Bilateral Teleoperation of Multiple Cooperative Robots over Delayed Communication Networks: Application

Transcription

1 Proceeings of the 5 IEEE International Conference on Robotics an Automation Barcelona, Spain, April 5 Bilateral Teleoperation of Multiple Cooperative Robots over Delaye Communication Networks: Application Dongjun Lee, Oscar Martinez-Palafox, an Mark W. Spong Coorinate Science Laboratory University of Illinois at Urbana-Champaign W. Main St. Urbana IL 6 USA Abstract In a companion paper [], we propose a control framework for the bilateral teleoperation between a single robot an multiple cooperative slave robots over elaye communication network. In this paper, we perform simulation an semi-experiment (i.e. real an simulate slaves) to illustrate an valiate properties of the propose control scheme. In particular, the three key properties of the propose control framework are highlighte in this paper: ) cooperative fixtureless grasping an manipulation of inertial an eformable objects by multiple slave robots; ) passive teleoperation of the overall behavior of the multiple slave robots (an the graspe object) over the elaye communication with force reflection; an ) grasping safety (i.e. secure grasping) an interaction stability regarless of the communication elay an human comman. I. INTRODUCTION In a companion paper [], we propose a semiautonomous bilateral teleoperation control framework for the SMMS (single multiple slave) system. See Fig. for an example of such SMMS systems. The key component of the propose framework is the passive ecomposition [], [], with which the ynamics of multiple slave robots is ecompose into two ecouple systems while enforcing energetic passivity: shape system escribing cooperative grasping aspect, an locke system abstracting overall motion of the multiple slave robots. Then, a local control is esigne for the shape system to achieve the cooperative grasping, while a bilateral teleoperation control-loop is constructe between the locke system an the robot s.t. humans can teleoperate the overall behavior of the multiple slaves (an the graspe object). In this paper, we present simulation an semi-experiment (i.e. real an simulate slaves) results of the propose control framework. In particular, the following three key properties of the propose control framework in [] are emonstrate an highlighte:. Fixtureless cooperative grasping: Multiple slave robots can cooperatively grasp an manipulate an object having inertia an flexibility without any rigi fixture. This is achieve by controlling the shape system;. Teleoperation with force reflection: By manipulating the robot of reasonably small-dof, a human operator can control the overall behavior of the multiple slave robots an the graspe object while perceiving combine environmental forces acting on them. This is achieve via the bilateral teleoperation control-loop between the robot an the locke system, in which scattering-base communication [], [5], [6] is use to passify the elaye communication;. Safe an stable operation: Since the shape system is Research partially supporte by the Office of Naval Research uner grant N--- an N-5--6, the National Science Founation uner grants IIS - an CCR -9, an the College of Engineering at the University of Illinois. -lee@control.csl.uiuc.eu, {pomartin,m-spong}@uiuc.eu. Human Operator Robot (m-dof) Workspace Fig.. Communication Network (e.g. Internet) Robot Robot Common Object Workspace (Remote) Robot Single multiple slave (SMMS) system controlle locally an its ynamics is ecouple from that of the locke system, secure an tight cooperative grasping can be guarantee regarless of the communication elay an human comman. Thus, angerous situations entaile by ropping of graspe objects can be avoie. Also, exploiting the passivity property of the passive ecomposition an scattering-base communication, the propose control scheme can ensure passivity of the close-loop SMMS system, thus, interaction safety an stability are enhance. The rest of this paper is organize as follows. In section II, we provie a brief review of the control scheme propose in the companion paper []. Simulation an semiexperiment results are presente in sections III an IV, respectively. Section V contains some concluing remarks. II. REVIEW OF THE SEMI-AUTONOMOUS TELEOPERATION ARCHITECTURE A. Plant, Communication, an Grasping Shape Function Let us consier the m-dof robot ynamics M h (q h ) q h + C(q h, q h ) q h = T h + F h, () where q h,t h,f h R m are the configuration, the control (to be esigne), an the human force, respectively. Also, M h (q h ) R m m an C h (q h, q h ) R m m are the inertia an Coriolis matrices s.t. M h (q h ) is positive-efinite an symmetric an Ṁh(q h ) C h (q h, q h ) is skew-symmetric. Let us enote the total DOF of N slave robots by n := N i= n i with n i being the DOF of the i-th slave. Then, the group ynamics of the N-slave robots can be written in the following n-dof robotic ynamics: M(q) q + C(q, q) q = T + F, () where q := [q T,..., q T N ]T, T := [T T,...T T N ]T, F := [F T,..., F T N ]T R n, M(q) :=iag[m (q ),.., M N (q N )], C(q, q) :=iag[c (q, q ),.., C N (q N, q N )] R n n with q i, T i, F i, M i, C i being the configuration, the control, the environmental force, the inertia an the Coriolis matrices of the i-th slave robot, respectively. Obviously, M(q) is -7-9-X/5/$. 5 IEEE. 6

2 Locke System Environ F L v L Locke System T L ' v L Locke System Control T L v L Scattering Transform s L + s L - Delay τ Delay τ s h - s h + Scattering Transform T h v h Control T h. q h Robot F h. q h Human Operator agent (x,y ) R f φ Fig.. Close-loop Teleoperator Symmetric teleoperation architecture. symmetric an positive-efinite an Ṁ(q) C(q, q) is skew-symmetric. We suppose that n m. We also assume that there exists a centralize communication an computing moule for the slaves, which communicates with the environment over the elaye communication network. To escribe internal grasping shape among the slaves, we efine the grasping shape function q E : R n R n m on the configuration space of the slaves (). Then, a esire grasping shape can be achieve by enforcing the following conition: q E (q(t)) q E, () where q E Rn m is a (constant) target grasping shape. B. Passive Decomposition In [], using the passive ecomposition, the ynamics of the multiple slaves () is partially ecompose s.t. M L (q) v L + C L (q, q)v L locke system ynamics M E (q) q E + C E (q, q) q E } {{ } shape system ynamics + C LE (q, q) q E = T L + F L, () coupling = T E + F E, (5) + C EL (q, q)v L coupling where M (q) are symmetric an positive efinite matrices s.t. Ṁ (q) C (q, q) are skew-symmetric ( L, E), an C LE (q, q) = CEL T (q, q) (i.e. skew-symmetric each other). Here, the shape system ynamics escribes the grasping aspect having q E (t) as its configuration, while the locke system ynamics represents the overall ynamics of the multiple slave robots. Also, F L an F E are the portion of the environmental forces affecting the overall slaves motion, an the internal grasping force, respectively, while T L an T E are the transforme controls esigne below. C. Control Design The locke an shape controls T L,T E in ()-(5) are esigne to be ( ) ( ) ( ) TL CLE (q, q) q T := E T E C EL (q, q)v + L L T E, (6) passive ecoupling teleoperation an grasping where the ecoupling control is passive s.t. vl T C LE(q, q) q E + q E T C EL(q, q)v L =(from C LE = CEL T ), an T E R n m an T L Rm are the local grasping control an the bilateral teleoperation control esigne as the following. The local grasping control T E (t) is esigne s.t. T E(t) := K E v q E (t) K E p (q E (t) q E) F E (t), (7) where F E (t) is the estimate of F E (t), qe is the esire constant grasping shape in (), an Kv E,Kp E are the PD-gain matrices. The FF (feeforwar) term F E (t) in (7) woul be necessary for such applications where high Fig.. agent (x,y ) φ agent φ (x,y ) R o φ ο Y Inertial Frame Fo Three slave robots on (x, y)-plane. grasping precision is crucial or the contact force is so large that excessively large PD-gains are require to compensate for it. This FF-term, however, oes not generally ensures passivity, as it might generate unboune energy (e.g. with corrupte force sensing). Thus, in [], to enforce passivity, this FF-term is implemente in some passive implementation structures (e.g. [7], []) s.t. its energy generation is always limite. We also choose the symmetric teleoperation architecture in Fig., where local impeance controls are given by the following PI-control with amping injections: T (t) := Kv (t) Kv ve(t) Kp ve(θ)θ, () =: T (t) O X t where {L, h}, v e := v v, an we set T h := T h for notational convenience. To passify the communication elay, we utilize scattering-base communication as shown in Fig.. Then, we set K v = Z to achieve the matching conition [6], where Z R m m is symmetric an positiveefinite line characteristic impeance. With this matching conition, we can ensure position coorination in the teleoperation control loop. III. SIMULATION For this simulation, we consier three -DOF point mass slave robots on the (x, y)-plane as in Fig., whose motions are specifie by (x i,y i,φ i ) R (i.e. translation an yaw angle) w.r.t. a common inertial frame F o (i =,, ). Theisalsoassumetohave-DOF point mass ynamics. We assume that each slave robot has kg mass an kgm rotational inertia, while the robot has kg an kgm. These somewhat unrealistic slave masses an inertias are chosen to achieve a simple expression for the ecomposition (i.e. v L with v E = q E )asbelow. We consier the following grasping shape function: x x Lcos(φ + π 6 ) x x + Lcos(φ π 6 ) y q E := y Lsin(φ + π 6 ) y y + Lsin(φ π 6 ) R 6. (9) φ φ φ φ If q E =, three slave robots will make an equilateral triangle with sie length of L, whose rotation is specifie by the yaw angle of robot. See Fig.. Then, following 69

3 Rigi Grasping Shape with the Decoupling at &sec.5 Shape Distortion [m]... Grasping Shape Distortion w/ ecoupling w/o ecoupling robot Alignment Error [ra].6.. w/ ecoupling w/o ecoupling Fig Grasping Shape Distortion ue to the Coupling at &sec.5.5 robot.5.5 Rigiity of grasping with or without ecoupling. [], the locke system velocity in () can be foun to be (ẋ +ẋ +ẋ ) v L = (ẏ +ẏ +ẏ ) ( φ + φ + φ R, () )+ω + ω where ω := L [ẋ sin(φ + π 6 ) ẏ cos(φ + π 6 )] an ω := L [ẋ sin(φ π 6 ) ẏ cos(φ π 6 )]. This locke system velocity v L () represents translation an rotation of the equilateral triangle when q E (t) =. We assume % uncertainty for the inertias. With this, the locke an shape systems can not be perfectly ecouple from each other by the ecoupling control in (6), as accuracy of the ecomposition epens on the system s inertia structure. We assume.5sec communication elay between the an slave environments. We also moel humans as a PD-control loop for the robot, whose set point is given by the elaye average motion of the slaves (i.e. i= (x i(t τ),y i (t τ),φ i (t τ)) R ). A. Effect of the Coupling on the Rigi Grasping We o not inclue an object for this simulation. However, grasping shape is still controlle by the PD-control in (7). In the first sec, a human operator stabilizes three slave robots on top of the larger circle (of raius R o ) while they form the equilateral triangular heaing to the x-axis (i.e. φ o = φ =); an then, she/he operates the s.t. the triangle revolves on the arc of the larger circle Fig. 5. Grasping shape error q E(t) with or without ecoupling. counterclockwise while the formation itself is rotating with the same rate (i.e. t φ o = t φ ). See Fig. for notations. We set the rotating rate w := π t φ o(t) =.[Hz]. Simulation is performe with or without the ecoupling control in (6). Snapshots are taken on the (x, y)-plane with shooting spee /w =.5[sec] uring sec, an shown in Fig. where the positions an heaings of robots are represente by the circles (or for the ) an the line stemming from them, respectively. To highlight the grasping shape rigiity, eight circles of raius R f (= L) are also rawn in Fig., on whose arc the slave robots shoul make the equilateral triangle if q E =. Shape istortion ( (qe (t),q E (t),q E (t),q E (t)) ) an alignment error ( (qe 5 (t),q6 E (t)) ) are also given in Fig. 5. As shown in Figures -5, when the ecoupling control in (6) is omitte, human comman on the locke system also excites the shape system through the coupling terms in ()- (5). Thus, the rigiity of the grasping shape is perturbe. However, when the ecoupling control is use, rigiity of the grasping shape can be maintaine regarless of the human comman an the communication elay. Even with the ecoupling, the grasping shape error in Fig. 5 is still not zero. This is because of the assume moel uncertainty. When this moel uncertainty is remove, this error completely isappears an the rigi grasping is ensure. Also, notice the phase-lag between the motions of the an the slave formation. This is ue to the lack of a feeforwar action in the teleoperation control loop an coul be reuce by increasing the PI-gains in (). B. Manipulation of Heavy Object We inclue a circular eformable object uner a similar scenario of section III-A. Mass an inertia of the object are assume to be kg an kgm. To achieve the fixtureless grasping using flexibility of the object, we set L in (9) s.t. three slave robots will be on a circle whose raius is % of that of the object. We moel the contact force between slaves an the object by spring an amper. We also assume frictionless contact, i.e. no torque is exerte on rotations. Consiering inertia of the object, we ecrease the rotating rate s.t. w =.5 [Hz]. We use the grasping control (7) with three ifferent settings: ) PD-control with high PD-gains (nf F/HG); ) PD-control with small PD-gains (nf F/SG); an ) FF-control with small PD-gains (FF/SG). With each setting, simulation is performe for 5sec. In the first sec, the three slaves approach to the object an grasp 7

4 Heavy Object Manipulation: High PD gain Heavy Object Manipulation: Small PD Gain w/o FF.5.5 robot object robot object.5.5 Contact Force Human/Env Force at 5sec: secure grasping.5.5 Contact Force an Force Reflection: High PD Gain 6 robot F x F y F [Nm] φ Fig. 6. Cooperative manipulation of a heavy object: uner the PD-control with high-enough gain (nf F/HG). it cooperatively without a rigi fixture, while the human stabilizes the object on the top of the large circle (i.e. φ o = φ =in Fig. ). Then, the human operates the to make the graspe object revolve on the larger circle with the perioicity of w. Contact an human force profiles, an snapshots on the (x, y)-plane (uring sec with shooting spee /w =.5 [sec]) are shown in Figures 6 an 7 for the cases nf F/HG an nf F/SG, respectively, where the eight circles (raius.5m) in the snapshots represent the object without eformation. Snapshot for the case FF/HG is omitte, since it is almost ientical to that of the case nf F/HG in Fig. 6. However, its contact an human force profiles are shown in Fig. (above). Grasping shape error of each case is also shown in Fig. (below). As Figures 6 an show, by enforcing the rigiity of the grasping shape, the PD-control with high enough PDgains (nf F/HG) can ensure secure grasping of the object without any fixture. This secure grasping is also achieve by the FF-base control (FF/SG) with even a better grasping precision (see Fig. ), although smaller PD-gains are use. Also, uner the FF-base control (FF/SG), the contact forces among the slave robots are better-balance, since w is slow enough w.r.t. the system ynamics s.t. the object s position can be stabilize insie of the rigi grasping shape quickly enough. Uner the PD-base control with insufficient PD-gains (nf F/SG), as Figures 7- show, secure grasping of the at 7.5 sec: object escape.5.5 Contact Force an Human Force: Small PD Gain w/ no FF robot 6 loss of contact Contact Force Human Force F x F φ [Nm] Fig. 7. Cooperative manipulation of a heavy object: uner the PD-control with insufficient PD-gains (nf F/SG). Contact Force an Human Force: with FF Cancellation Contact Force Human Force 6 robot F x F y F [Nm] φ Grasping Shape Distortion. FF/SG nff/hg nff/sg. Shape Distortion[m] Alignment Error[ra] FF/SG nff/hg nff/sg Fig.. Above: contact/human forces with the FF-control an small PD-gains (FF/SG). Below: effects of PD-gains an FFterm on the grasping shape error. 7

5 object coul not be maintaine, an the slaves completely lose the object aroun 7.5 sec. Sensation of this lost grasping, however, can be perceive by the human as shown by abrupt change in the human force in Fig. 7. Also, contact force is built up on some slave robots as their portion of the triangle unergoes larger eformations by the graspe object. In all three cases, the human can perceive the combine inertia of the graspe object an slaves as she/he rives them along the larger circle. Although we assume moel uncertainty s.t. the FF-term in (7) is not correct, no unstable behavior has been observe with the case FF/SG. Moreover, since q E (t) quickly enough, this FF-term coul be activate all the time without violating passivity. C. Force Reflection We use the FF-control with the small PD-gains (FF/SG of section III-B). Once the human stabilizes the slave triangular formation at the top of the larger circle (i.e. φ o (t) =φ (t) =in Fig. ), we impose an external force on the center of the object, which is along the x-axis an increasing uring sec with the rate of.n/sec. Human an contact forces are shown in Fig. 9. As Fig. 9 shows, the human operator is able to perceive the external force acting on the object. This external force is reflecte through the ynamics of the slave robots an the bilateral teleoperation control loop over the elaye communication. As this external force increases uring sec, contact force of the robot ecreases while those for the robots an increase. This is ue to the flexibility of the object: the external force eforms the object so that its center is pushe away from the robot (i.e. pushe towar the robot an ), while the grasping shape is still rigily maintaine. It is worthwhile to point out that a human operator can perceive external forces acting on iniviual slave robots, too. IV. SEMI-EXPERIMENT In this semi-experiment, we use a commercial haptic evice (PHANToM R Desktop TM, Sensable Technologies Inc.) as a robot, which has -DOF motions with force feeback capability. Similar to section III, we also simulate three slave robots an one isc-shape object in the virtual slave environment. We assume that these slaves an object have -DOF point mass translational ynamics in the (x, y)-plane (i.e. no rotation) with mass of kg. We also implement an obstacle in the slave environment, which is fixe on the (x, y)-plane an prouces reaction force only along the x-irection. Interactions among the slaves, object, an obstacle are moele by spring an amper. We use GHOST R SDK software to generate this slave environment an show it to the human operator. We also constrain the haptic evice s -DOF workspace in its horizontal plane s.t. its constraine workspace matches with the slave environment (i.e. (x, y)-plane). We also impose.5sec time-elay between the an slave environments utilizing ata buffering. Data upate rate is set to be khz. We consier the following grasping shape function: ( ) q q q E := q q R, () where q i =(x i,y i ) R is the position of the i-th slave. Note that this function q E completely specifies the shape Fig. 9. Human/Env Force Contact Force 5 Force Reflection an Contact Force F x F φ [Nm] Environmetnal Force on the object (in x irection) 6 robot Human/contact forces with external force on the object. (an the size) of the triangular formation among the three slaves (see Fig. with no yaw angle). If q E = c, overall motion of the three slaves (total DOF= 6) will be reuce to the -DOF translation of the slave triangle formation. We set the esire value qe in () s.t. the three slaves form an equilateral triangle heaing to the negative x-axis (i.e. φ =in Fig. ) an also squeeze the object for the fixtureless cooperative grasping. We use the FF-base grasping control (7). No unstable behavior has been observe with this FF-control. We think that this is because our measurements an parameters are accurate enough. Note also from [] that moel uncertainty of the haptic evice oes not affect passivity at all. A. Manipulation of Deformable Object Once the fixtureless cooperative grasping of the object is stabilize, the human operator starts riving the haptic evice along the x-irection between two en-points of its workspace with a fast spee. Results are shown in Fig.. Since the x-irectional motion is ominant, we omit ata relate to the y-irectional motion. As the Figure shows, grasping rigiity (i.e. q E (t) ) an tightness (i.e. almost constant contact force) can be ensure regarless of the human comman an the communication elay. The human operator can also perceive combine inertias of the slaves, the, an the graspe object as s/he rives them. Although contact forces are overall well-balance among the slaves, when the object is accelerate (or ecelerate), those on some slave robots increase while those of others ecrease (e.g. at sec, forces on the slaves an increase while that of the slave ecreases). This is because the object is eforme by the inertial force while the graspe shape is preserve rigily, i.e. the contact force on a slave woul increase (or ecrease, resp.) if the graspe object is eforme towar it (or away from it, resp.). Such contact force imbalance woul be eliminate if the graspe object is rigi or the object oes not experience any inertial force (i.e. no acceleration or light inertia). B. Perception of External Obstacles In this semi-experiment, by operating the haptic evice, the human pushes the graspe object against the obstacle fixe on the (x, y)-plane. Results are shown in Fig.. The human coul feel the obstacle as shown by the static force reflection uring 7sec. This force reflection is essentially generate by position error between the graspe 7

6 Position [m] q E [m] Force CF Position in "x" ireccion Manip Obj 5 6 Formation error magnitue q E 5 6 Force 5 6 Contact Force Magnitue 5 6 F x Fig.. Semi-experiment (coorination): an graspe object positions, grasping shape error, an human/contact forces. q E [m] Position [m]... Position in "x" ireccion Manip Obj. 5 6 Formation error magnitue q E Force CF Force 5 Contact Force Magnitue 5 F x Fig.. Semi-experiment (force reflection): an graspe object positions, grasping shape error, an human/contact forces. object an the haptic evice, an can be mae sharp by increasing the PI-gains in the local impeance control (). During this contact with the obstacle, the contact force of the slave ecreases while those for the slaves an increase. This is ue to the fact that the graspe object is eforme by the obstacle s.t. its center is pushe towar to the slaves an (or away from the slave ) while the grasping shape is rigily preserve with the FF-term in (7). V. CONCLUSION In this paper, we perform simulation an semiexperiment (real an simulate slaves) to illustrate an valiate properties of the multirobot semi-autonomous teleoperation control framework propose in []. In particular, the following key properties are highlighte:. Multiple slave robots can cooperatively grasp an manipulate an object having inertia an flexibility without any rigi fixture;. By manipulating the with reasonably small-dof, a human can tele-control the overall group behavior of the multiple slave robots an the graspe object, while perceiving the combine external forces acting on them;. By ensuring security an tightness of the grasping regarless of the communication elay an human comman, the propose control scheme enables us to avoi any anger entaile by ropping of an object. Moreover, by enforcing energetic passivity, the propose scheme also enhances interaction safety an stability of the close-loop system. We believe that these properties woul make the propose scheme a promising caniate in such a application as remote repair of Hubble telescope where multiple robots are teleoperate from the earth to perform repair/replacement cooperatively. REFERENCES [] D. J. Lee an M. W. Spong. Bilateral teleoperation of multiple cooperative robots over elaye communication networks: theory. In Proceeings of IEEE International Conf. on Robotics an Automation, 5. [] Dongjun Lee. Passive Decomposition an Control of Interactive Mechanical Systems uner Coorination Requirements. Doctoral Dissertation, University of Minnesota,. Also available at -lee/dissertation.pf. [] D. J. Lee an P. Y. Li. Passive ecomposition for multiple mechanical systems uner coorination requirements. In Proceeings of the IEEE Conference on Decision an Control, pages 5,. [] R. J. Anerson an M. W. Spong. Bilateral control of tele-operators with time elay. IEEE Transactions on Automatic Control, (5):9 5, 99. [5] G. Niemeyer an J. J. E. Slotine. Stable aaptive teleoperation. IEEE Journal of Oceanic Engineering, 6():5 6, 99. [6] S. Stramigioli, A. van er Schaft, B. Maschke, an C. Melchiorri. Geometric scattering in robotic telemanipulation. IEEE Transactions on Robotics an Automation, ():5 596,. [7] D. J. Lee an P. Y. Li. Passive bilateral feeforwar control of linear ynamically similar teleoperate manipulators. IEEE Transactions on Robotics an Automation, 9(): 56,. [] B. Hannafor an J. Ryu. Time omain passivity control of haptic interfaces. IEEE Transactions on Robotics an Automation, ():,. 7