Sliding-Mode Bilateral Teleoperation Control Design for Master-Slave Pneumatic Servo Systems

Transcription

1 Thi paper appear in Control Engineering Practice, Sliding-Mode Bilateral Teleoperation Control Deign for Mater-Slave Pneuatic Servo Syte R. Moreau 1, M.T. Pha 1, M. Tavakoli 2, M.Q. Le 1, T. Redarce 1 1 Laboratoire Apère, UMR CNRS 55, Univerité de Lyon, INSA-Lyon, F Villeurbanne Cedex, France 2 Departent of Electrical and Coputer Engineering, Univerity of Alberta, Edonton, AB T6G2V4, Canada Abtract Thi paper preent a novel bilateral control deign chee for pneuatic ater-lave teleoperation yte that are actuated by low-cot olenoid valve. The otivation for uing pneuatic actuator in lieu of electrical actuator i that the forer ha higher force to a ratio than the latter and i inert to agnetic field, which i crucial in certain teleoperation application uch a MRI-guided, robot-aited urgery. A liding ode approach, called the three-ode control chee, i incorporated into a two-channel bilateral teleoperation architecture, which can ipleent a poition poition, force force, or force poition chee. An analyi of tability and tranparency of the cloed-loop teleoperation yte i carried out. The propoed control deign perforance i experientally verified on a ingle-degree-of-freedo pneuatic teleoperation yte actuated by on/off valve. Experiental reult how high accuracie in ter of poition and force tracking under free-pace otion and hard-contact otion in the teleoperation yte. Another purpoe of thi paper i to deontrate the poibility to iprove the valve lifetie by increaing the nuber of control level. To do thi, a new control deign, called the five-ode control chee, i developed and copared with the three-ode chee in tie doain a well a in frequency doain. Keyword: Pneuatic actuator, on/off olenoid valve, liding ode control, bilateral teleoperation, tability, tranparency. 1. Introduction A telerobotic yte allow a huan operator to perfor anipulation or ening tak in reote, hazardou or confined environent. A bilateral teleoperation yte conit of a lave (reote) robot and a ater (local robot). The ater i handled by the huan operator for controlling the lave robot and ening the lave/environent contact force. Bilateral teleoperation yte have any proiing application epecially in inially invaive urgery and pace and underwater exploration, or hazardou environent where huan action i clearly retricted (Maurette et al., 1997; Sabater et al., 26; Ro et al., 29; Sanchez et al., 212). Tranparency i the principal perforance goal in bilateral teleoperation controller deign (Lawrence, 1993). It 1

2 eaure the quality of recreation of the echanical propertie of the reote environent for the huan operator. Abundant control theorie have been propoed to achieve high teleoperation tranparency when the lave i in free otion and/or contact otion. For an overview of control approache in teleoperation yte, the reader i referred to (Staen and Set, 1997; Hokaye and Spong, 26). Alo, quantitative perforance coparion between different teleoperation control ethod were reported in (Arcara and Melchiorri, 22; Aliaga et al., 24). It ha been hown that adding force feedback to a teleoperation yte ephaize the ene of telepreence, and iprove the uer ability to perfor coplex tak (Sheridan, 1995). Poition-poition and force-poition chee are exaple of conventional bilateral controller coonly ued in practice (Salcudean et al., 2; Fite et al., 21; Ki et al., 25). Beide tranparency, tability i alo a key iue in the control of bilateral teleoperation yte. Energetic paivity of teleoperation yte ha been widely ued to enure huan-robot interaction afety. Indeed, ipleenting each coponent of a teleoperation yte (e.g., the ater, the lave, the counication channel, etc.) a a paive eleent and interconnecting the in a power preerving way lead to a paive yte, which i conequently characterized by a table behavior. Several paivity baed trategie have been propoed for teleoperator uch a thoe in (Anderon and Spong, 1989; Nieeyer and Slotine, 1991; Straigioli et al., 22; Lee and Li, 23). In certain application involving bilateral teleoperation, the ater and the lave robot work at different power cale (e.g., icrourgery or teleanipulation with a large-cale lave robot for extra-vehicular activity in pace application). Several reearcher have addreed thi proble, reulting in control algorith that iprove the perforance of the teleoperation yte in a way that i copatible with the velocity/force caling. For intance, (Itoh et al., 2) propoed a control law baed on a cancellation of the open-loop nonlinear dynaic, which wa replaced by a deired virtual tool dynaic. (Lee and Li, 25) decopoed a teleoperation yte into a hape and a locked yte in order to ipleent caled coordination between ater and lave robot. Thi control chee allowed to render the cloed-loop teleoperator a a coon paive echanical tool with which both the huan and the environent interact, and whoe inertia and dynaic can be adjuted according to a given tak objective. Coonly, the actuator ued in ot of teleoperation yte are electrical direct-current otor. They are eay to intall, quiet, and iple to control. However, when gear-boxe are ued to produce large actuation torque, they ay reult in backlah and high inertia, which are undeirable becaue they introduce dicontinuity and ditortion in the force reflected to the operator. In thi tudy, we invetigate the developent and control of pneuatic actuator in a teleoperation yte. Copared to the electrical actuator, pneuatic actuator have higher force-to-a ratio and can 2

3 generate larger force without the need for any reduction echani uch a a gear-box. Moreover, they are inert to agnetic field, which i crucial in certain application uch a robot-aited urgery under MRI guidance (Ningbo Yu et al., 28). Due to the above advantage, pneuatic actuator have found ue in variou application of bilateral teleoperation. For intance, (Ben-Dov and Salcudean, 1993) preented force-reflecting control of a 6-DOF haptic ater actuated by flapper ervovalve and low-friction cylinder. More recently, (Tadano and Kawahia, 27) propoed a forcep anipulator for a urgical ater-lave yte capable of etiating external force without uing any force enor. (Durbha and Li, 29) propoed a paive bilateral teleoperation yte with huan power aplification through pneuatic actuator. The input huan force wa aplified through the pneuatic teleoperator to provide aitance for the huan operator in ter of perforing the tak. Thi would help the huan operator to perfor tak that required high force or power uch a lifting a heavy object. (Guerriero and Book, 28) controlled the foot poition of two 3-DOF legged lave robot driven by pneuatic actuator. In thi yte, bilateral teleoperation provided force feedback to the operator through two PHANToM ater haptic device a a function of the foot poition error. Pneuatic ucle actuator have been recently ued in a teleoperation yte (Tondu et al., 25). Thee are copact and have high power/weight denity actuator that are difficult to control and require accurate experiental characterization. In oe of the recent work involving pneuatic actuation, ervovalve rather than olenoid (on/off) valve have been ued to achieve high perforance in variou poition control or force control tak. However, it ut be noted that ervovalve are typically expenive coponent a they involve high-preciion anufacturing. Therefore, in thi paper, fat-witching on/off valve are ued due to their additional advantage in ter of low cot and all ize over ervovalve. One of the objective of thi paper i to how that good teleoperation tranparency can be obtained with thee inexpenive coponent a actuator of a teleoperation yte. The traditional control approach for yte with olenoid valve involve uing Pule Width Modulation (PWM) to control the output a flow rate of the valve (Noritugu, 1985; Shih and Ma, 1998; Taghizadeh et al., 29). A ain diadvantage of the PWM control i the chattering phenoenon in teady tate caued by the high-frequency witching of the valve (Hodgon et al., 211; Le et al., 211). Chattering can dratically reduce the valve lifetie and generate noie that are poibly diturbing for certain application. To overcoe the drawback of PWM-baed control of olenoid valve, thi paper preent a nonlinear liding-ode teleoperation control inpired by the chee ued in (Nguyen et al., 27). The firt contribution of our tudy i to ue a 3

4 liding approach in a two-channel bilateral teleoperation with three different architecture, naely poition poition, force force, and force poition. Thee architecture are choen due to their ipleentation iplicity and efficiency. A tracking perforance analyi and a tability analyi are provided for the cloed-loop yte uing a Lyapunov candidate function. Another contribution of our work i extending the liding ode trategy baed on the three-ode control chee (3MCS) to a five-ode control chee (5MCS). Thi new chee reult in reduced valve-witching activity and, therefore, iprove the overall lifetie and reliability of the teleoperation yte. For the ake of iplicity, the ater and lave actuator are conidered to be identical in thi tudy indeed, the ater and the lave are one-degree-of-freedo (DOF) anipulator with pneuatic on/off actuation. It hould be noted that thi paper doe not conider the poible preence of tie delay in the teleoperation yte counication channel for tie delay copenation in haptic teleoperation, the reader ay refer to (Aziinejad et al., 28; Chopra et al., 28). Such delay are coonly preent in long-ditance teleoperation yte but are generally negligible in local teleoperation yte I i noteworthy that local teleoperation yte are currently ore coon that long-ditance teleoperation yte and have application uch a inially invaive urgery, caled teleoperation for dexterity enhanceent. Thi paper i organized a follow. Section 2 preent the dynaical odel of the pneuatic anipulator. Section 3 decribe the ipleentation of a three-ode control chee in a two-channel ater-lave teleanipulation yte. To evaluate the propoed controller perforance, experiental reult a well a data analyi and interpretation appear in Section 4. Section 5 preent the extenion of the three-ode chee to the five-ode chee. A coparion of both chee i alo carried out in thi ection. Finally, Section 6 draw concluion and highlight the future work. 2. Modeling of the Pneuatic Syte A entioned above, the ater and the lave anipulator are identical, thu only one pneuatic robot i preented in thi ection. To decribe the air flow dynaic in a cylinder, we aue that air i a perfect ga and it kinetic energy i negligible in the chaber, the preure and the teperature are hoogeneou in each chaber, the evolution of the ga in each chaber i polytropic, the teperature variation in chaber i negligible with repect to the upply teperature, the a flow rate leakage are negligible, and 4

5 the upply and exhaut preure are contant. A cheatic of the 1-DOF pneuatic actuation yte i hown in Fig. 1. The device conit of a pneuatic cylinder, four olenoid valve, a force enor, and a poition enor. Each chaber i connected to two olenoid valve, where valve 1 and 4 are connected to the upply preure while valve 2 and 3 are connected to the atophere preure. Chaber p Chaber n Ma Force enor P p, V p, T p P n, V n, T n Poition enor q p q n Valve 1 Valve 2 Valve 3 Valve 4 P a P at P at P a U 1 U 2 U 3 U 4 DSP controller Deired force or otion Fig. 1. Electro-pneuatic yte with four valve y F The behavior of the preure inide each chaber of the cylinder can be expreed a (Blackburn, 196) rt P a p P& γ p = qp ( U1, U 2, Pp ) S p y& Vp( y) rta rta Pn P& γ n = qn ( U3, U 4, Pn ) + Sn y& Vn ( y) rta (1) where U 1, U 2, U 3 and U 4 are the dicrete control voltage (1 or ) of valve 1, valve 2, valve 3, and valve 4, y and y& are the poition () and velocity (/) of the piton, P p and P n are the preure inide chaber p and n (Pa), V p and V n are the volue of chaber p and n ( 3 ), S p and S n are the piton cylinder area in the chaber p and n ( 2 ), q p and q n are the a flow rate in chaber p and n (kg/), T a i the teperature of the upply air (K), r i the perfect ga contant (J/(kg.K)) and γ i the polytropic contant. The a flow rate characteritic of the on/off valve can be expreed a function of the dicrete control voltage and the preure: 5

6 q ( Pa, Pp ) for U1 = 1 and U2 = (chaber p fill) qp ( U1, U2, Pp ) = for U1 = and U2 = (chaber p cloe ) q ( Pp, Pat ) for U1 = and U2 = 1 (chaber p exhaut) q ( Pa, Pp ) for U3 = and U4 = 1 (chaber n fill) qn ( U3, U4, Pn ) = for U3 = and U4 = (chaber n cloe ) q( Pp, Pat ) for U3 = 1 and U4 = (chaber n exhaut) (2) where P a and P at are the preure of the upply air and atophere. The tate of the input voltage correpond to a cloed valve and the 1 tate correpond to an open valve. All the tate where U 1 = U 2 = 1 and U 3 = U 4 = 1 are prohibited to avoid a bypa of the valve. The function in (2) are given by a tandard expreion in which the a flow rate of the valve i regulated by the air paage through an orifice (McCloy, 1968): Tat Pdown C valpup if.433 (onic) T up P up 2 q( P, ) down up Pdown = P Cr T P at up C valpup 1 otherwie (ubonic) T up 1 C r (3) In the above expreion, C val i the valve flow rate coefficient, C r i the critical preure ratio, P up and P down are repectively the abolute uptrea and downtrea tagnation preure of the valve (Pa), T at i the atophere teperature, and T up i the uptrea tagnation teperature. Finally, the dynaic of the piton and the load are My && = S P S P by& F + F (4) p p n n t ext where b i the vicou friction coefficient (N./), M i the oving load (kg), F t i the tiction force (N), and F ext i the external force (N). For iplicity, the tiction force i aued to be negligible. 3. Teleoperation Baed on Sliding Control In order to facilitate the control law deign, a witching chee for the four olenoid valve in Fig. 1 i defined o that each of the ater and lave robot ha the three ode of operation hown in Table I. TABLE I: THREE POSSIBLE CONTROL MODES 6

7 Mode 1 Mode 2 Mode 3 Chaber p fill exhaut cloed Chaber n exhaut fill cloed Control u 1 1 U = [U 1 U 2 U 3 U 4 ] [1 1 ] [ 1 1] [ ] Here, U (the 4 th row) i defined a the input voltage vector of the valve. Alo, u (the 3 rd row) i a newly introduced dicrete (witching) control input that ha three level to atch the three ode of operation. Thi new input can be choen either a u = ign() or u = ign(), where i the liding urface and i a eaure of tracking error. The exact choice of the witching control u depend on the definition of the liding urface. A it will be hown later, thi choice i crucial to enuring the tability of the teleoperation yte. Note that ode 1 and 2 in Table I are ued for changing the direction of the force on the piton, and ode 3 i ued to ave energy and reduce the chattering phenoenon when the tracking error i all enough. In order to bring the yte to the liding urface = at teady tate, which correpond to perfect tracking perforance, we define a neighbourhood of radiu ε << 1 around zero. When i within thi neighbourhood, the third ode (u = ) i ued to conerve energy and oewhat reduce chattering. In uary, in general the control law take the for + / ign( ) if > ε u = if ε (5) 3.1. Open-loop Model of Mater and Slave anipulator Ignoring the tiction force in (4), the echanical dynaic of the ater and lave anipulator can be written a My && = S P S P by& + f p p, n n, h My && = S P S P by& f p p, n n, e (6) where f h and f e are the operator force exerted on the ater and the environent force exerted on the lave, and y and y are the ater and lave poition. Differentiating (6) and uing (1) (2), the dynaic of the ater and lave anipulator are obtained after oe calculation (Nguyen et al., 27): + + α + β + f& h M, u = 1 α + β f& e M, u = 1 &&& y = α β + f& h M, u = 1, &&& y = α β f& e M, u = 1 α + f& h M, u = α f& e M, u = (7) where u and u denote the dicrete control input a defined in Table I. In the above, 7

8 α && S P S P & (8) 2 2 b γ p p, i n n, i i = y i + y i M M Vp ( yi ) Vn ( yi) S p q( Pa, Pp, i ) S q( Pn, i, Pat ) + n βi = γ rta + M Vp ( yi ) M Vn ( yi ) S p q( Pp, i, Pat ) S q( Pa, Pn, i ) n βi = γ rta + M Vp ( yi ) M Vn( yi ) with i = or (for ater or lave, repectively). (9) (1) 3.2. Cloed-loop Teleoperation Syte In thi ubection, the liding ode control i applied to a two-channel bilateral teleoperation architecture with variou chee (i.e., poition-poition, force-force, and force-poition chee). It i noteworthy that there exit ore coplex teleoperation control architecture, e.g., 4-channel and 3-channel chee, which involve the tranfer of ore inforation (force and poition) fro/to the ater and the lave (Zhu and Salcudean, 1995; Hahtrudi-Zaad and Salcudean, 21; Tavakoli et al., 27). More coplex control architecture ay be needed for ultilateral cooperative teleoperation, which involve ultiple ater robot and/or ultiple lave robot. There are three clae of uch yte reported in the literature, i.e., ingle-ater/ultiple-lave, ultiple-ater/ingle-lave, and ultiple-ater/ultiple-lave. The ipleentation of the liding ode control in uch architecture i ore coplicated than the 2-channel fraework propoed in our tudy. However, it wa choen for the iplicity of the control validation Poition Error Baed (PEB) Control A poition-error-baed, alo called poition-poition, teleoperation yte involve the iplet bilateral controller in which no force enor are required. Thi architecture involve the traniion of two ignal between the ater and the lave: poition (or velocity) fro the ater to the lave and vice vera. The ai of thi architecture i to iniize the difference between the ater and the lave poition (Anderon and Spong, 1989; Salcudean et al., 1995; Fite et al., 21; Aliaga et al., 24). The pneuatic-actuated PEB teleoperation yte with our propoed liding ode control i hown in Fig. 2. Note that throughout thi paper, we ue poition intead of velocitie in our forali. Thi i due to the fact that enuring velocity tracking between the ater and the lave ight caue all offet between the ater and lave poition (i.e., teady-tate error in poition tracking). Generally, when the delay in the counication channel i negligible, the ue of poition controller or velocity controller doe not affect the tability of the teleoperation yte, thu we opt to ue poition controller (Tavakoli et al., 27). 8

9 Sliding ode control ign() ign() u Sliding urface (11) u f h * + f h Valve (2), (3) q n, q p, Cylinder (1), (4) y e + y Valve (2), (3) q n, q p, Cylinder (1), (4) f e f * e + + Electro-pneuatic yte Electro-pneuatic yte hand dynaic Mater Slave environnent dynaic Fig. 2. Poition-Error-Baed approach with liding ode control In Fig. 2, i the liding urface, u and u are the dicrete control ignal for the ater and the lave anipulator, and e = y y i the poition tracking error. Alo, f * h and f * e are the operator and the environent exogenou input force, repectively, and are independent of teleoperation yte behavior. In the PEB chee, the liding urface can be defined a && & (11) 2 = e + 2ξωe + ω e where e = y y i the poition error between the ater and the lave and ξ and ω are contant and poitive paraeter. The control law u and u are defined a u = u = ign(). In the following, we analyze the poition error convergence and the tability of the cloed-loop yte. Conider the following Lyapunov candidate function V = (12) The liding urface = i reached within a finite tie if the following condition i atified (Slotine et al., 1991; Utkin and Chang, 22): for oe contant η >. Thu, fro (11) and (13), we need V& = & < η (13) &&& && & (14) 2 ( e + 2 ξωe + ω e) < η Cae 1: >. In thi cae, (14) becoe 9

10 (&&& &&& ) + 2ξω&& + ω & < η (15) 2 y y e e Since >, then u = 1 and u = 1. Therefore, the ater and lave open-loop dynaic in (7) becoe Subtituting (16) in (15) lead to the following condition &&& y = α + β + + f& M, &&& y = α β f& M (16) h e ( α α ) ( β + β ) ( & + & ) + 2ξω&& + ω & < η (17) + 2 fh fe M e e In other word, where + λ ( β + β ) < η (18) λ = α α & + & + ξω&& + ω & (19) 2 ( fh fe) M 2 e e Cae 2 : <. In thi cae, (14) becoe (&&& &&& ) + 2ξω&& + ω & > η (2) 2 y y e e Since <, then u = 1 and u = 1. Hence, the ater and lave dynaic in (7) can be expreed a Subtituting (21) in (2) yield where λ i defined in (19). &&& y = α β + f& M, &&& y = α + β + f& M (21) h e + λ + ( β + β ) > η (22) Note that, fro (9) and (1), + β and β are poitive, and can be ade a large a deired by chooing a ufficiently large i i valve orifice C val in (3). Thu, to enure that the condition (18) and (22) (depending on the ign of ) are atified, we only need to how that λ i bounded note that η > i an arbitrary contant. To how that λ i bounded, we utilize the following dynaic odel of the operator and the environent (Oboe and Fiorini, 1998; Yohikawa and Ichinoo, 23) f = M && y B y& K y + f * h h h h h f = M && y + B y& + K y + f * e e e e e (23) where M h, M e, B h, B e, K h and K e are aued to be poitive value correponding to the a, daping and tiffne of the operator hand and the environent, repectively. Subtituting (23) into the ater and the lave dynaic (6) yield 1

11 ( M + M )&& y = S P S P ( b + B ) y& K y + f * h p p, n n, h h h ( M + M )&& y = S P S P ( b + B ) y& K y f * e p p, n n, e e e (24) To etablih the boundedne of λ, we conider the following point: Since we are dealing with a phyical yte, the chaber preure P p,i and P n,i are uppoed to be bounded at all tie. In fact, they are lower-bounded by the atopheric preure (P at ) and upper-bounded by the upply preure (P a ). The exogenou input force f h * and f e * and their derivative are uppoed to be bounded a they originate olely fro the huan operator and the environent, which have liited energy. Since the coefficient of poition, velocity and acceleration ter in (24) (after oving the to the left ide of the equation) are poitive, and ince the preure, the operator and the environent exogenou force f h * and f e * are alway bounded, thu each relationhip in (24) i a econd order BIBO table yte. A a reult, the poition y and y are alway bounded. In a iilar way, (24) conit two firt-order table differential equation in ter of velocitie and the other ide of the equation (coniting of poition, preure and exogenou force) are bounded, thu the ater and lave velocitie y& and and y&&, which are the u of bounded function, are alo bounded. y& are bounded. Hence, again becaue of (24), the acceleration Since the velocitie and the acceleration are bounded, fro (6), knowing that the preure are bounded, we can infer that the interaction force f h and f e are alo bounded at all tie. V p (y i ) and V n (y i ), the chaber volue of the cylinder, are alway bounded and non-zero function. The rate of change of preure, i.e., P & p, i and P &, are bounded at all tie becaue each relationhip in (1) i defined n, i by a a flow rate, a velocity, a preure, a chaber volue, which are all bounded function. Baed on the previou point, differentiating (24) yield the boundedne of y&&& and y&&&. Conequently, by taking the derivative of (23) we infer that f & and h f & are alo bounded at all tie. e Eventually, it i found that λ, which i the u of everal bounded function, i bounded. Conequently, the liding condition in (13) i enured at all tie, which iplie that the poition tracking error tend to zero (and that the overall yte i table). In fact, fro (13), will be bounded and converge to zero. According to (11), which repreent a BIBOtable econd-order LTI yte, thi will enure the boundedne and convergence to zero of the poition tracking error. A drawback of the PEB ethod i that it doe not guarantee good tranparency in ter of force tracking. In order to y&& 11

12 iprove the tracking perforance, other chee are propoed in the next ection Force Error Baed (FEB) Control A force-error-baed, alo called force-force, yte i not coonly ued in two-channel bilateral teleoperation ince two force enor are required, which will ake the ipleentation expenive, and ince the reulting poition tracking i not good. However, copared to the PEB architecture, thi architecture can iprove the force tracking perforance. Fig. 3 how the pneuatic-actuated FEB teleoperation yte with a propoed liding ode control. + Sliding ode control Sliding urface (25) ign() Valve (2), (3) u u Valve (2), (3) q n, q p, q n, q p, f h * + f h Cylinder (1), (4) y y Cylinder (1), (4) f e f * e + + Electro-pneuatic yte Electro-pneuatic yte hand dynaic Mater Slave environnent dynaic Fig. 3. Force-Error-Baed approach with liding ode control Conider the control law u = u = ign() where the liding urface i defined a = f f (25) h e Uing the Lyapunov function (12), we need to how that the liding condition (13) i atified. Fro the ater and lave odel (7), we calculate f & and h f & a e + + M (&&& y α β ), u = 1 M ( &&& y + α + β ), u = 1 f& h = M (&&& y α + β ), u = 1, f& e = M ( &&& y + α β ), u = 1 M (&&& y α ), u = M ( &&& y + α ), u = (26) where Cae 1: >. In thi cae u = u = 1. Fro (13), we need + + & = f& f& = M ( λ β β ) < η (27) h e 12

13 λ = &&& y α + &&& y α (28) The condition in (27) can be verified when λ, which i defined in (28), i bounded. A it wa deontrated in ection 3.2.1, every ignal i bounded, including &&& y, α, &&& y and α. Thi iplie the boundedne of λ at all tie. Finally, by chooing a valve with a large enough orifice, β + and β + can be ade ufficiently large to atify (27). Cae 2: <. In thi cae, u = u = 1. We have where λ i defined in (28). f f M ( λ β & = & & = + + β ) > η (29) h e Siilar to Cae 1, λ i bounded at all tie. Thu, the tability of the yte (29) can be guaranteed by chooing a large enough value of β and β. Conequently, the force tracking error converge to zero and the overall yte i table. However, the FEB ethod doe not guarantee a good poition tracking perforance. In order to overcoe the PEB and FEB architecture drawback, we ue the chee decribed in the following ection Direct Force Reflection (DFR) Control A direct-force-reflection, alo called force-poition, yte ha advantage over the poition poition and force force architecture. Copared to the PEB ethod, iproveent in ter of force tracking are achieved due to the eaureent of the interaction force between the lave and the environent. Furtherore, it poition tracking perforance i better than the FEB cae thank to poition inforation. The pneuatic-actuated DFR teleoperation yte with our propoed liding ode control i illutrated in Fig

14 Electro-pneuatic yte Sliding ode control Valve (2), (3) u ign( ) f h * + f h q n, q p, Cylinder (1), (4) y + e Sliding urface (25) hand dynaic Mater environnent dynaic f e * + + f e Cylinder (1), (4) y + e Sliding urface (11) q n, q p, Valve (2), (3) u ign( ) Electro-pneuatic yte Sliding ode control Slave Fig. 4. Direct-Force-Reflection approach with liding ode control Here, and are the liding urface for the ater and lave yte, repectively, e = f h f e i the force tracking error calculated for the ater controller, and e = y y i the poition tracking error calculated for the lave controller. Thi architecture involve the traniion of two type of data between the ater and the lave: force fro the lave to ater and poition fro the ater to the lave. Hence, the tranparency i iproved in ter of force and poition tracking, copared to thee previou ethod. Thi tateent will be jutified later in our experient, Section 4. In thi ection, we ue a Lyapunov function to prove the tability of the liding-ode controlled DFR yte. Firt, we will how the tability of the force-controlled ater anipulator. Afterward, we will how the tability of the poitioncontrolled lave anipulator. However, the tability of the overall yte i difficult to how due to the coplexitie introduced by uing different liding urface for the ater and for the lave. a. Force convergence of the cloed-loop ater yte Since the deired force for the ater robot, i.e., the lave/environent contact force f e i aued to be bounded at the beginning, we need to how that f h converge to f e in a finite tie. The liding urface and the Lyapunov function V are defined a in (25) and (12), repectively. The controller u i choen to be iilar to the FEB yte in ection

15 Cae 1: >. In thi cae, u = 1. Uing the expreion of f & in (26) and the definition of h a in (25) we have & = f& + My &&& Mα M β + (3) e To enure the liding condition (13), we need to how that f& + My &&& Mα M β < η (31) + e Siilar to how it wa deontrated in ection 3.2.1, f &, e y&&& and tability condition (31) i atified by chooing a large enough value for β +. Cae 2: <. In thi cae, u = 1. Fro (25) and (26) we need α can be hown to be bounded at all tie. Thu, the f& + My &&& Mα + M β > η (32) e Siilar to Cae 1, it i poible to chooe a large enough value of β in order to enure the tability of the ater device. Conequently, the liding urface (the force tracking error) tend to zero, i.e., f h tend toward f e. b. Poition convergence of the cloed-loop lave yte The liding urface and the Lyapunov function V are defined a in (11) and (12), repectively. The controller u i choen to be iilar to the PEB yte in ection Cae 1: >. In thi cae, u = 1. The liding condition (13) i equivalent to (&&& y &&& y ) + 2ξω&& e + ω e& < η (33) 2 Uing the expreion of y&&& in (16) lead to the following condition α β f& M &&& y + 2ξωe&& + ω e& < η (34) 2 e or ϕ β < η (35) 2 where ϕ = α f& M &&& y + 2ξω&& e + ω e& e The traightforward reaoning decribed in ection allow u to infer that φ i bounded at all tie. Thu, there exit a value of β uch a (33) i atified. Cae 2: <. In thi cae, u = 1. Thu, we need 15

16 α + β &&& y f& M + 2ξω&& e + ω e& > η (36) + 2 e or ϕ + β > η (37) + Thi condition i achieved by chooing a large enough β +. Note that for both cae, the convergence of the liding urface (and thu the poition tracking error) to zero i proved, o x tend toward x. Aong the different tability analyi ethod baed on the paivity theory that were entioned in Section I, thi paper ha directly tudied the tability of the overall teleoperation yte, which ha the potential to reduce deign conervati and allow for higher teleoperation perforance. It hould be noted that our tability analyi i achieved when the realworld liit of oe yte tate (i.e., the boundedne of the preure chaber between the atophere preure and the upply preure) are taken into account. Showing the tability without uing the knowledge on bounded preure i very difficult becaue we are dealing with a coplex nonlinear, dicrete-input pneuatic yte. 4. Experient 4.1. Experiental Setup In thi ection, experient with a 1-DOF teleoperation yte are reported. A illutrated in Fig. 5, the etup conit of two identical pneuatic anipulator (a the ater and the lave). The low friction cylinder (Airpel odel M16D1D) have a 16 diaeter and a 1 troke. The piton are connected to a a of approxiately M = 1 kg. In ter of actuator, each pneuatic cylinder ue four olenoid valve. The pneuatic olenoid valve (Matrix odel GNK821213C3K) ued to control the air flow have witching tie of approxiately 1.3 (opening tie) and.2 (cloing tie). With uch fat witching tie, the on/off valve are appropriate for the purpoe of the propoed control. In ter of enor, a low-friction linear variable differential tranforer (LVDT) i connected to each cylinder in order to eaure the ater and the lave linear poition. Alo, each of the end-effector of the ater and the lave anipulator i equipped with a force enor thi will help to eaure the operator and the environent force, repectively. The yte wa upplied with air at an abolute preure of 3 kpa. The controller i ipleented uing a dspace board (DS114), running at a apling rate of 5 Hz. Thi value ha been choen according to the open/cloe bandwidth of the witching valve and to guarantee an acceptable tracking 16

17 repone. Thi apling rate i alo higher than the bandwidth above which the huan finger cannot ditinguih two conecutive force tiuli, which i 32 Hz (Shioga, 1993). Force enor Solenoid valve Preure enor Poition enor Cylinder Ma Environeent Fig. 5. Pneuatic ater lave teleoperation experiental etup In thi tudy, the ater and the lave' valve/actuator are conidered to be iilar. However, the propoed liding ode controller provide robut perforance depite odel uncertaintie and variation. Firt, the tability condition (13) baed on the Lyapunov candidate function i alway et even when the paraeter in Tab. II are not the ae for the ater and the lave robot. Second, in practice, the valve and actuator ued in the ater and lave are not exactly the ae due to ipreciion of anufacturing of electronic and echanic coponent. The above point are further evidence of the robutne of our controller. For teleoperation with different kineatic and drive actuation for the ater and lave anipulator (e.g., in icro-acro yte), the reader can refer to (Lee and Li, 25). For the PEB and DFR yte, the liding urface of the poition-controlled lave i noralized a e = && ξ 2 e e 2 ω + & ω + (38) Thi i becaue, in practice, it i eaier if the liding urface for poition control i choen in order to have the ae dienion a poition a in (38) and not acceleration a in (11). The firt derivative of the poition error in (38) i coputed through a backward difference ethod applied on the poition ignal followed by a de-noiing econd-order Butterworth filter with a cutoff frequency of 7Hz. The econd derivative i coputed in the ae way fro the filtered 17

18 firt-derivative ignal. The filter bandwidth wa choen to be large enough (7 Hz) with repect to the bandwidth of the huan hand oveent, i.e. the input bandwidth of the yte. According to (Shioga, 1993), the axiu bandwidth with which the huan finger norally react to a tactile input i about 8-1 Hz. A a reult, ot of inforation in poition, velocity and acceleration ignal i conerved. Only high frequency ocillation and vibration are attenuated when uing uch a filter. There exit everal trategie to etiate the velocity and acceleration fro the poition inforation. Backward difference ethod, which i conidered to be the iplet nuerical ethod for differentiating a ignal, i ued in our application for an eaier experiental ipleentation. The differentiator i apled at 5 Hz and aociated to the denoiing Butterworth low-pa filter (i.e. defined previouly). However, the ue of low-pa filter to copute the velocity and acceleration can introduce additional phae hift that oewhat liit the cloed-loop perforance. A a reult, alternative olution for differentiation of ignal with noie attenuation that do not introduce ignificant delay have been propoed in the literature. The ai of thee ethod i to realize filter that approxiate the ideal differentiator in a certain range of frequencie. Auing that the poition can be approxiated with a low-order polynoial, a differentiator baed on the Newton predictor wa propoed in (Ovaka and Vainio, 1992). Differentiator baed on FIR or IIR filter have been preented in (Vainio et al., 1997); thee approache are norally called predictive pot-filtering. Another ethod for the velocity etiation relie on the tate oberver theory. Knowing the plant odel, etiator baed on Kalan filter (Belanger, 1992; Jaritz and Spong, 1996), Nicoia oberver (Nicoia and Toei, 199), and Luenberger oberver and nonlinear oberver (Bodon et al., 1995; Yang and Ke, 2) have been invetigated. Alo, (Janabi-Sharifi et al., 2) preent ethod for the velocity etiation fro dicrete and quantized poition aple uing adaptive windowing. Other olution baed on the liding ode oberver were preented in (Levent, 1998; Sidho et al., 21). There i a trade-off between tracking error and chattering to achieve good perforance. In theory, the characteritic of the control yte i deterined by the pole of the econd-order reference odel (38), which depend on the paraeter ω and ξ. It i noteworthy that when ξ and ω 2 in (38) increae, the averaged tracking error i better but the chattering increae. It ean that the repone i around the reference in the tranient and teady tate but ore ocillation can be oberved due to the noie of velocity and acceleration etiation. Thi i undertandable fro the perpective of oving the pole of a econd-order tranfer function farther to the left of the iaginary axi fater pole location reult in fater convergence of the tracking error to zero. Since ξ/ω i ultiplied by e& in the liding urface (38), the noie in e& (correponding to undeired ocillation and vibration) will be aplified with a all value of ξ/ω, 18

19 reulting in increaed chattering proble. Siilarly, when 1/ω 2 i all, the contribution of the noie preent in e&& i aplified in (38). To efficiently dap the ocillation and vibration in e&&, which uffer fro differentiation noie, ω i generally not choen to be too high in practice. For a good trade-off between the poition tracking perforance and the chattering proble, the paraeter ξ =.5 and ω = 7 rad/ will be ued in our experient. Since the coefficient of e in (38) equal 1, in the teady tate we will have = e. We define the tolerable range (or threhold ) of thi error a a neighbourhood of radiu ε p. In the experient, ε p i choen equal to.5 in order to guarantee good poition tracking perforance without cauing too uch witching of the valve. Concerning the force controller, a force error threhold ε f need to be choen. In practice, we chooe ε f equal to.1 N to achieve good force tracking repone. With the ideal poition and force tracking error choen a.5 and.1 N, repectively, high tranparency i obtained in the pneuatic actuated teleoperation yte with inexpenive on/off valve. To reue, the following table preent all phyical paraeter ued in the paper. TABLE II: MODEL AND CONTROLLER PARAMETERS Paraeter Value Unit Decription P at 1 5 Pa Atophere preure P a Pa Supply preure r 287 J/kg/K Perfect ga contant T a K Supply teperature C r.433 Critical preure ratio α 1.2 Polytropic contant l.1 Cylinder troke S p ² Piton area of chaber p S n ² Piton area of chaber n M 1 kg Moving load b 2 N./ Vicoity coefficient T op 1.3 Opening tie of olenoid valve T cl.2 Cloing tie of olenoid valve T 2 Sapling tie of controller f c 7 Hz Cut-off frequency of filter ω 7 rad/ Angular frequency ξ.5 Daping coefficient ε p.5 Poition threhold ε f.1 N Force threhold 19

20 4.2. Experiental Reult Tie Analyi Figure 6 how the ater and the lave force and poition tracking profile in free pace and in contact otion for the PEB teleoperation yte. Figure 7 and 8 illutrate the ae profile for the FEB and the DFR yte, repectively. In the experient, for the firt few econd, the ater i oved back and forth by the uer when the lave i in free pace. The all but nonzero value for F e when the lave i in free pace are due to the a of the handle-like connector between the lave force enor and the lave end-effector (tip). Siilarly, the all but nonzero value for F h during lave free otion are due to the a of the ater handle, which lie between the force enor and the operator' hand. Note that the fat oveent of the ater in the firt few econd do not repreent ocillation; rather, they are intentionally created by the operator to exaine the yte tability and perforance in free otion. Next, the lave ake contact with a hard environent, i.e., a ponge with rigid tructure. The operator puhe againt the ater handle leading to different level of the lave/environent contact force. The fact that the poition profile reain contant during the contact ode i iply becaue under hard contact the lave cannot penetrate the environent regardle of the operator force. A it can be oberved in Fig. 6 to Fig. 8, liited aount of vibration in the force and poition repone are introduced by the dicrete operation of the on/off olenoid valve. Thee vibration increae under hard contact for the force profile due to higher valve witching activitie but are otherwie negligible. Another effect caued by the on/off olenoid valve, which cannot be een in the above figure, i the acoutic noie. Indeed, a a olenoid valve witche between the two operating poition (open or cloed), a clicking ound i generated. A illutrated in Fig. 6, the PEB yte provide a good poition tracking repone. It can be een that the lave rapidly track the ater oveent in free pace and alo in contact ode. However, the force repone i not a good becaue no force enor i ued. On the other hand, the force tracking perforance of the FEB yte i uch better, thank to the knowledge of the force inforation. Nonethele, the poition tracking deteriorate in FEB control a it can be een in Fig. 7, the lave oveent doe not accurately track the ater oveent. Fig. 6 and Fig. 7 how the tradeoff between poition tracking and force tracking a long a only either both poition or both force are available for feedback (i.e., PEB and FEB control, repectively). Interetingly, the DFR yte in Fig. 8 provide an iproveent in ter of poition tracking repone copared to 2

21 the FEB yte. It alo diplay a uperior force tracking perforance copared to the PEB, epecially under contact otion. However, a drawback of the DFR yte i that higher ocillation and vibration are preent in the force and poition repone under contact otion. Conequently, when operator force level increae, the DFR yte i le table than the other cae. Thi reult agree with the previou theoretical work but i hown for the firt tie for on/off valve actuated pneuatic teleoperation yte. It i noteworthy that the agnitude of the hand-ater interaction force in the following Figure (Fig. 6, 7, and 8) i higher than expected during free otion. Thi behavior i due to friction induced by our rail-guide yte, which ue floating ball between the carriage and the rail profile. Thi coponent introduce friction during the diplaceent of the robot. However, during the contact phae, the friction ha a negligible influence ince the pneuatic actuator ove little. Force (N) Contact F e F h Poition () Free otion Maître Eclave tep () Fig. 6. Poition and force repone of the PEB yte 21

22 3 Force (N) 2 1 Free otion Contact F h F e Poition Error (N) () Mater Slave tie () Fig. 7. Poition and force repone of the FEB yte 3 Force (N) 2 1 Free otion Contact F h F e Poition () Mater Slave tie () Fig. 8. Poition and force repone of the DFR yte Aong the three architecture, the DFR chee ee to be a better choice to obtain a good tranparency. Although the variou teleoperation controller have previouly been copared fro a perforance perpective in the literature (Lau and Wai, 25; Tavakoli et al., 27), thi i the firt tudy to how that it i poible to achieve tability and atifactory perforance uing anipulator actuated by low-cot witching on/off valve. 22

23 Frequency Analyi In the following, we ue another experiental ethod for aeing yte tranparency that approxiate the yte with an LTI odel. If thi auption cannot be ade for the nonlinear odel of pneuatic actuator, the tie-doain profile of Fig. 6 8 ufficiently evaluate tranparency. For the frequency analyi of the approxiate LTI odel, we ue the claical hybrid repreentation of the two-port network odel of a ater-lave yte. A coplete dicuion of the hybrid atrix analyi can be found in (Lawrence, 1992; Salcudean et al., 2). In thi repreentation, F h = h h Y h21 h 22 Y F e (39) In an ideally tranparent teleoperation yte, the ater and the lave poition and force will atch regardle of the operator and environent dynaic: Y = Y, F = F (4) h e Fro (39) and (4), perfect tranparency i achieved if and only if the hybrid atrix H ha the following for: H ideal 1 = 1 (41) Thu, by finding the hybrid atrix of our experiental pneuatic teleoperation yte through yte identification tet and coparing to the above ideal hybrid atrix, the tranparency of the yte can be evaluated. Each eleent of the H atrix ha a phyical eaning. The hybrid paraeter h = F Y i the input ipedance in = 11 h F e free-otion condition. The paraeter h = F F i a eaure of force tracking when the ater i locked in otion = 12 h e Y (perfect force tracking when h 12 = 1). The paraeter h = Y Y i a eaure of poition tracking perforance when = 21 F e the lave i in free pace (perfect poition tracking when h 21 = 1). The paraeter h = Y F i the output = 22 e Y adittance when the ater i locked in otion. Nonzero value for h 22 indicate that even when the ater i locked in place, the lave will ove in repone to lave/environent contact. Since F e = in the free-otion tet, the frequency repone h = F Y and = 11 h F e h = Y Y can be found by = 21 F e applying the pectral analyi function pa of Matlab. Alo, by uing contact-ode tet data, the other two hybrid paraeter can be obtained a h12 = Fh Fe h11 Y F and e h22 = Y Fe h21 Y F (Tavakoli et al., 28). e 23

24 The agnitude of the hybrid paraeter of the PEB, FEB and DFR teleoperation yte i hown in Fig. 9. A it can be een, h 12 and h 21 in the DFR chee are cloe to db, reflecting excellent tranparency in ter of force and poition tracking for frequencie up to 1 rad/. With regard to the PEB chee, cloene to db of h 21 indicate that the yte enure good poition tracking in free pace. On the other hand, the degradation of h 12 pectra under PEB i in agreeent with the tie-doain force profile in Fig. 6 8, where force tracking in the PEB cae i not on par with that in the other cae. Contrary to the PEB yte, the FEB yte only guarantee good tranparency in ter of force tracking but not poition tracking, a illutrated in the h 12 and h 21 paraeter of Fig. 9. Relatively high value of h 11 for the PEB chee are an evidence of the fact that even when the lave i in free pace, the uer will feel reidual force that depend on the poition tracking error of the ater and the lave robot. Concerning the DFR and FEB chee, thank to the eaureent of f e, their input ipedance in free-otion condition (h 11 ) will be lower, which ake the feeling of free pace uch ore realitic (Tavakoli et al., 27). Latly, conitent with (41), low value of the output adittance (h 22 ) in the three architecture how that the lave oveent in repone to external force diturbance quickly converge to zero when the ater i locked in otion. 3 h 11 5 h db rad/ec db rad/ec 2 h 21-2 h db -1 db rad/ec rad/ec Fig. 9. Frequency pectra of the hybrid paraeter under liding control: PEB (Solid), FEB (Dahed), DFR (Dotted) 24

25 5. Extenion to a five-ode Control Schee 5.1. Principle In thi ection, we invetigate the ue of a liding control with five witching ode (ee Table III) intead of the three tandard ode preented in ection 3. The new yte ha two extra ode, which are defined by connecting only one chaber to the upply while leaving the other chaber locked. TABLE III: FIVE POSSIBLE CONTROL MODES Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Chaber p fill exhaut cloed fill cloed Chaber n exhaut fill cloed cloed fill Control u U = [U 1 U 2 U 3 U 4 ] [1 1 ] [ 1 1] [ ] [1 ] [ 1] A it can be een in Table III, the firt three ode in the 5MCS are inherited fro the 3MCS. Mode 4 and 5 are added in the 5MCS in order to offer ore poibilitie in ter of witching choice and iprove the behavior of the yte by reducing witching activity of the valve. Siilar to ode 1, ode 4 allow oving the cylinder rod in the ae direction but with a lower dynaic (becaue in ode 4 the chaber n i cloed a oppoed to exhauting a in ode 1). Mode 4 ay be conidered a an interediate ode (or average) between ode 1 and 3, where the control vector u i choen equal to.5 (Table III). On the other hand, ode 5 whoe control vector u equal.5 i ued to ove the cylinder rod in the other direction and could be regarded a an interediate option between ode 2 and 3. The operation of the 5-ode liding controller i baed on the following three principle: 1. When i within the interval [, ε], ode 3 (u = ) i ued to conerve energy and reduce chattering. 2. To be able to witch between ode 1 and 4 or ode 2 and 5, a threhold ε 1 i introduced where ε 1 > ε. When i within the interval (ε, ε 1 ), either ode 4 or ode 5 (u = ±.5) i ued to provide lower dynaic copared to ode 1 or 2 (u = ± 1), repectively. Still, the piton i actuated to ove in the direction that iniize. 3. When i within the interval [ε 1, [, either ode 1 or ode 2 (u = ± 1) i ued to provide fat dynaic, highly accelerating the piton in the direction that iniize. A preentation of the 5-ode controller diagra can be hown in Fig

26 Mode 2 Mode 5 Mode 3 Mode 4 Mode 1 u = 1 Chaber n fill Chaber p exhaut u =.5 Chaber n fill Chaber p cloed u = Chaber n cloed Chaber p cloed u =.5 Chaber n cloed Chaber p fill u = 1 Chaber n exhaut Chaber p fill ε 1 ε ε ε 1 Fig ode controller diagra In uary, the new control law for the 5MCS can be given a + / ign( ) if ε1 u = + /.5 ign( ) if ε < < ε1 if ε (42) A it can be een later in experient, the 5MCS offer an advantage in ter of valve witching activitie over the 3MCS. However, the addition of a new threhold (i.e., ε 1 ) can ake the tuning ore coplex in the 5MCS. Siilar to ε, ε 1 i choen baed on the trade-off between accuracy and chattering. If ε 1 i very all (i.e., ε 1 ε), the dynaic behavior of the 5MCS becoe iilar to the 3MCS. In thi cae the two additional ode will not offer additional benefit and chattering wil not be iproved. On the other hand, a odet value of ε 1 allow to reduce the witching activity of the valve and aintain the tracking propertie of the yte Coparion between the 5MCS and the 3MCS To facilitate a coparion of the 5MCS and 3MCS perforance, all controller paraeter are choen to be iilar for both cae, i.e., ξ =.5, ω = 7 rad/, ε p =.5 for the poition controller, and ε f =.1 N for the force controller. In addition, for the 5MCS, two ore paraeter need to be adjuted (i.e., a poition threhold ε 1p and a force threhold ε 1f ). Their value found by experiental trial are 1 and.5 N, repectively. Fig. 11 how the ater and the lave force and poition tracking profile in the 5MCS teleoperation yte. In the PEB and FEB yte, the tranparency under 5MCS ee to be iilar with that under the 3MCS (copared with Fig. 6 Fig. 7). On the other hand, under DFR control, le ocillation i oberved in the 5MCS cae than in the 3MCS cae. Thi allow to achieve higher contact force quality, iproving the operator perception. A previouly explained, the high value of free-otion force reading are due to the friction in our rail-guide yte. 26