 434054 solid 1225 Processing Sons and MIT Jacobsen John Wiley of skin pre bars edges and 4661204 Image Signal spatial model to responses Digital Tactile mechanics Neurophysiol 1978 gential Nordhoffl 1981 .1 Smith pp 765771 Basic Problems aan Using curvature Res Robot Contact Alphen mechanoreceptor Siegel Electrical andAutomation mm dicting Digital Prentice-Hall 1981 continuum III En Cambridge 1975 N.J Cliffs and Johnson Phillips 13 Press Schafer Cambridge Mass. 1988 for sensing Sijthoff of Department Hollerbach of Elasticity and for systems Syst 81 Control Mechanics Contact Englewood Processing sensing tactile IEEE University gland Cambridge gratings grasping sensing Robotics Theory 1985 Pratt University 1980 Gladwell Hillis Con American North Carolina Binford tactile Fearing grasping hands IEEE mt Conf pp 96102 thesis Stanford IEEE mt Conf on chanics Francisco Tactile Ph.D and cylindrical and iEEE liv andAutomation pp 16371643 1987b Fearing on of Design manipulators Johnson resolution sensing Robotics interpretation Simplified robot Raleigh tactile Fearing Trans re-orientation 987a Conf on IEEE silicon 1988 Oppenheim Diego dextrous object iments with cell capacitive andAutomation Fearing performance pp 3238 Conference Fearing 1067 high 196120 San with manipulation trol on based imager dextrous 1985 Wise Devices Phillips pp 1062 and Automation Robotics Chun tactiie motion IEEE mt Conf on and New York and control Department Reserve Calculus of of robotic manip Biomedical Engi University and Analytic Geometry Addison-Wesley and Goodier 1951 Theory of Elastic McGraw-Hill APE L0007563 Fearing 23

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