Development of a hybrid control for a pneumatic teleoperation system using on/off solenoid valves

Transcription

1 Developent of a hybrid control for a pneuatic teleoperation yte uing on/off olenoid valve M.Q. Le, M.T. Pha, M. Tavakoli, R. Moreau Abtract Thi paper preent a new predictive hybrid control law for a pneuatic teleoperation yte uing olenoid valve. Baed on a predictive odel of the a flow rate of the valve, thi ethod i ued within a fourchannel (4CH bilateral control architecture for haptic teleoperation. An analyi of the controller paraeter i carried out in order to achieve acceptable perforance. The reult how that a good accuracy in poition and force tracking of the teleoperation yte i obtained. Index ter Pneuatic actuator, on/off olenoid valve, hybrid control, teleoperation, bilateral control, tranparency. I. INTRODUCTION Fro it early ue in the reote anipulation of radioactive aterial, the application of teleoperation ha expanded to include anipulation at different cale and in virtual world [14]. Teleoperation yte have the potential to play an iportant role in future reote or hazardou operation uch a pace and underea exploration, foretry and ining, and alo delicate operation uch a icrourgery and icroaebly. In a teleoperation yte, a lave anipulator track the otion of a ater anipulator, which i driven by a huan operator. To iprove the tak perforance, inforation about the environent i needed. Feedback about the environent can be provided to the huan operator in any for including audio, viual, or tactile inforation. Force feedback fro the lave ide to the ater ide, repreenting lave/environent contact inforation, provide a highly intuitive and natural enation for the huan operator [5]. When the contact force i reflected via the ater actuator to the operator hand, the teleoperation yte i aid to be bilateral. In a bilateral teleoperation yte, apart fro the baic requireent of tability, there are priarily two deign goal that enure a cloe coupling between the huan operator and the environent. The firt goal i that the lave anipulator track the poition of the ater anipulator, and the econd goal i that the environental force acting on the lave, when a contact with the environent occur, i accurately tranitted to the ater [6]. Such a bilateral control allow to enure the tranparency of the teleoperation yte. M.Q. LE, M.T. Pha, and R. Moreau are with the Laboratoire Apère, UMR CNRS 55, Univerité de Lyon, INSALyon, F6961 Villeurbanne Cedex, France (correponding author eail: inhquyen.le@ inalyon.fr. M. Tavakoli i with the Departent of Electrical and Coputer Engineering, Univerity of Alberta, Canada, and currently on a reearch viit at INSALyon. In thi tudy, we invetigate the poibility to ue electropneuatic yte a actuator in a teleoperation yte. Pneuatic yte have recently becoe ore popular due to their advantage of high atoforce ratio, being inert to agnetic field, and recent breakthrough in valve technology. Therefore, they have found ue in new application uch a telerobotic over the lat few year [7], [8]. Two type of valve are generally ued to control pneuatic yte: proportional ervovalve and olenoid valve ( on/off valve. Proportional ervovalve have been uccefully ued to achieve high perforance in variou poition or/and force control yte with pneuatic actuator, but they are uually expenive a they require highpreciion anufacturing. In thi paper, fatwitching on/off valve were choen due to their low cot and all ize. One of our objective i to how that a good tranparency in bilateral control can be obtained with thee cheap coponent. The traditional ethod for controlling yte with olenoid valve i to ue Pule Width Modulation (PWM to control the output a flow rate of the valve [9], [1]. A ain diadvantage of the PWM control i the chattering phenoenon due to the high frequency witching of the valve in teady tate [11]. To overcoe the PWM diadvantage, thi paper preent a new control ethod, which i baed on the hybrid control theory recently developed by Retif et al. [1]. For thi trategy, a predictive approach ha been developed to deterine the bet control vector at each aple tie to track the reference tate [13]. In thi paper, the hybrid control algorith i applied for the force and poition tracking in a 4CH bilateral teleoperation architecture. An analyi of the controller paraeter i carried out in order to achieve an acceptable perforance in ter of teleoperation yte tranparency. Without lo of generality and for the ake of iplicity, the ater and lave actuator are uppoed to be identical in thi tudy. The ater and lave are one degree of freedo pneuatic anipulator. It hould be noted that thi paper doe not deal with the preence of tie delay in the teleoperation yte counication channel. The tructure of thi paper i a follow. Firt, the odeling of the pneuatic anipulator copoed of a cylinder and four olenoid valve i preented in Section II. Section III decribe the deign of a 4CH bilateral control architecture and provide the tranparency condition. Section IV preent experiental reult that validate the propoed theorie. Finally, concluding reark appear in Section V.

2 II. MODEL OF THE PNEUMATIC SYSTEM A entioned above, the ater and the lave anipulator are identical, thu only one pneuatic robot odel i preented in thi ection. A cheatic of a ingle degree of freedo pneuatic actuation yte i hown in Fig. 1. The doubleacting cylinder ha equal area on either ide of the piton. To decribe the cylinder air flow dynaic, we aue that Air i a perfect ga, The preure and the teperature are hoogeneou in each chaber, The teperature variation in chaber i negligible The a flow rate leakage are negligible, The upply and exhaut preure are contant. P p Valve 1 Valve Valve 3 Valve 4 P q p Preure enor Chaber p P p, V p, T p P at Hybrid control Preure enor Chaber n P n, V n, T n P at U 1 U U 3 U 4 Deired force or otion q n P Poition enor Fig. 1. Electropneuatic force control yte with four valve A. Model of the pneuatic chaber The behavior of the preure inide each chaber of the cylinder can be expreed a [14] dp γrt P q U U P Sv dp n γrt a P n = qn ( U3, U4, Pn Sv dt Vn ( y rta p a p = p( 1,, p dt Vp( y rta where U 1, U, U 3 and U 4 are the control voltage of valve 1, valve, valve 3, and valve 4; y and v 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 i the piton cylinder area ( ; 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. B. Model of the valve The a flow rate characteritic of the on/off valve can be expreed a a function of the dicrete control voltage and the preure: y P n (1 ( q P, Pp for U1 = 1 and U = qp ( U1, U, Pp = for U1 = and U = q ( Pp, Pat for U1 = and U = 1 ( q P, Pn for U3 = 1 and U4 = (3 qn ( U3, U 4, Pn = for U3 = and U4 = q ( Pn, Pat for U3 = and U4 = 1 where P and P at are the preure of the upply air and atophere. The value of the input voltage correpond to cloed valve and the 1 value correpond to open valve. All the tate where U 1 = U = 1 and U 3 = U 4 = 1 are prohibited to avoid a bypa of the valve. The function in ( and (3 are given by a expreion for a flow rate through an orifice of contant area, which depend only on the uptrea and downtrea preure [15]: Tat Pdown CP up if Cr (onic Tup Pup (4 q (, down Pup P P down = Cr T P at up CP up 1 otherwie (ubonic T up 1 C r where C r i the critical preure ratio and C i the onic conductance; 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. III. CONTROL DESIGN A. Hybrid control of a ingle pneuatic anipulator 1 Hybrid control principle Hybrid control ue a hybrid odel where the continuou tate variable of the continuou yte depend on the configuration of the energy odulator: Xɺ ( t = f X ( t, u( t (5 ( with X=(x 1, x,, x R where x i, 1 i, are the tate variable of the yte. Here, f i the dynaic function governing the tatepace odel and u i a control vector that include the N poible value correponding to the N configuration of the energy odular u { u1, u,, u N } (6 N For a all apling period T, the odel (5 can be approxiated by a dicrete odel uing Euler ethod: X (( k 1 T X ( kt f ( X ( kt, u( kt. T (7 The full tate X(kT i aued to be eaured at tie kt. The tate at tie (k1t, denoted X j ((k1t, for each value of the configuration j, 1 j N, can be calculated by (7. The N direction d j in the tate pace are defined a d j = X j (( k 1 T X ( kt (8 For a given reference tate X ref the hybrid control calculate the N poible direction d j. Thereby an optial control (

3 aong the N configuration i choen in order to track thi reference in the tate pace. For the twodienional exaple hown in Fig., the deired value (target point can be placed in the plane of x 1 and x. To track the reference ignal at each aple tie, the hybrid control algorith proceed a follow: Acquiition of the tate variable at tie kt: x 1 (kt and x (kt. Baed on the tate knowledge at tie kt, an etiation of the tate at tie (k1t i carried out baed on (7. Becaue the control ignal u belong to a finite et of poibilitie a aued in (6, thi tep i equivalent to the calculation of the different direction d j, correponding to the j th configuration of the energy odulator (d 1 to d 5 in Fig.. Knowing the target point at tie kt, the algorith elect the bet poible configuration aong the N configuration. The choen configuration i the olution that iniize the Euclidean ditance between the different reachable point and the target point. For intance, the hortet Euclidean ditance correponding to d 4 i choen in the exaple of Fig. and, therefore, the correponding control u 4 i applied to the energy odulator. x d d 1 d 5 Target point The objective, knowing the preure at the aple tie kt, i to etiate the evolution of the preure at the next aple tie (k1t in chaber p and n for the nine control (Table I, and then chooe the bet control for reaching the deired force. Auing the variation of the preure during a apling tie i all, the derivative of the preure can be rewritten a dicrete expreion d Pp (( k 1 T ( Pp ( t T Pp ( kt dt (9 t= kt d Pn (( k 1 T ( Pn ( t T Pn ( kt dt t= kt where the derivative of the preure are calculated baed on (1(4. The expreion dp p /dt and dp n /dt are function of P p, P n, y and v. At each aple tie, P p, P n and y are eaured by enor, while v i etiated by nuerical derivation of the poition eaureent y. Thu, for each of the nine control vector, the algorith calculate P p ((k1t and P n ((k1t baed on (9. Conequently, the nine direction d 1 to d 9 define the et of reachable point at tie (k1t in the tate pace [16]. B. Bilateral 4channel control of a pneuatic aterlave teleoperation yte Figure 3 depict the general 4CH bilateral teleoperation architecture propoed by Lawrence [18]. Z e * Tak x (kt d 3 X(kT d 4 y C Z 1 C 5 F Slave x 1 (kt Fig.. Principle of hybrid control Application to a pneuatic yte Becaue the control ignal of the ater and lave anipulator in a teleoperation yte are force ignal [17], the hybrid algorith preented in Section III.A.1 i applied to a force tracking proble. The bilateral control of the teleoperation yte will be detailed in ection III.B. For the yte of Fig. 1 and the force tracking proble, the preure in chaber p and n can for the tate vector X(t=(P n P p T. Each valve ay how three different behavior (preure adiion, cloed, and preure exhaut, leading to nine different control vector u 1 to u 9, a hown in Table I. TABLE I NINE DISCRETE POSSIBLE STATES OF CONTROL u 1 u u 3 u 4 u 5 u 6 u 7 u 8 u 9 U U U U x 1 * C 4 C 3 C 6 F Z h C Z 1 C C 1 Counication Channel Fig. 3. 4CH bilateral control architecture y Mater Operator In thi figure, ipedance Z h and Z e denote the dynaic characteritic of the huan operator hand and the environent, repectively; Z and Z denote the ater and lave anipulator linearized dynaic, which are generally approxiated by iple apringdaper yte; and are the operator force exerted on the ater and the environent force exerted on the lave; F and F are the (force control ignal for the ater and lave anipulator; y and y are the ater and lave poition; C and C denote the local poition controller of the ater and the lave

4 ide; C 5 and C 6 are local force feedback ter for the ater and the lave; and C 1 to C 4 are poition or force controller ebedded in the counication channel. Alo, F * * h and are the operator and the environent exogenou input force, repectively, and are independent of teleoperation yte behavior. It i generally aued that the environent i paive (F * e = and the operator i paive in the ene that he/he doe not perfor action that will ake the teleoperation yte untable. The architecture in Fig. 3 involve four type of data traniion between the ater and the lave: force and poition (or velocity fro the ater to the lave and vice vera. It i hown in [18] that having thee four channel of data traniion i of critical iportance in achieving highperforance telepreence (i.e., full tranparency in ter of accurate traniion of takrelated inforation uch a the environent ipedance to operator. Nonethele, by proper adjutent of the local feedback paraeter (C 5 and C 6, it i poible to obtain two clae of threechannel architecture, which can perfor a well a the 4CH yte [19]. We aue that counication tie delay between the ater and the lave i negligible. The dynaic of the ater and lave robot can be written a F Fh = Z y, F Fe = Z y (1 and the dynaic of the operator and the environent are * * Fh = Z h y Fh, Fe = Ze y F (11 e Note that we have ued poition in the above intead of velocitie a hown in Lawrence architecture [18]. 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., teadytate 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 [18], thu we opt to ue poition controller. In an ideally tranparent (highperforance teleoperation yte, the ater and the lave poition and force will atch regardle of the operator and environent dynaic: y = y, Fh = F (1 e Thi will enure that the teleoperation yte diplay unditorted dynaic of the environent to the operator. In the 4CH yte of Fig. 3, perfect tranparent teleoperation can be achieved if and only if the controller atify the following condition [19]: C1 = C Z, C4 = ( C Z, C6 1 = C, C5 1 = C (13 3 Applying (13 to Fig. 3 yield C ( Fh Fe = ( Z C ( y y (14 C3( Fh Fe = ( Z C ( y y On the other hand, a dicued before, the ater and lave dynaic Z and Z can generally be odeled by iple apringdaper yte. A it i evident fro the cloedloop equation (14 for the ater and the lave, if the ater and lave dynaic include daping ter, they contribute to the cloedloop equation in the ae way a the derivative ter of the ater and lave PD controller (i.e., C and C. Siilarly, the pring tiffne ter in the ater and lave dynaic can be cobined with the proportional ter in C and C. Therefore, in ot of the teleoperation literature, Z and Z are conidered to be pure inertia. The control law decribed in (13 for C 1 and C 4 require acceleration eaureent (due to the inertial contribution of Z and Z. If a good tranparency i required over a large frequency bandwidth, accurate etiation of inertial paraeter baed on acceleroeter ay be jutified []. However, at low frequencie, neartranparency can be obtained by ignoring the ater and lave dynaic in the expreion for C 1 and C 4 [1], in which cae the original control deign (13 i odified to C1 = C, C4 = C, C6 1 = C, C5 1 = C (15 3 With the choice of controller in (15, baed on Fig. 3 the ater and lave cloedloop equation becoe C ( Fh Fe = Z y C ( y y (16 C3 ( Fh Fe = Z y C ( y y There i ore than one way to chooe the controller in (15. Norally, the poition controller are choen uch that C /C = Z /Z to achieve iilar cloedloop dynaic for the ater and the lave []. Since in our experient the ater and the lave robot are identical Z = Z = Z, we take their controller to be iilar a well: C = C = C, C = C = C (17 p 3 f where C p and C f are the poition and force controller to be deterined.. Norally, C p i a PDtype controller and C f i a calar gain. With the choice of controller in (17 and baed on the cloedloop equation (16 and, the poition error dynaic becoe ( Z C ( y y = (18 p indicating that the lave and ater poition track each other ayptotically. A coplete dicuion of thi point uing the hybrid atrix analyi can be found in []. With perfect poition tracking, (16 can be rewritten a C ( F F = Zy = Zy (19 f h e Therefore, force tracking i not perfect for a high agnitude of Z (i.e., for high inertia or high frequencie. Had we ued the acceleration eaureent needed in (13, the force tracking error would have converged to zero a fact corroborated by (14. It i alo intuitively clear that lack of knowledge about the anipulator dynaic in (15 can deteriorate the force tracking perforance epecially over high frequencie. However, for low frequencie, the righthand ide of (16 can be aued to be negligible. Thu, fro (16, converge to zero. A good tranparency can therefore be achieved at a low bandwidth. Worthy of note i

5 that ince voluntary otion of the huan hand are theelve bandliited, force tracking will be very good hort of feeling highfrequency phenoena uch a the harp edge or texture of an object. Thank to the tranparency condition (15 and the iplifying auption (17, the bilateral architecture in Fig. 3 with eight controller paraeter (C 1 to C 6, C and C can be iplified to only two controller paraeter (C p and C f, a hown in Fig. 4. F * h F * e C f, C p, F deired Z e Z h Hybrid algorith Inner loop Voltage ignal Meaure of preure Inner loop Electropneuatic yte Z 1 Mater ide Slave ide F C f, Electropneuatic deired Hybrid Voltage F Z 1 algorith ignal yte C p, Meaure of preure Fig. 4. 4CH bilateral teleoperation block diagra with hybrid control A ain difference between the original diagra in Fig. 3 and the diagra preented in Fig. 4 i that the hybrid algorith i introduced. The input ignal F and F correpond to the deired force of the hybrid control loop. If the force tracking obtained with the hybrid control i perfect, that ean the behavior of the inner loop i equivalent to a unitary tranfer function. Thu the diagra Fig. 3 i equivalent to the tandard diagra Fig. 3. Thereafter the hybrid control loop i conidered to be perfect to iplify the paraeter controller calculation. The auption will be verified in experient in ection V. IV. EXPERIMENTAL RESULTS AND DISCUSSION A. Experiental etup F y y In thi ection, experient are conducted with a one degree of freedo teleoperation yte. The yte etup conit of two identical device (ater and lave, actuated by two pneuatic cylinder uing eight olenoid valve. The low friction cylinder (Airpel odel M16D1D have a 16 diaeter and a 1 troke. The endeffector of each anipulator i equipped with a force enor in order to eaure the operator and the environent force. The pneuatic olenoid valve (Matrix odel GNK8113C3 ued to control the air flow have witching tie of approxiately 1.3 (opening and. (cloing. With uch fat witching tie, the on/off valve are perfect for the purpoe of the propoed control. The valve flow rate characteritic (4 ued in the control chee of Fig. 4 coe directly fro the data heet of the coponent. A lowfriction LVDT (Linear Variable Differential Tranforer poition enor i connected to each cylinder in order to eaure the ater and the lave poition. Each cylinder chaber i equipped with a preure enor. The yte wa upplied with air at an abolute preure of 3 kpa. The control yte i ipleented uing a dspace board (DS114, running at a apling rate of 5 Hz. Thi value ha been choen according to the bandwidth of the valve and to guarantee acceptable tracking repone. B. Experiental reult Figure 5(a give the force tracking repone and Fig. 5(b preent the poition tracking repone obtained in the experient. For the firt few econd, the ater i oved back and forth by the uer wherea the lave i in free pace. It can be een that the lave rapidly track the ater oveent in free pace. Next, the lave ake contact with a rigid environent. The operator puhe againt the ater leading to different level of the lave/environent contact force. The fact that the poition profile reain contant during the contact ode i that under hard contact the lave cannot penetrate the environent regardle of the operator force. Force (N Error (N Poition ( Error ( Freeotion Contactotion 1 tie ( (a. Force tracking x Freeotion Contactotion Mater Slave tie ( (b. Poition tracking Fig. 5. Experiental reult of the aterlave yte Thank to the force inforation, the operator can feel the lave/environent interaction in real tie. Moreover, he/he can accurately tranit hi/her force to the lave anipulator in order to perfor a tak. Note that the fat oveent of

6 the ater in the firt few econd do not preent ocillation, but are intentionally created by the operator to exaine the yte tability and the perforance in free otion. The nonzero value for, even when the lave i in free pace, i ainly due to the uncopenated friction of the pneuatic actuator. The experiental reult how a good poition and force tracking perforance in free otion and under hard contact. A entioned in Section III.B, the tranparency in Fig. 4 can be achieved when the inner force control loop i perfect. Thi condition i verified in Fig. 6, where the force generated by the lave actuator accurately track the deired force F. A iilar reult can be oberved for the ater yte. The experiental reult highlight that good perforance for the force tracking of the inner cloedloop are obtained within the bandwidth of the oveent. In our experiental validation, the oveent were low enough to aue that the preure variation i all. The approxiation (9 i entirely jutified in thi cae. For fater oveent, the tracking perforance decreae but thi drawback can be overcoe by chooing a aller aple tie. Error (N Force (N Freeotion Contactotion F Deired F 1 Tie ( Fig. 6. Perforance of the inner force control loop V. CONCLUSION In thi paper, pneuatic actuator with inexpenive olenoid valve are choen for the developent of a ater and lave teleoperation yte. To control efficiently the witching on/off valve, a new hybrid algorith ha been uccefully ipleented in experient. Thi technique not only take into account the nonlinear behavior of the a flow rate but alo the witching control of the olenoid valve. The reult how that it i poible to achieve an acceptable tranparent teleoperation perforance without uing claical proportional ervovalve. With a fourchannel bilateral architecture, under freeotion condition or contactotion condition, the force and poition tracking obtained i atifactory. Latly, future work conit of ipleenting the bilateral control with the hybrid algorith on a ultiple degree of freedo ater/lave yte. Another apect of thi work i the tability tudy of the hybrid control baed teleoperation yte, e.g., with repect to paraeter uncertaintie in the odel. REFERENCES [1] H. Kazerooni, Huanrobot interaction via the tranfer of power and inforation ignal, IEEE Tran. Sy. Man. & Cyber, pp , 199. [] B. Hannaford, Scaling, ipedance, and power flow in force reflecting teleoperation, Rob. Re. ASME DSC, pp. 93, 199. [3] S.P. DiMaio, S.E. Salcudean, C. Reboulet, S. Tafazoli, K. Hahtrudi Zaad, A virtual excavator for controller developent and evaluation, IEEE Int. Conf. Rob. & Auto. ICRA, pp. 558, [4] C. Melchiorri, A. Euebi, Teleanipulation: Syte apect and control iue, Proc. Int. Suer chool Modeling & Control of Mechani and Robot, Ed. Singapore, World Scientific, pp , [5] D. Stokic, M. Vukobratovic, D. Hritic, Ipleentation of force feedback in anipulation robot, Int. J. 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