World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:9, No:6, 2015

Transcription

1 Vol:9, No:6, 5 Impliit ore Control of a Poition Controlle A Comparion with Expliit Algorithm Alexaner Winkler, Jozef Suhý International Siene Inex, Computer an Information Engineering Vol:9, No:6, 5 waet.org/publiation/576 Abtrat Thi paper invetigate imple impliit fore ontrol algorithm realizable with inutrial robot. A lot of approahe alreay publihe are iffiult to implement in ommerial robot ontroller, beaue the ae to the robot joint torque i neeary or the omplete ynami moel of the manipulator i ue. In the pat we alreay eal with expliit fore ontrol of a poition ontrolle robot. Well known heme of impliit fore ontrol are tiffne ontrol, amping ontrol an impeane ontrol. Uing uh algorithm the ontat fore annot be et iretly. It i further the reult of ontroller impeane, environment impeane an the ommane robot motion/poition. The relationhip of thee propertie are worke out in thi paper in etail for the hoen impliit approahe. They have been aapte to be implementable on a poition ontrolle robot. The behavior of tiffne ontrol an amping ontrol are verifie by pratial experiment. or thi purpoe a uitable tet be wa onfigure. Uing the full mehanial impeane within the ontroller truture will not be pratial in the ae when the robot i in phyial ontat with the environment. Thi fat will be verifie by imulation. Keywor Damping ontrol, impeane ontrol, robot fore ontrol, tability, tiffne ontrol. I. INTRODUCTION IN ome fiel of robot appliation it i uitable to ue fore ontrol intea of poition ontrol, e.g. when the robot i in phyial ontat with the environment or for ome kin of human-robot interation. In the lat eae the reearh fiel of robot fore ontrol ha been invetigate in epth an a lot of intereting onept have been preente. An overview of ifferent fore ontrol algorithm an be foun e.g. in [], [] an [3]. One oul think that the reearh fiel of fore/torque ontrol i omplete, however, mot of the inutrial robot work only poition ontrolle. It an be een that fore ontrol only lowly fin it way from roboti laboratorie into inutry. or the purpoe of aelerating thi tren we think that fore ontrol algorithm houl be a imple a poible to be realizable with ommerial robot ontroller. Aitional attention ha to be pai to the fat that we often have only ae to the eire en-effetor poition, beaue ae to joint torque or motor urrent i not enable by the manufaturer. So the fore ontrol loop i loe aroun the poition ontrol loop whih lea to the o alle poition bae fore ontrol approah [4], [5]. Generally, fore ontrol algorithm an be laifie into expliit an impliit fore ontrol []. In expliit fore ontrol the ontat fore an torque between en-effetor an the environment () are ompare with the eire value of A. Winkler i with the Hohhule Mittweia, Univerity of Applie Siene, Mittweia, Germany ( alexaner.winkler@h-mittweia.e). J. Suhý i with the Univerity of Matej Bel, Banká Bytria, Slovakia. ig.. ig.. ore U General heme of expliit fore ontrol. ore Poition U General heme of impliit fore ontrol. the ontat fore/torque. rom their ifferene a onvenient motion of the manipulator arm i generate with the aim to reah the eire fore. A implifie ignal flow iagram of expliit fore ontrol an be een in ig.. The urrent ontat fore/torque meaure by fore/torque enor () are repreente by vetor.the vetor, an U inlue the eire ontat fore/torque, the urrent en-effetor poition/orientation an the generalize ontroller output, repetively. In the ae that the output ignal of the fore ontroller in vetor U are the eire value of the en-effetor poition, we peak about poition bae fore ontrol alreay mentione. In [6] we invetigate an ompare imple approahe of poition bae fore ontrol uing an inutrial robot with it ommerial robot ontroller. In thi ontext the preferre algorithm wa a imple proportional ontroller with poitive feebak of the urrent robot poition. In [7] an [8] thi promiing approah wa ue for the evelopment of algorithm of two-imenional fore/poition ontrol an orientation ontrol, whih may be applie in ome ontour following tak, e.g. in polihing, eburring or grining. In ontrat to thi, with impliit fore ontrol the eire value annot be et iretly. rom the meaure fore, the eviation vetor Δ i alulate, whih moifie the eire en-effetor poition given by vetor o that a efine ontat fore an arie. The bai truture of impliit fore ontrol how the ignal flow iagram of ig.. We will here fou on the impliit fore ontrol of an inutrial robot, but now an then we will bring impliit fore ontrol in relationhip to expliit fore ontrol. Thi paper i further organize a follow: In the next etion ome aitional bai of robot fore ontrol will be hown. The experimental etup an the tet proeure whih will be ue later to analyze ifferent fore ontrol algorithm will be preente in etion III. Thereafter, three general type of impliit fore ontrol namely tiffne ontrol (etion IV), International Sholarly an Sientifi Reearh & Innovation 9(6) holar.waet.org/37-689/576

2 Vol:9, No:6, 5 International Siene Inex, Computer an Information Engineering Vol:9, No:6, 5 waet.org/publiation/576 amping ontrol (etion V) an impeane ontrol (etion VI) will be invetigate an verifie on an inutrial poition ontrolle robot. inally, in the lat etion a hort onluion i given. II. ROBOT ORCE CONTROL A alreay mentione, fore ontrol algorithm an be generally ivie into expliit an impliit ontrol. Another important fat when regaring fore ontrol algorithm i the type of atuating variable whih i provie by the algorithm. In many publiation it i aume that there i ae to the eire value of the joint torque of the robot. In thi ae the behavior of a robot an be eribe only by it ynami equation: τ = M(q ) q + C(q, q ) q + G(q ) () In () τ i the vetor of applie joint torque, vetor q inlue the joint angle, M i the inertia matrix, C repreent the Corioli an entrifugal fore/moment an G inlue the gravitational fore/moment. If the value of M, C an G are known, it may be poible to eouple an linearize the ontrolle plant, whih will reult in approahe enote a moel bae ontrol [9], [], ompute torque ontrol [], invere ynami ontrol [], et. However, inutrial robot are uually poition ontrolle in joint pae uing aae ontrol a a rule heme an ae to joint torque or motor urrent i not enable by the manufaturer. or that reaon the ynami moel () i not pratial for poition ontrolle manipulator. It harateriti i efine by truture an the parameter of the eentralize joint ontrol. A alreay een, uing an inutrial robot in fore ontrol moe, the fore ontrol loop ha to be loe aroun the poition ontrol loop. The algorithm of impliit fore ontrol invetigate in thi paper are alo poition bae approahe. One general approah of impliit ontrol i impeane ontrol introue by Hogan [3]. Mehanial impeane in the ontat ituation of robot an environment i given in one iretion a follow: () [Δ ()] = m + + () where m, an are the parameter of ma, amping an tiffne. In ontrat to thi efinition of the impeane often the relationhip between fore an poition i ue: () Δ () = m + + (3) or every Carteian egree of freeom it mehanial impeane may be parameterize iniviually. The blok iagram of poition bae impeane ontrol an be een in ig. 3. There are ome peial kin of impeane ontrol. One of it i tiffne ontrol introue by Salibury [4]. He propoe an approah on the bai of the robot joint torque. or thi purpoe the Carteian tiffne matrix i tranforme into joint pae q uing the Jaobian matrix J of the robot: q = J T J (4) ig. 3. ig. 4. ig. 5. m Po. Controlle Poition bae impeane ontrol. Po. Controlle Poition bae tiffne ontrol. Veloity U. Damping ontrol. Another type of tiffne ontrol publihe e.g. in [] an [5], ue Carteian poition orretion value to ontrol the robot manipulator intea of joint torque. Setting ma an amping in (3) to zero, the ontrol law for one egree of freeom follow to: Δ = (5) Thi lea to the ignal flow iagram of the loe loop ontrol whih an be een in ig. 4. Auming that the environment i loate at poition =an that it an be moele jut by it mehanial tiffne the ontat fore in teay tate will epen on the ommane poition : (t )= + (6) One of the firt publihe kin of impeane ontrol i the amping ontrol [6]. One poible ignal flow iagram of amping ontrol how ig. 5. A it an be een, now the ma m an the tiffne of the target impeane have been et to zero. Aoring to the following ontrol law the output ignal of the amping ontroller i the eire veloity of the robot: ΔẊ = (7) Hene, a ontat fore will reult in a proportional hange of the eire veloity. The ontat fore in teay tate will reah the following value: (t )=Ẋ (8) In the literature ome moifiation of amping ontrol an be foun, e.g. in [] an [5] a ombination of tiffne an amping ontrol i propoe. III. EPERIMENTAL SETUP In the following etion primary type of impliit fore ontrol are invetigate uing the experimental equipment whih an be een in ig. 6. The manipulator i a ix axe low payloa robot of type KUKA KR6/. It i ontrolle by the ommerial robot International Sholarly an Sientifi Reearh & Innovation 9(6) holar.waet.org/37-689/576

3 Vol:9, No:6, 5 International Siene Inex, Computer an Information Engineering Vol:9, No:6, 5 waet.org/publiation/576 ig. 6. Trajetory generator ig. 7. RSI Experimental etup ue for experiment. Manipulator arm ore/torque enor loa limiter Gripper Contat urfae Z-axi ompliane writ element Invere q Deentral Kinemati joint ontrol q Ae to the poition ontrol loop uing RSI. ontroller KUKA KRC. The robot i equippe with the ix omponent fore/torque enor SCHUNK T-Delta. rom it meaure value we ue only the fore omponent whih i vertially orientate towar groun. A in thi paper poition bae fore ontrol approahe are invetigate, it i neeary to have an ae to the poition ontrol loop. Thi feature i available with the KUKA Senor Interfae (RSI) [7], whih allow the realization of enor guie robot motion. Uing RSI for the implementation of iniviual ontroller, thee algorithm will be exeute in real time perioially within the interpolation yle of m in parallel to the uer robot program written in KUKA Language (KRL). It i poible to influene the en-effetor poition/orientation by Carteian poition orretion repreente by vetor Δ with repet to the eire poition. The whole truture of motion ontrol an be foun in ig 7, where q an q are the vetor of eire an urrent joint angle, repetively. It i very iffiult to fin a moel for the motion behavior of the RSI-ontrolle robot beaue we have not enough information about it internal ontrol algorithm. One poibility to get it i experimental moeling, by reoring tep an frequeny repone. An unfavorable fat i that the robot behavior inlue ome nonlinear part, e.g. the ifferene between mall-ignal an large-ignal behavior. The ynami of the robot motion in one Carteian DO may be approximate be a firt orer ytem with time elay [8]. The tranfer funtion G Rob () repreent the relationhip between ommane poition or poition orretion an the urrent en-effetor poition : G Rob () = () () = +T Rob e T, (9) where T Rob i aume to be.5 an the time elay T i et to 3 interpolation yle (36 m). or the realization of a efine ontat environment the o alle z-axi ompliane writ element i ue. The tiffne of the z-axi ompliane writ an be ajute by the preure of the ompree air. Auming relatively low veloitie of the robot uring ontating the environment we an eribe the environment by imple pring behavior { } E ( = E ) for > E, () for E where i the environment tiffne an E i the poition of the ontat urfae in robot frame. The value of in experiment preente here i 8 Nmm. It inlue alo the ompliane of the robot aue by it mehani, fore/torque enor, robot loa limiter, et. Two ifferent experiment are uitable to verify fore ontrol algorithm. irt one i ontat etetion. Starting point of the robot en-effetor i loate in free pae with a ertain itane away from the environment urfae. The tak of the fore ontroller i to etablih the ontat between en-effetor an environment an reah a ertain ontat fore. Criteria of the ontrol quality are fore overhoot an approahing veloity. In the eon experiment we aume that the environment ontat i alreay etablihe. We moify the eire ontat fore value are reoring tep repone of the ontat fore. Here riteria of ontrol quality are fore overhoot an tranient time. IV. STINESS CONTROL The ignal flow iagram of tiffne ontrol ha been alreay hown in ig. 4. With the help of the tiffne parameter of the ontroller, the tiffne of the whole ontrol ytem C oniting of poition ontrolle robot an ontat environment an be ajute. Auming that the poition ontrolle robot ha proportional behavior with tranfer fator, with the help of the environment tiffne, C an be etermine a follow: C = () + So, hypothetially, the value of C an be moifie between an. However, ereaing will bring the loe loop ontrol loer to the tability margin. Uing the tranfer funtion of the poition ontrolle robot G Rob (), introue alreay in etion III an taking only the tiffne parameter of the mehanial impeane of the environment into onieration, the tranfer funtion of the loe loop ontrol G C () an be written a follow (ee alo ig. 4): G C () = () () = G Rob () +G Rob () () The tati tranfer fator of G C () repreent the relationhip between fore an poition hange. There are ifferent poibilitie for the implementation of the imple onept of poition bae tiffne ontrol, epening on the pratial robot ontroller. Very important i the fat, how the robot repon to a rapi hange of the eire poition or Δ, epeially when the en-effetor i loate relatively far from the environment. It may be uitable to integrate aitional low pa filter into the ontroller International Sholarly an Sientifi Reearh & Innovation 9(6) holar.waet.org/37-689/576

4 Vol:9, No:6, 5 G ( ) G 3 ( ) Po. Controlle Po. Controlle G ( ) ig. 8. Poition bae tiffne ontrol with low pa filter. ig.. Poition bae amping ontrol. International Siene Inex, Computer an Information Engineering Vol:9, No:6, 5 waet.org/publiation/576 t ig. 9. ig.. ore, Poition (norm.) ore, Poition (norm.) Trajetory Generator Po. Controlle Poition bae tiffne ontrol with trajetory generator ilter iable ilter enable Deire value =. mm ( N) =.4 mm ( N) =. mm (5 N) Deire value =. mm ( N) =.4 mm ( N) =. mm (5 N) Experimental reult of poition bae tiffne ontrol. truture to prevent abrupt ignal hange. Thereto, ig. 8 how ome poibilitie where the filter an be inlue. Keeping the funamental behavior of tiffne ontrol filter G () houl be preferre beaue in that ae only ignal will be moothe. Uing filter G () or G 3 () in priniple the ignal of the ontrat fore will be aitionally filtere, whih lea to a time elay in the loe ontrol loop. A an be een in ig. 9, it may be alo poible to ue the trajetory generator of the robot ontroller to avoi rapi en-effetor motion. Bae on the target poition t the trajetory generator ompute the time erie of the eire poition, e.g. uing linear ontinuou path interpolation. The funtioning of tiffne ontrol in the experiment i hown in ig.. or thi purpoe two ifferent type are implemente into the robot ontroller. irt one i poition bae tiffne ontrol a in ig. 4. Seon one ue aitional low pa filter G () for moothing, ee alo ig. 8. In both ae the target tiffne C i hoen to be 5 Nmm. With the value of the environment tiffne =8Nmm the ontroller gain an be alulate a follow to 8 Nmm : = C (3) C In the experiment the robot en-effetor i alreay in ontat with the environment. We have prealulate three poition value of. mm,.4 mm an. mm whih repreent a ontat fore of N, N an 5 N, repetively. The eire en-effetor poition wa hange rapily. Regaring ig. it an be een, that in the ae when the filter G (p) i iable, the tep repone of the ontat fore trongly oillate, whih make thi verion of tiffne ontrol uele, epeially when higher value of the ontat fore houl be reahe. Stiffne ontrol may be improve by ativating the low pa filter in the branh of the eire poition. Correponing tep repone an alo be een in ig.. or thi purpoe firt orer low pa filter wa ue: G () = (4) +T It time ontant T wa hoen to.. Uing a poition ontrolle robot, tiffne ontrol an be relate to proportional ontroller of expliit ontroller omain. In the ae that we o not know the poition of the environment an the robot en-effetor i loate in free pae, tiffne ontrol will not work uefully. V. DAMPING CONTROL Another type of impliit fore ontrol i amping ontrol. One verion an be een in ig. 5. However, ae to the veloity ontroller i often not available with an inutrial robot. Having ae to the eire poition in Carteian pae, one poible realization of amping ontrol i hown in ig.. A it an be emontrate in ontrat to tiffne ontrol, now the tati value of the ontat fore i inepenent from the environment tiffne. Aoring to (8) the ontat fore in teay tate epen only on the amping parameter of the ontroller an on the value of the eire veloity Ẋ. rom the ignal flow iagram of ig. the tranfer funtion of the loe loop ontrol an be etermine: G C () = () () = G Rob () G Rob () + (5) Comparing amping ontrol with poition bae approahe to expliit fore ontrol, it may be relate to integral ontrol. Regaring the integral fore ontroller ating on a poition ontrolle robot [6], it an be reognize that the veloity of the robot motion i proportional with repet to the fore ontrol error. Uing amping ontrol the ontat fore i proportional with repet to the eire veloity. So the avantage in omparion to tiffne ontrol i that amping ontrol i alo pratial to etablih the ontat between robot an environment approahing the environment from free pae. International Sholarly an Sientifi Reearh & Innovation 9(6) holar.waet.org/37-689/576

5 Vol:9, No:6, 5 International Siene Inex, Computer an Information Engineering Vol:9, No:6, 5 waet.org/publiation/576 ig.. ore, Vel.Ẋ (norm.) ore, Vel.Ẋ (norm.) Contat etetion Environment ontat Deire value Ẋ =mm ( N) Ẋ =4mm ( N) Ẋ =mm (5 N) 3 4 Experimental Reult of amping ontrol. The ilemma of the integral ontroller [6] an be alo aigne to amping ontrol. On the one han when the robot en-effetor i loate in free pae the goal i to reah a relatively high approah veloity of the robot to ontat the environment. So the ontroller gain houl be hoen a high a poible, whih mean that amping parameter houl be a low a poible. On the other han, when the robot i in ontat with the environment the loe ontrol loop ha to be table an oillation of the fore houl be prevente. Due to thi it eem to be onvenient to with the ontroller gain in epenene on the ontat ituation [6]. In the experiment preente in thi paper ontroller gain of amping ontrol will be optimize to fat ontat etablihment. In the firt experiment the following etting will be elete: In the ae that the eire value of the ontat fore i 5 N, the robot houl move towar the ontat urfae with eire veloity of Ẋ =mm. So, aoring to (8) amping parameter ha been hoen 5 Nmm. ig. how the ontat fore both in the enario of ontating the environment from free pae an in the enario when the environment ontat i alreay etablihe. In both ae ifferent value of Ẋ are ue to reah ifferent value of the ontat fore. irt, it an be een that the maller the veloity the longer the time before getting environmental ontat. After the ontat i etablihe an oillation of the fore value an reognize. Thi oillation may be arien by the reolution of the robot poition. The amplitue of the fore oillation an be reue by inreaing amping. However, the eire veloity Ẋ ha to be ereae to hol the fore value. Moifying the amping i the eon poibility to ajut the ontat fore. or thi purpoe the value of Ẋ will be kept ontant. In our experiment Ẋ i et to mm. Caue by the relative fat approah veloity the fore overhoot i high, epeially when the eire fore i low, ee ig. 3. The permanent fore oillation an be reognize again when ore, Vel.Ẋ (norm.) ore, Vel.Ẋ (norm.) Contat etetion 3 4 Environment ontat Deire value =Nmm ( N) =Nmm ( N) =5Nmm (5 N) 3 4 ig. 3. Experimental reult of amping ontrol when moifying the amping parameter. ig. 4. Impeane ontrol. Po. Controlle the robot i in ontat with the environment. m VI. IMPEDANCE CONTROL Impeane ontrol, whih take the full mehanial impeane into onieration, i the general type of impliit fore ontrol. The onept of poition bae impeane ontrol wa alreay introue in ig. 3. ig. 4 how the ignal flow iagram of impeane ontrol for one egree of freeom. A an be een, the impeane term wa eompoe. The orreponing loe loop tranfer funtion follow to: G C () = () () = G ( Rob() ) E + + m G Rob () m (6) With virtual ma m, in omparion to tiffne ontrol or amping ontrol, aitional inertia will be integrate into the ytem. It may be reaone that when ontating the environment tability problem our, epeially in the ae if the ontat urfae i tiff. However, impeane ontrol play an important role in the fore bae human-robot interation [9]. It i poible to efine the target impeane for every Carteian egree of freeom or in joint pae for every joint within a ertain range iniviually. Setting tiffne parameter =will reult in ma-amper ytem whih an be applie to the o alle International Sholarly an Sientifi Reearh & Innovation 9(6) holar.waet.org/37-689/576

6 Vol:9, No:6, 5 Im m = m = kg m = kg m = kg m = Re Amplitue ratio A [B] m = kg m = m =75kg m =5kg m =5.5kg Phae hift φ ig. 5. Root lou of the ma-amper ytem with repet to ma a parameter. ig. 6. Nihol hart of the ma-amper ytem with ifferent value of the ma parameter. International Siene Inex, Computer an Information Engineering Vol:9, No:6, 5 waet.org/publiation/576 han guiane. Here the human operator take the robot arm an move it through the workpae. Han guiane of robot manipulator may be ue for intuitive robot programming or to human robot ooperation. In the ae that tiffne i ativate, i.e. >, the manipulator ha the behavior of a pring-ma-amper ytem. Then, uring han guiane robot woul move bak to the tart poition when interation fore iappeare. The etabilizing property of impeane ontrol eribe in [] will be now emontrate on a hort example. or thi purpoe we take the amping ontroller from the previou etion with =Nmm an a a variable ma. The impeane ontroller ha then the behavior of a ma-amper ytem. The loe loop tranfer funtion an be reue to: G C () = () () = G ( Rob() ) E + m G Rob () + + m (7) Taking (9) an negleting the ea time, the behavior of the poition ontrolle robot an be implifie to firt orer ytem G Rob () = +T Rob, (8) where the time ontant T Rob ha a value of.5. The loe loop tranfer funtion reult in: + m G C () = + + T Rob+m + T (9) Robm 3 ig. 5 how the root lou of the loe ontrol loop with repet to the ma m of the target impeane. It value ha been moifie between an kg. The tability margin an be foun where the root lou reahe the right -half-plane. In the example preente here, the ritial ma i approximately 5.5 kg. One may ome to the ame onluion for Nihol hart (ig. 6). It i bae on the tranfer funtion of the open ontrol loop: G O () = +(T Rob + m) + T Rob m 3 () The Nihol hart how the amplitue ratio a a funtion of the phae hift. The hart an be ubivie by B-axi an by 8 -axi into quarant. When the graph pae the eon quarant (top left) the loe ontrol loop will be untable. The alreay hown tability margin, an be foun again. VII. CONCLUSION In thi paper ome bai algorithm of impliit robot fore ontrol, namely tiffne ontrol, amping ontrol an impeane ontrol, were elete for the implementation with an inutrial robot. or thi purpoe the orreponing approahe have been aapte to poition bae ontroller truture, whih are realizable with a poition ontrolle robot. To parameterize robot ontroller ome relationhip between ommane robot motion/poition, parameter of the ontat environment an ontroller parameter are worke out. Thi may be neeary to alulate the tati value of the ontat fore. A for the tiffne ontroller it an be reognize that it behavior i imilar to the behavior of the proportional ontroller of expliit fore ontrol. Thi mean that it an be only ue in the ae when the ontat between robot an environment i alreay etablihe. When the robot i loate in free pae an the itane between it en-effetor an the ontat urfae i unknown, tiffne ontroller i not uitable. Damping ontroller i imilar to integral ontroller. Therefore, it an be ue in both ituation, i.e. ontating the environment from free pae or when the robot i alreay in ontat with the environment. It an be learne from integral ontroller [6], that optimal ontroller gain (amping) for ontat etetion i ifferent from optimal gain/amping in ontat ituation. inally, impeane ontrol with truture of full mehanial impeane i not uitable when the robot i in ontat with the environment, beaue the ma omponent an be een a a oure of intability. An example wa worke out to emontrate thi fat by imulation. However, impeane ontrol may be ue for ome kin of human-robot interation. REERENCES [] G. Zeng an A. Hemami, An overview of robot fore ontrol, ia, vol. 5, no. 5, pp , 997. [] M. Vukobratović an A. Tuneki, Contat ontrol onept in manipulation roboti an overview, IEEE Tranation on Inutrial Eletroni, vol. 4, no., pp. 4, 994. [3] R. Volpe an P. Khola, A theoretial an experimental invetigation of expliit fore ontrol trategie for manipulator, IEEE Tranation on Automati Control, vol. 38, no., pp , 993. International Sholarly an Sientifi Reearh & Innovation 9(6) holar.waet.org/37-689/576

7 Vol:9, No:6, 5 International Siene Inex, Computer an Information Engineering Vol:9, No:6, 5 waet.org/publiation/576 [4] J. De Shutter an H. Van Bruel, Compliant robot motion I. A formalim for peifying ompliant motion tak, International Journal of i Reearh, vol. 7, no. 4, pp. 3 7, 988. [5] E. Dégoulange an P. Dauhez, External fore ontrol of an inutrial PUMA 56 robot, Journal of i Sytem, vol., no. 6, pp , 994. [6] A. Winkler an J. Suhý, Poition feebak in fore ontrol of inutrial manipulator an experimental omparion with bai algorithm, in IEEE International Sympoium on i an Senor Environment,, pp [7], ore ontrolle ontour following on unknown objet with an inutrial robot, in IEEE International Sympoium on i an Senor Environment, 3, pp [8], ore ontrolle ontour following by an inutrial robot on unknown objet with tool orientation ontrol, in Pro. of Joint Conferene on i 45th International Sympoium on i an 8th German Conferene on i, 4. [9] J. J. Craig, Introution to i Mehani an Control. Pearon Prentie Hall, 5. [] T. A. Laky an T. C. Hia, ore ontrol of roboti manipulator, in Applie Control, S. G. S. G. Tzafeta, E. Marel Deker, 993, h., pp [] A. A. Golenberg, Implementation of fore an impeane ontrol in robot manipulator, in Pro. of IEEE International Conferene on i an Automation, vol. 3, 988, pp [] C. Natale, B. Siiliano, an L. Villani, Robut hybri fore/poition ontrol with experiment on an inutrial robot, in Pro. of the IEEE/ASME International Conferene on Avane Intelligent Mehatroni, 999, pp [3] N. Hogan, Impeane ontrol, an approah to manipulation: Part i, ii, iii, ASME Journal of Dynami Sytem, Meaurement an Control, vol. 7, pp. 4, 985. [4] J. K. Salibury, Ative tiffne ontrol of a manipulator in arteian oorinate, in Proeeing of the IEEE International Conferene on Deiion an Control, vol. 9, 98, pp. 95. [5] D. E. Whitney, Hitorial perpetive an tate of the art in robot fore ontrol, International Journal of i Reearh, vol. 6, no., pp. 3 4, 987. [6], ore feebak ontrol of manipulator fine motion, Journal of Dynami Sytem, Meaurement an Control, vol. 99, no., pp. 9 97, 977. [7] KUKA er GmbH, KUKA.SenorInterfae (RSI)., 7. [8] A. Winkler an J. Suhý, An approah to ompliant motion of an inutrial manipulator, in Pro. of the 8th International IAC Sympoium on Control, 6. [9], Poibilitie of fore bae interation with robot manipulator, in Human--Interation, N. Sarkar, E. I-Teh Euation an Publihing, 7, pp [] N. Hogan an S. P. Buerger, Impeane an interation ontrol, in i an Automation Hanbook, T. R. Kurfe, E. CRC Pre, 4, h. 9. International Sholarly an Sientifi Reearh & Innovation 9(6) 5 46 holar.waet.org/37-689/576