Auton Robot (2014) 36:7991DOI 10.1007/s10514-013-9360-1A compliant self-adaptive gripper with proprioceptive hapticfeedbackBruno Belzile Lionel BirglenReceived: 28 February 2013 / Accepted: 30 July 2013 / Published online: 15 August 2013 Springer Science+Business Media New York 2013Abstract Grippers and robotic hands are an important eldin robotics.Recently,the combinationof graspingdevicesand haptic feedback has been a promising avenue for manyapplications such as laparoscopic surgery and spatial telema-nipulation. This paper presents the work behind a new self-adaptive, a.k.a. underactuated, gripper with a proprioceptivehaptic feedback in which the apparent stiffness of the gripperas seen by its actuator is used to estimate contact location.Thissystemcombinesmanytechnologiesandconceptsinan integrated mechatronic tool. Among them, underactuatedgrasping, haptic feedback, compliant joints and a differentialseesaw mechanism are used. Following a theoretical mod-eling of the gripper based on the virtual work principle, theauthors present numerical data used to validate this model.Then, a presentation of the practical prototype is given, dis-cussing the sensors, controllers, and mechanical architecture.Finally, the control lawand the experimental validation of thehaptic feedback are presented.Keywords Grasping Underactuation Haptics Compliant mechanism1 IntroductionMany signicant improvements in the design and the man-ufacturing of complex robotic grippers can be attributed toself-adaptive mechanisms (Birglen et al. 2008). While thereB. Belzile (B) L. BirglenDepartment of Mechanical Engineering, cole Polytechniquede Montral, Montral, QC, Canadae-mail: bruno.belzile@polymtl.caL. Birglene-mail: lionel.birglen@polymtl.cawere some early examples in the literature about prosthet-ics and patents database several decades before, one of therst well-known prototype in robotics was the Soft Gripper(Hirose and Umetani 1978). These mechanisms, also oftenreferred to as underactuated when used in grasping, distributean actuation force or torque to a driven systemand, combinedwith a robotic hand, lead to a mechanical adaptation of thelatter to the object seized. In recent years, these systems havebeen more and more prevalent in robotics, because they areusually cheaper and easier to manufacture and control. Self-adaptive mechanisms have been adapted for many applica-tions, including spatial robotic arms (Butterfass et al. 2001;Martin et al. 2004) and prosthetics (Kyberd et al. 2001; Car-rozza et al. 2004). They are particularly efcient in unstruc-tured environments because of their inherent ability to adaptthemselves to the grasped object with a minimal effort fromtheoperatorandbecausetheyrequireonlysimplecontrollaws.Inthiswork,compliantjointsareusedtoactasthepassive elements required to fully constrain the systemif lessactuators than degrees of freedom(DOF) are used. Extensivework have been done in the past on this combination includ-ing by the authors Birglen et al. (2008); Birglen (2010); Dol-laretal. (2010);Lottietal. (2002,2005);BoudreaultandGosselin (2006). Another main advantage of using compli-ant joints is that it signicantly reduces the number of parts.Indeed, multi-part revolute joints can be replaced by a singlepiece with notch hinges appropriately located. Backlash andfriction in the joints are also eliminated in compliant mech-anisms at the cost of a smaller range of motion and internalenergy stored (Howell 2001).In this paper, a newself-adaptive compliant gripper is pre-sented with the particularity of including proprioceptive hap-ticfeedback. Thelatterisaveryinterestingadditiontoateleoperated gripper (or robotic hand), because it reduces theusersdependencetovisionwhenitcomestograspingan1 380 Auton Robot (2014) 36:7991object, which can be very useful when the view is obstructedeither partially or in totality. It is also critical when it is essen-tial to control the contact forces or the type of grasp (pinch orpower grasp). For example, during laparoscopic surgery, thesurgeon only receives a limited amount of haptic feedback,even more so when the surgical tool is teleoperated eliminat-ing the physical link between the user and the tool. Accuratefeedback is essential for a surgeon to identify several anatom-ical structures and to control the tool motion and its graspingforce (Schostek et al. 2009). Proprioception is dened as theperception of internal motion and forces between body parts.Here, proprioceptive haptics refers to the restitution of thesense of touch with proprioceptive information. The sense oftouch, a.k.a. haptics, consists of two elements, kinaestheticand tactile feedback. Kinaesthetics refers to information pro-vided by internal perception (proprioception). On the otherhand, tactile feedback corresponds to information providedbysupercialsensors(exteroception).Hapticdevicesgivea tactile and/or kinesthetic feedback to the user in order tosimulate the sense of touch. To quote Kern (2009): whereastactile perception describes forces and elongations betweenskinandobject whicharelowinamplitudesandhighinfrequencies, kinaesthetic perception happens within musclesand joints at higher forces but with lower dynamics. Hapticdevices are useful for instance with teleoperated robotic armsin space or to help people with disabilities.Much effort has been done to nd an adequate substitutefor the sense of touch in terms of sensors and control laws(Dubey et al. 1999; Goethals 2008; Hayward and Maclean2007; Kern2009; LinandOtaduy2008). However, mostworkhavebeendoneintheeldofexteroceptivehaptics,whichmainlyusetactilesensors(whichcanbeexpensiveand hard to use) as opposed to proprioceptive haptics whichuse internal sensors such as position and electrical (voltageand current) sensors. In this paper, the device presented pro-videsbothtactileandkinaestheticfeedbackssimplyusingproprioceptivesensorsandalgorithms. Whilepropriocep-tivefeedbackhasbeendescribedandcharacterisedintheliterature (extended physiological proprioception) (Simpson1974; Doubler and Childress 1984) and some prior work usedsmall-signal impedance changes (Backus and Dollar 2012),this is the rst time that proprioceptive haptic feedback basedon current measurements is used with underactuated hands tothe best of the authors knowledge. Also, the gripper designedhere is aimed as being a rst step toward an integrated med-ical tool, as seen in (Doria and Birglen 2009) without hapticfeedback. Because of the relative stiffness of the gripper, tograsp soft tissues, modications must be done to the com-pliantjoints.Itshouldbenotedthatmultiplemechatronicdeviceshave beenpresented in the past in the aim of per-forming surgery, some including haptic feedback (Kode andCavusogl 2007; Tholey and Desai 2007) but not with an adap-tive grasper.Whilehapticfeedbackandunderactuationhaveindeedbeen combined in virtual reality systems (Luecke and Beck-man 2008) in the past, the term underactuation in the latterdoes not describe the type of devices referred here to as self-adaptive. It is not the same underactuation as in compliantrobotic hands. Inthis former type of underactuation, the unac-tuated DOF are free to move constrained only by the dynam-ics of the system, as opposed to self-adaptive mechanismswhere the motion is constrained by passive elements. Thisalso makes the approach presented in this paper innovative.The prototype presented here has the distinction of havingonly two actuators and a small number of sensors, making itlow cost and simple. Thus, the challenges encountered dur-ing the design and testing phases were to build an efcientgripper with a realistic haptic feedback with little informa-tion from the teleoperated device. The theoretical model andexperimental data used to achieve this result are presented inthis paper.2 Self-adaptive mechanismTo be underactuated, or self-adaptive, a gripper must havemore DOFthanactuators. This type of grippers have the inter-esting characteristic of being capable to envelope an objectwhile been driven by as fewas only one actuator (e.g. the pre-sented prototype), making themcheaper and easier to control(Birglen et al. 2008). Figure 1 illustrates how self-adaptivengers work. The input force (bottom arrow) distributes theactuation force at the base of the gripper to each nger. Thesengers have three phalanges and if there is no contact with anobject, the actuation force is balanced by the torques inducedby the deections of the rotational springs. When contact ismade with the object, the actuation force is still opposed bythe torques of the springs, but also by the contact forces ateach phalanx which are in contact with the object, makinggrasping easy and efcient.A valid model of the motion of the gripper and the trans-mission of the forces is crucial to establish what is the contactsituation with only proprioceptive sensors. While nite ele-ment analyses (FEA) and empirical data could be used to thisaim, a theoretical model makes it possible to do many simula-tions by conveniently changing the parameters of the gripperandtheobject. Furthermore, theeffect ofeachparametercan be readily found without requiring long simulations orexperiments. To have an accurate model of the mechanism,it is essential to combine together two different cases. First,the motion of the gripper before any contact is made withthe object and, second, the transmission of the input forceto the object after contact is established. The purpose of thisanalysis is to model the interactions in the device and withits environment, i.e. the object to be grasped. Furthermore,the geometric conguration of the gripper and its actuation1 3Auton Robot (2014) 36:7991 81Fig. 1 Pseudo-rigid-body model of the gripper with input and outputforcesforce are especially important in the case of haptic teleop-eration, because the actuation force before contact is madeshould not be included in the feedback provided to the user.Therefore, with a proper model, it is possible to have a moretransparent hapticdevice. Transparencyinhapticdevicesis an important property related to the impedance from theinput to the output forces and motions, ideally close to anunitarytransferfunction(Kern2009). Basically, it meansthat the user only feels the contact forces between the objectgrasped and the hand without external disturbances such ashysteresis, frictionor dynamiceffectsintheteleoperatedgripperandhapticdevice. Todeterminetheshapeofthegripper and the contact forces generated by every phalanx, aquasi-static analysis can be used (Birglen 2006, 2009; Quen-nouelle and Gosselin 2010). This method allows obtainingthe desired solution (i.e. the output forces) without havingto express internal forces in the mechanism, which are, as arst approximation, often unnecessary in the analysis of self-adaptive mechanisms. Furthermore, the kinetic energy of alight-weight slow-moving mechanismas the one presented inthis paper is very small in comparison to the potential energystored into the compliant joints.2.1 NotationThroughout this paper, a specic notation is used to refer tothe gripper. First of all, because the gripper has two ngers,Fig. 2 Geometric parameters of the gripperthe indexes R and L (for the right and left side respectively)are used. If the index k is mentioned in an equation (in placeof Ror L), itmeansthatitisvalidforbothsidesandk

corresponds to the opposite nger in the same equation. Theangles i and i are absolute and i are relative. The parame-ter Yais the vertical position of point A, which is the inputprismatic joint. Furthermore, to simplify some equations, theabbreviation s is used as a shorthand notation for sin . Also,the anglesRi, Riand2(cf. Fig. 2) are considered posi-tive in the counter-clockwise direction, while Li and Li aredened positive in the clockwise direction.2.2 Quasi-static analysisAsmentionedbefore, thevirtualworkprincipleispartic-ularlyefcient intheanalysisof compliant mechanisms.Forthepurposeoftheanalysis,thecompliantmechanismis replaced by its equivalent pseudo-rigid model (PRM). Byapplyingthisprincipletoaself-adaptivemechanism, oneobtainsaset of equationsrelatingtheinput andtheout-putforcesasafunctionofthegeometriccongurationofthe mechanism. As previously presented in (Birglen 2009),the analysis of a three-phalanx nger can be done by com-biningthetwokinematicloop-closureequations andthethreeequationsobtainedfromthevirtual workprinciple.The same approach is used in this paper where the gripper is1 382 Auton Robot (2014) 36:7991constituted by two ngers connected by a seesawmechanismat the base. The seesaw mechanism used here is similar tothe one presented in (Birglen et al. 2008) with the addition ofcompliance. The design parameters of the compliant gripperwith two three-phalanx underactuated ngers are detailed inFig. 2. The kinematic loop-closure equations for the ngerand the base are presented in appendix.By applying the virtual work principle to the gripper withthe input forcefa, the following equation is obtained:W =8

i =1TRiRi +8

i =1TLiLi + Tcc faYa 3

i =1fRiTzRi 3

i =1fLiTzLi(1)where ki is the relative angle associated with each compliantexure (e.g. 2 = 2 1). In Eq. (1), fkiTzki is the virtualwork done by each contact force. The vector zkimeasuresthe position of the associated contact point from the originof the reference frame. The variable kkiis the distance fromthe base of the phalanx to the contact point, as illustrated inFig. 1. Therefore, one has:fk1Tzk1 = || fk1|| kk1k1, (2)fk2Tzk2 = || fk2|| (L1 cos(k2 k1)k1 + kk2k2), (3)fk3Tzk3 = || fk3|| (L1 cos(k3 k1)k1+L2 cos(k3 k2)k2 + kk3k3). (4)Becausetherearesixindependentvariables(R1, R2,R3, L1, L2 and L3), six independent virtual work equa-tions can be obtained and expressed as:Mkxk = 0, (5)where___xk =_tTkfk1fk2fk3fa_T,tk =_Tk1. . . Tk8TCTk

7Tk

8_T.(6)The coefcients of matrix Mk are also presented in appen-dix. By taking the partial derivatives of the kinematic loop-closure Eqs. (14)(18) with respect to the independent vari-ables (R1, R2, R3, L1, L2, L3) and using Cramersrule to solve the linear equation systems, one obtains:k4k1=L1 sin (k5 k1)b sin (k4 k5),k5k1=L1 sin (k1 k4)a sin (k4 k5),k4k2=L2 sin (k5 k2)b sin (k4 k5),k5k2=L2 sin (k2 k4)a sin (k4 k5),k4k3=c sin (k5 k3)b sin (k4 k5),k5k3=c sin (k3 k4)a sin (k4 k5). (7)Subsequently, using the loop-closure Eqs. (16)(18), oneobtains for the seesaw linkage of the device:bk = ckgk5hki, (8)wherebk =_k1kik

1kik2kiYaki_T, (9)ck =____kmsk

1+k6s+k2 + nskk

1+2sk6kmsk1k6s+k2 nsk1k6s2(sk

1sk1k6)h(mAk + nBk)kh__kmsk

1+k1s+k2 + nskk

1+2sk1, (10)with_Ak = sk1+k

1sk6k2 + s+k2k1sk

1+k6,Bk = sk

1+k2sk1k6.(11)and where R = 1 and L = 1.Thissystemofequationsgoverningthegrippercanbesolved numerically to obtain the latter geometric congura-tion and the generated contact forces in case of an object tobe grasped, both as a function of the input forcefa.2.3 Compliance modelingThe analytical values of the stiffnesses Ki approximating thenotch hinges used in the gripper can be computed using equa-tions found in the literature. According to (Lobontiu 2003),inthecaseofrectangularnotchhinges,areasonablesim-plication of the compliant joint used in the prototype (seeSect. 3), the following can be used:__MzFyFx__=__K11K120K12K2200 0 K33____zyx__= K__zyx__(12)where _MzFyFx_Tis the internal force vector as denedin(Lobontiu2003), _zyx_Tisthedeectionvector,and K the stiffness matrix. The componentsFyandFxcanactually be neglected because of the reaction force with thesame intensity but opposed direction at the other end of theexure hinge. The geometric parameters of the hinge usedinthisworkareillustratedinFig. 3. Theparameter wisthe width of the joint (which is also the width of the wholegripper), Eis the Young modulus of the material, liis thelength of the hinge and tiis the thickness of the joint.Thetorquegeneratedbyeachcompliant joint is thenKi_zyx_T, where Kiis the equivalent stiffnessmatrix of the hinge obtained fromEq. (12) and_zyx_Tis the corresponding deection of the hinge. Relevant coef-cients of the stiffness matrix are presented in appendix.1 3Auton Robot (2014) 36:7991 83Fig. 3 Compliant rectangularnotch hinge2.4 Numerical dataByusingthequasi-staticmodel obtainedinthepreviousanalysis, the behavior of the gripper can be predicted. Thegeometric parameters of the prototype used in this paper arepresented in Table 1.Figure 4 for instance shows the variation of Ya as a func-tion of the input forcefa. The upper curve corresponds to thecase when the gripper is closed without any obstacle in itsworkspace. Hence, in that case the input force only balancesthe deection of the compliant hinges. The other lower curveis when there is a contact for a particular grasp-state (denedastheassociationofthegeometriccongurationandcon-tact location) and the gripper subsequently adapts its shapeto the corresponding object. The dashed curves are obtainedfrom a dynamic simulation package (DSP), MD ADAMS.The main reason for this choice of software is its effective-ness to approximate compliant joints. The solid curves arethe results obtained from the numerical quasi-static model.One can see clearly that both curves are very close, validatingthe theoretical quasi-static model with respect to the motionof the gripper.Additionally, one should notice the motion of the gripperafter a contact. What is interesting is that this motion and itsforce/deection curve depend on the geometric location ofthis contact. Therefore, it is possible to estimate where thecontact occurs by considering the deviation of the positionof the gripper slider (Ya) with respect to the input force anditsoriginalvaluewhencontactismade.Indeed,whenthe0 10 20 30 40 50 60 700123456||fa|| (N) Ya (mm)free closing (PRM)grasping an object (PRM)free closing (DSP)grasping an object (DSP)contact occursFig. 4 Slider position variation Ya as a function of the actuation forcefa (i.e. gripper equivalent stiffness)contact is near the palm of the hand, the curve is closer to thecontactless curve, unlike the case where the object is pinched(with distal phalanx). While a contact on the proximal pha-langeisthesituationclosertoacontactlessscenario,itisstill possible to distinguish both cases as there is a notabledifference in terms of gripper stiffness. Furthermore, theoret-ically, the location of contact on the proximal phalanx has noeffect on the after-contact motion. Therefore, if the contact isnear the end of the proximal phalanx or at its base, the resultshould be the same and should be noticeable at the actuator.This property is thereupon used to provide tactile feedbackwithout tactile sensors. It should be noted that solely with theforce and position sensors at the actuator, it is impossible todistinguish between a contact on the same location on eitherthe right or the left nger. Thus, the authors only consideredsymmetrical grasping in their subsequent analyses.To again verify the model and the results obtained, threedifferent situations werecompared: thecompleteclosureofthegripperwithout anycontact andtheclosureofthegripperonacylinderwithcontactoccurringontheproxi-mal or the intermediate phalanx. Table 2 presents the dataTable 1 Parameters of thegripper and the compliant jointsL1 (mm) 9.1 l1 (mm) 1.7 t1 (mm) 1.0L2 (mm) 9.6 l2 (mm) 2.5 t2 (mm) 1.2L3 (mm) 9.1 l3 (mm) 2.5 t3 (mm) 1.5a (mm) 15.0 l4 (mm) 2.5 t4 (mm) 1.0b (mm) 20.5 l5 (mm) 2.5 t5 (mm) 1.0c (mm) 6.0 l6 (mm) 1.4 t6 (mm) 1.0d (mm) 11.6 l7 (mm) 2.5 t7 (mm) 1.0f (mm) 9.8 l8 (mm) 2.5 t8 (mm) 1.5g (mm) 6.4 lc (mm) 2.5 tc (mm) 1.8h (mm) 26.5 () 90.0 w (mm) 5.0m (mm) 19.8 () 71.0 E (MPa) 300.0k (mm) 10.3 () 36.21 384 Auton Robot (2014) 36:7991Table 2 Actuation force neededto close the gripper and contactforces for a typical graspFull closure force(||fa||) (no object)(N)1st phalanx force(input 100 N) (N)2nd phalanx force(input 100 N) (N)Theoretical model 69 29.51 4.91Dynamic simulation package 70 29.22 4.86Fig. 5 FEA of the grippercorresponding to these situations. These values are obtainedfor a typical closing sequence. For another object and inputforce, the results would be different.The results fromthe two methods are again close, suggest-ing that the theoretical model is accurate. The observed slightdiscrepancies between the different models can be attributedtosimplications, suchasthenumerical precisionof thedynamic package solver, the approximation of the contacts asone point on the phalanges in the theoretical model and of thenumerical method (NewtonGauss) used to solve the theoret-ical model. Asecond validation was done by a FEAsoftware(Ansys Workbench), as shown in Fig. 5. The main objectivewas to validate the PRMby comparing its motion to the FEAmodel. While the input force required to fully close the grip-per was practically the same between the actual gripper andthe FEA model (60 N), it is lower than what is obtained fromthe PRM. This difference can be attributed to the deformationof the links which are considered completely rigid and theapproximation of the compliant joints. However, differencesof this magnitude are normal and acceptable for the analysisof compliant mechanisms.3 Prototype3.1 OverviewThenewhaptic/graspingdevicepresentedinthispaperismade of two subsystems: the self-adaptive gripper and thehaptic interface. These two systems are controlled by a real-timecontrol platform, allowingtheacquisitionofexperi-mental data in order to validate, and in the future, improvethe device. For the sake of simplicity and compactness, bothsubsystems are attached together, but nothing prevents thegripper from being the teleoperated end-effector of a robot.Then, theuseroperatingtherobot will receivethetactileinformation through haptic feedback while the robot and thegripper will autonomously seized the object desired, takingfull advantage of the mechanical adaptation of the gripper tothis objects shape.3.2 Mechanical and electronic designAs mentioned before, the gripper is constituted of two three-DOFngers.Thematerialchosenforthegripperispoly-caprolactone. Thispolymerhasseveral advantages: alowmelting point (60C) which makes it very easy to use withamold, it isalsobiocompatible, biodegradableandverydurable. The Young modulus of the polycaprolactone used inthe theoretical model has been determined experimentally toaccount for the grade of the particular plastic obtained fromthe manufacturer and variations due to the fabrication process(3D printing). Several experiments were done to determinethe Young modulus and the yield point. Initial results showeda decrease of the elasticity of the gripper caused by a plasticdeformation in some joints. A FEA validated that the yieldpoint of the polycaprolactone can be exceeded under someconditions during the grasp of an object. Because the width ofthe compliant joints cannot be increased without signicantlyincreasingthestiffnessofthejoints, thegripperwaspreworn mechanically to endure a plastic deformation that willnot be exceeded under normal conditions of use. It was doneby bending the hinges beyond their limits under normal use.Thepropertiesofthepolycaprolactonewerecharacterizedafter this process to have an accurate theoretical model. Theplastic deformations subsequently apparent were relativelysmall compared to the usual elastic deformations occurringduring normal utilization. Indeed, this process did not haveanysignicant impact onthereliabilityofthegripper, asno failure at the joints was observed during the tests doneafterward (which involved hundreds of closing and openingmotions).The input force of the gripper is transmitted by a nyloncable attached to a pulley on the shaft of a Maxon RE25 DC1 3Auton Robot (2014) 36:7991 85Fig. 6 Prototype of the haptic grasping deviceFig. 7 Inside view of the haptic devicemotor with a planetary gearbox. This transmission mecha-nism was chosen to reduce friction as far as possible, whichcan have substantial impacts on the realismof the haptic ren-dering.The handle of the device has two purposes. First of all, therotation angle commanded by the user gives the reference tobe followed by the controller. This angle is read from opticalencoder attached to the Maxon RE10 DC motor driving thehandle. Another gear train (with a ratio of 20:1) signicantlyincreases the precision of the measured angle and the max-imum torque available at the output shaft (the handle). Thevalue of the torque produced by this motor is computed withthecontrollawpresentedinSect.4.2.Also,avibrotactileinterface is used to send haptic signals to the user. It consistsof a small motor with an off-centered weight applied on theusers skin. While it is not ideal to send a continuous feed-back due to habituation of the skin receptors, it can be usedto send momentary haptic icons. The device and its interiorare illustrated in Figs. 6, 7 and 8.Fig. 8 Side view of the haptic device3.3 Sensors and controllersThe motor controllers used here are Maxon ADS 50/5 4-Q-DCServoampliers. They were selected for their compatiblerange of voltage and current to the actuators. The ADS 50/5also has built-in current sensors proving very useful to collectdata. The output of the motor controller is a current, whichmeans this system is force controlled.4 Experimental dataManydifferent experimentswereperformedtoassesstheperformances of the device and to solve problems that werenot anticipated. First, thedevicewastestedinopen-loop,i.e. without anycomplexcontrol algorithm. Then, severaliterations of the control scheme were experimented with dif-ferent parameters to nd the most suitable to achieve a stableand efcient grasp. Finally, the algorithms for haptic feed-back were implemented with different types of grasp (pinch,powergrasp, etc.)anddifferent objects. All theseexperi-ments were necessary to achieve an accurate haptic feedbackwhich requires a control scheme that accounts for undesir-able effects such as friction, exibility of the assumed rigidlinks and hysteresis in the transmission.4.1 Nylon cableThecableusedtotransmit theactuationforcefromthemotorshafttotheinputofthecompliantgripperismadeofnylon,amaterialchosenforitsstrengthandexibility.However, the force it transmits induces a signicant deec-tion. The experimentally obtained force-elongation relation-ship for the cable is shown in Fig. 9. This effect is taken intoaccount in the control law as detailed below. A stiffer cable1 386 Auton Robot (2014) 36:7991Fig. 9 Elongation of the nylon cable as a function of its tensionwould not necessarily have been a better solution, becauseit would havebeen difcult, if not impossible, to wind upthe cable around the pulley and the rods in the casing of thegripper. Additionally, a deformation of the cable preferabletoadeformationoftherigidsectionsofthegripperwhenthere is no longer any adaptation of the gripper to the objectgrasped.4.2 Control lawThe block diagram shown in Fig. 10 illustrates how the grip-per is controlled and how the haptic feedback is calculatedand sent to the user holding the device. The plant correspondsto the RE25 motor and the gripper itself. The RE10 motoroperates in open-loop with a servoamplier used to controlthe current in the motor. As mentioned before, there are onlytwosensors, bothbeingproprioceptive. Therefore, traditionalforcecontrol algorithmsusingtactilefeedbackcannot beimplemented. First of all, a feedforward algorithmis used forhysteresis compensation(as explainedinSect. 4.3) andworkswell for a computed reference. However, this method has alimitation when the reference input comes froma human user(through the handle). For example, during a normally clos-ing sequence, the user can momentarily stop or slightly gobackward multiple times. This cause the algorithmto changefromtheclosingestimationcurvetotheopeningestima-tion curve very rapidly. Then the system tends to oscillateand makes the haptic device unusable. To solve this prob-lem, a hybrid solution which combines two approaches wasimplemented.Firstly, two thresholds were set to detect a closingsequence or an opening sequence. In other words, the angularvelocity of the handle must be greater than +> 0 to use theclosing algorithm and must be lower than < 0 to use theopening algorithm. Between + and , the previous state isused. This is similar to a Schmit trigger. Secondly, low-passlters are used to eliminate noise and high-frequency mea-surements which are undesired for a device like this one withonly slow dynamics. This hysteresis controller computes thereference to be sent to the servoamplier which as a build-infeedbackloopthatcontrolsthecurrentpassingthroughthe actuator. One should note that the hysteresis controllercannot differentiate a deviation from the contactless behav-ior caused by grasping an object or the hysteresis itself. Itwould thus increase the input force until the desired pulleyangle, as measured by the optical encoder and function ofthe reference angle provided by the handle, is obtained. Ifevery DOF of the gripper are blocked, it would theoreticallyincrease indenitely. However, one can take advantage of theelasticity of the nylon cable which is easier to deform thanthe gripper itself. Indeed, the cable will stretch and the refer-ence angle will be reached. It is thus essential to characterizethe properties of the nylon cable to the relationship betweenthe cable tension and the cable stretch.Fig. 10 Block diagram of the controller1 3Auton Robot (2014) 36:7991 874.3 HysteresisThroughout initial experiments, one particular phenomenonwasobserved,namelyhysteresis.Thisproblemarosedur-ing experimentation. After investigation, it was found to bemainly caused by the friction between the polycaprolactonegripperanditscasing. Thenonnegligiblefrictioncoef-cient between the materials used is the cause. Different typesoflubricantswereusedtoreducefriction. Solidlubricant(graphite powder) had the best results, but the gain was notsignicant. Another material which would induce less fric-tioncouldbeusedforthecasing, but it wasnot deemednecessaryfortherst prototypeastheproblemcouldbesolved otherwise. It should be noted that any liquid betweenthecasingandthegrippercouldalterthehysteresiscurveand thus the haptic feedback. A sealed casing or no casing atall should prevent this issue from happening. The gearboxsbacklash has no signicant effect compared to this friction.Thishasanimportantimpactandleadstoadeadzoneatthe beginning of the closing and opening sequences, as illus-trated in Fig. 11. While the closing curve roughly follows thetheoretical curve obtained from the model presented earlier,the opening curve is distinctively different. Fortunately, thehysteresis curve is mostly identical for any closing velocityexperimented (from 0.5 up to 5 s), thus simplifying the com-pensation process. Many solutions can be used to compensatefor hysteresis. Cavallo et al. (2004) used a position controllercombined with a hysteresis compensator while commandinga magnetostrictive actuator. Cruz-Hernandez and Hayward(1998) used an algorithm compensating phase distortion. Inthe present work, a feedforward algorithm is again used toachievethisgoal.Byusingexperimentaldata,theclosingand opening curves are approximated by two lookup tables.These tables were built by compiling several experimentalresults where the input torque varied until the gripper wasfullyclosed(withoutanyobject). Tomakesurethatther-mal variations did not have an impact on the lookup tables,an experiment was done where the gripper was fully closedforacompletehour(whichismuchlongerthananaver-age closing sequence). Although temperature did rise up by25C (which is still lower than the maximum rated temper-ature of the motor), there was no noticeable change in theforce-position curve used in the lookup tables. While heat-ingisnotanissuefortheprecision, long-termwearmayrequireoccasionalcalibration.Itisthenpossibletocalcu-late the valid current input for a particular position referencedepending on the instantaneous closing or opening motion ofthe gripper. Also, a feedback PID controller is added to com-pensate for the small errors still present. Thus, the dead zoneis mostly compensated when there is a change of directionand the device nowpresents only insignicant errors betweenthe reference and the position output as illustrated in Fig. 12where the gripper is closed and opened multiple times.Fig. 11 Hysteresis curve during a closing motion followed by an open-ing motion of the gripper0 5 10 15 20 25 30 35 4050050100150200250300350400Time (s)Angular position of RE25 ()referencemeasured without compensationmeasured with compensationFig. 12 Angular position of the RE25 motor with and without com-pensation4.4 Haptic interfaceAs one could point out, a simple passive purely mechanicalhaptic system could be achieved by simply connecting thehandle directly to the nylon cable or by using any other sim-ilar transmission mechanisms such as bevel gears. However,the aimed transparency property would be difcult to reach,because a feedback would be transmitted to the user (due tothe joint compliances) even if there is no object grasped. Itwould thus be difcult for the user to precisely know whencontact is made. Moreover, unwantedside effects suchas hys-teresis andfrictioncouldnot be signicantlyreduceddirectly.Therefore, a second actuator (RE10) and an associated con-trol law are used for the haptic interface.As shown in Fig. 13, the measured current of the RE25motor is different whether there is a contact or not with anobject, which is the case for the rst, the second, the fourthand the fth grasping motion. In this gure, where the gripperis again closed and opened multiple times, the solid curve is1 388 Auton Robot (2014) 36:799110 20 30 40 50 60 70 80 9000.511.522.53Time (s)Current of RE25 (A)measuredexpected (without contact)Fig. 13 Expected (if closing without contact) and measured angles ofthe RE2510 20 30 40 50 60 70 80 900.20.40.60.81Time (s)Handle command voltage (V)10 20 30 40 50 60 70 80 90050100150200250Torque at the handle (mNm)Fig. 14 Haptic feedback at the handlethe current of the RE25 expected when no object is seized,which is a function of the handle angle. Because the mea-suredcurrentishigherthanthedesiredcurrentduringtheseizing of an object, it is possible to compute the differencebetween those two values. Because the expected and mea-sured currents are not exactly the same even when there is noobject grasped, a tolerance zone is added to make sure no hap-tic feedback is sent when there is no contact. Also, the RE25motor does not always perfectly return at its original positiondue to the friction between the gripper and its casing. Thisis caused by the relatively low gains (most of the commandvoltage is computed by the feedforward algorithm) and thefact that negative command voltages are not used. However,this does not cause any signicant problem because it is onlya local problem (near the position of the motor at rest) andthe control law does not send negative haptic feedback.Figure 14 shows a particular feedback for the sequenceof Fig. 13 with several contact. This feedback is sent to theuser as a torque at the handle. The peaks on this gure at thebeginning and ending of the grasping are due to the imper-0 5 10 15 20 25 30 35 40 4500.20.40.60.81Time (s)Aftercontact Stiffness (mNm/rad)haptic signaldistal thresholdproximal thresholdFig. 15 Localisation of the contact point using the instantaneous stiff-ness Kcfectestimationbythefeedforwardalgorithmsduetotheirexperimental nature. The gripper closes six times, but thereis a contact with an object only for the rst, second, fourthand fth iteration. This is why no feedback is sent between3050 s and 7090 s.Thesecondpart of thehapticfeedbackconsistsinanapproximationofthelocationofthecontact betweentheobject and the ngers. It is useful for several applications,becauseit allowstheuser toknowwhether theobject ispinched or power grasped. Indeed, by considering the meanderivative of the input force of the gripper following the rstcontact, itistheoreticallypossibletomathematicallyesti-mate the location of the contact merely with proprioceptivesensorswhileconsideringthegraspingisnearlysymmet-rical. However, using this derivative is numerically unstablebecause of the signicant amount of noise caused by friction.Instead, it is possible to estimate the location by consideringthe deection caused by a certain increase of input force aftercontact. It is thus equivalent to performing a derivative. Withthis deection, it is possible to compute in real-time the valueof the after-contact stiffness with the following equation:Kc =RE25, f RE25,iTRE25, (13)where RE25,i is the measuredangular positionof the actuatorat the beginning of the contact, TRE25 is the predeterminedincrease in torque and RE25, fis the measured angular posi-tion after the torque increase. While the measured stiffnessdifference (as seen from the actuator) depending on the con-tact locationisnot large, it isstill possibletoinformtheuserwhetherthereisacontact ornot andonwhichpha-lanx it is located. Considering the small size of the gripperand the fact that it is not normally possible without tactilesensors, this information is still quite accurate. In the con-trol scheme (Fig. 10), the initial contact is rst detected by adeviation from the expected current inside the RE25. Then,1 3Auton Robot (2014) 36:7991 89Kc is computed with Eq. (13). The contact location is estab-lished with a table containing thresholds for each phalanx. Asignal is nally sent to the vibrotactile interface. An exam-ple of location detection for a contact occurring at differentstages of a grasping sequence is shown in Fig. 15 (a differ-ent test unrelated to the other gures). The rst, second andthird contacts occur respectively on the distal, intermediateand proximal phalanges, all occurring at the beginning of theclosing sequence. The nal peak is a pinch grasp (distal pha-lanx) occurring at the very end of the closing of the gripperwhich explains the high stiffness. The haptic signal from thegure (solid curve) is computed with Eq. (13) in real-time.The command sent to the vibrotactile device depends on thezone it reaches (proximal, intermediate or distal).Finally, thelastpieceofhapticinformationsenttotheuseriswhetherthegraspisstableofnot.Whiletherearemanycriteriatodetermineifstabilityisreachedornotinboth fully actuated and underactuated grasping (Howard andKumar 1996; Begoc et al. 2006; Kragten and Herder 2010),with only a limited amount of proprioceptive measured, theauthors have chosen a simple criterion to send feedback inreal-time: when the instantaneous stiffness of the gripper hasexceededapredeterminedlevel, whichmeansthereisnolonger any noticeable deformation of the compliant joints,the grasped object can be considered secured in the gripper(which is the case for instance with the nal grasp illustratedin Fig. 15. A signal is then sent to the user. Both signals onthe type of grasp and the relative stability are distinguishableby the operator because of their different frequencies.It should be noted that if a contact occurs on the outsideof the links while the base of the gripper is static, it mightbeimpossible(withsolelythepositionandforcesensors)to discriminate from a contact on the inside of the gripper.Forexample,theseconditionsweretestedbypressingthegripper on a surface with a high friction coefcient (rubber).Thehapticfeedbackinthissituationwasnolongeraccu-rate. However, the outward motion of the gripper is relativelysmall, thereby reducing the occurrence of such events.5 ConclusionThis paper has presented the design and experimental devel-opment of a new proprioceptive self-adaptive gripper withhaptic feedback. The amalgamation of many interesting fea-tures, such as compliant joints, underactuation and a hapticinterface makes this device unique. The theoretical model ofthe device has been reviewed using a quasi-static analysis andthe numerical and experimental results have been presented.The device succeeded in providing a tactile feedback to theoperator by only using data form proprioceptive sensors andcontrol algorithms, which is the novelty of this work. Futurework will include further experiments on the prototype andthe design of an improved version fromthe collected data andanalysis which will deepen the proprioceptive haptic inter-faceanditsalgorithmstohaveanevenmoretransparentfeedback. The possible miniaturization of the gripper wouldinvolve a new manufacturing technique and perhaps a newmaterial.Acknowledgments Thesupport oftheIngenieriedeTechnologiesInteractives en Readaptation (INTER) network is gratefully acknowl-edgedas well as the National Science andEngineeringResearchCouncil(NSERC), the Fonds de recherche du QuebecNature et Technologiesand the Canadian Foundation for Innovation. The authors would like tothank Maxime Blaise for his contribution on the design and fabricationof the prototype.Appendix 1: Kinematic loop-closure equations0 =L1 cos k1 + L2 cos k2 + c cos k3 + b cos k4+a cos k5 d cos , (14)0 =L1 sin k1 + L2 sin k2 + c sin k3 + b sin k4+a sin k5 d sin , (15)0 = m cos( + k2) + h cos (k1) g cos k6 f, (16)0 = m sin( + k2) + h sin (k1) g sin k6 Ya, (17)0 =(k + 1) f + g sin(R6 + (k + 1)4 )h sin(R1 + (k + 1)4 ) n sin(2 + (k + 1)4 )kh sin(L1+(k+1)4 )+kg sin(L6+(k+1)4 ).(18)Please note that the gripper is designed to be symmetrical,i.e. all lengths are the same on both sides.Appendix 2: Virtual work matricesThe virtual work matrices for each side of the gripper are:Mk = _mk1. . . mk15_, (19)mk1 = _1 0 0_T, (20)mk2 = _1 1 0_T, (21)mk3 = _0 1 1_T, (22)mk4 =_k4k1k4k2k4k3 1_T, (23)mk5 =____k5k1 k4k1k5k2 k4k2k5k3 k4k3__, (24)mk6 =_k5k1k5k2k5k3_T, (25)1 390 Auton Robot (2014) 36:7991mk7 =____k1k1 k5k1k1k2 k5k2k1k3 k5k3__, (26)mk8 =____k1k1 k2k1k1k2 k2k2k1k3 k2k3__, (27)mk9 =_2k12k22k3_T, (28)mk10 =_k

1k1k

1k2k

1k3_T, (29)mk11 =____k

1k1 + k2k1k

1k2 + k2k2k

1k3 + k2k3__, (30)mk12 = _kk10 0_T, (31)mk13 = _L1 cos(k2 k1) kk20_T, (32)mk14 =__L1 cos(k3 k1)L2 cos(k3 k2)kk3__, (33)mk15 =_Yak1 Yak2 Yak3_T. (34)Finally, the coefcient of the stiffness matrix are :K11,i =Ewit3i3li, (35)K12,i =Ewit3i2l2i, (36)K22,i =Ewit3il3i, (37)K33,i =Ewitili. (38)ReferencesBackus, S.B., &Dollar, A.M. (2012). Robust, inexpensiveresonantfrequency based contact detection for robotic manipulators. In IEEEInternational Conference on Robotics and Automation (pp. 15141519). Saint Paul, MN.Begoc, V., Durand, C., Krut, S., Dombre, E., &Pierrot, F. (2006). On theform-closure capability of robotic underactuated hands. In 9th Inter-national Conference on Control, Automation, Robotics and Vision(pp. 18). Singapore.Birglen,L.(2006).Anintroductiontotheanalysisoflinkage-drivencompliant underactuated ngers. In Proceedings of the ASMEIDETC/CIE (pp. 5563). Philadelphia, PA.Birglen, L. (2009). Type synthesis of linkage-driven self-adaptive n-gers. 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In P.Herberts, R. Kadefors, R. I. Magnusson, & I. Petersen (Eds.), Thecontrol of upper-extremity prostheses and orthoses. Springeld, MA:C.C. Thomas.Tholey, G., &Desai, J. P. (2007). Ageneral-purpose 7 dof haptic device:Applicationstowardrobot-assistedsurgery. IEEE/ASMETransac-tions on Mechatronics, 12(6), 662669.Bruno Belzile received theB.Eng. degree in MechanicalEngineeringin2011andheisnow pursuing a Ph.D. degree inMechanical EngineeringwithintheRoboticsLaboratoryafteradirect transition from undergrad-uatestudies. Histhesisfocusesonthecontrolofunderactuatedrobotic hands including hapticfeedback. He holds scholarshipsfrom NSERC and FRQNT.Lionel Birglen received theB.Eng. degreeinMechatronicsfromEcole Nationale SuprieuredesArtset IndustriesdeStras-bourg (France) in 2000. HethenpursuedaPh.D. degreeinMechanical Engineeringwithinthe Robotics Laboratory at Uni-versit Laval (Canada), afteranacceleratedpromotionfromM.Sc. In 2005, he was appointedbythe Department of MechanicalEngineeringat theEcolePoly-technique of Montreal (Canada)where heis nowanAssociateProfessor in Mechatronics. His work focuses on the kinematic analy-sis and control of self-adaptive mechanisms, especially underactuatedrobotic hands, and with a particular emphasis on force control. He is aMember of IEEE, ASME, and CCToMM.1 3