Manipulation and Active Sensing by Pushing Using Tactile Feedback

Transcription

1 Manipulation and Ative Sensing by Pushing Using Tatile Feedbak Kevin M. Lynh The Robotis Institute Carnegie Mellon University Pittsburgh, PA 1513 USA Hitoshi Maekawa Kazuo Tanie Cybernetis Division Biorobotis Division Mehanial Engineering Laboratory, AIST-MITI Namiki 1-, Tsukuba-shi, Ibaraki-ken, 35 Japan Abstrat We investigate manipulation and ative sensing by a pushing ontrol system using only tatile feedbak. The equations of motion of a pushed objet are derived using a model of the objet s limit surfae, and we design a ontrol system to translate and orient objets. The effetiveness of the proposed ontroller is onfirmed through simulation and experiments. Ative sensing of the objet s enter of mass is desribed. I. INTRODUCTION Pushing is a useful roboti apability for positioning and orienting parts. Several researhers have demonstrated the utility of pushing operations by planning open-loop pushing sequenes to position and orient polygonal objets despite the presene of unertainty in the initial state [1,, 3, 4, 5, 6, 7]. These operations typially plan for a known objet shape and enter of mass (CM) and a flat pushing fene or speially designed pusher geometry to exploit the mehanis of pushing. Others have proposed pushing ontrol systems based on visual feedbak [8, 9]. The pusher makes point ontat with the objet, and the position and orientation of the objet is determined by a vision system. The goal is to push the objet along a desired trajetory. Unertainty in the fritional fores governing the objet s motion is ompensated for by the appropriate design of a feedbak ontroller. The purpose of this work is to investigate the possibility of useful manipulation by a pushing ontrol system using only tatile feedbak. Try losing your eyes and ontrolling the motion of an objet on a table by pushing it with a finger. This is the type of apability we would like to give a robot. In ontrast to vision, tatile sensing requires very little data proessing. The tatile sensor is mounted diretly on the manipulator and the robot requires no peripheral sensors. The primary diffiulty arises from the fat that tatile sensing an only give loalontatinformation. The onfigurationof the objethas three degrees-of-freedom: two position oordinates and an orientation. When the pusher is in ontat with the objet, these three degrees-offreedom may be equivalently expressed by the loation of the pushing ontat, the ontat point on the perimeter of the objet, and the orientation of the objet. The tatile sensor we use is apable of sensing the ontat loation and the objet orientation at the ontat, but not the ontat point on the objet. With vision, all three degreesof-freedom are diretly sensed. Despite this missing information, we demonstrate that simple manipulation is possible by pushing using only tatile feedbak. Speifially, we implement a ontroller to translate the objet and regulate its orientation. Kevin Lynh was supported as a partiipant in the 1991 Summer Institute in Japan program sponsored by the U.S. National Siene Foundation, the Siene and Tehnology Ageny of Japan, and the Japan Foundation s Center for Global Partnership. The rest of the paper is organized as follows. The remainder of this setion desribes the problem formulation and the notation used in the paper. Setion II reviews the mehanis of pushing and develops a model of the motion of a pushed objet. Setion III defines ative sensing as it applies to the pushing ontrol system. In Setion IV we desribe the ontrol algorithm implemented. Setion V desribes the experimental setup and presents simulation and experimental results. We offer some onlusions in Setion VI. A. Problem Formulation The pusher is a disk. A tatile sensor detets the ontat point on the disk, and the ontat normal is in the diretion of the vetor from the enter of the disk to the ontat. The ontat orientation angle is defined by the tangent to the disk at the ontat. The objet to be manipulated is a onvex polygon. During exeution, the pusher remains in ontat with one edge of the objet. In Setion V we give an example of manipulation of non-polygonal objets. We assume that pusher motions are slow enough that inertial fores are negligible ompared to fritional fores. This is the quasistati assumption. We also assume that fritional fores onform to Coulomb s Law. At any ontat, the tangential fritional fore f t felt by an objet must satisfy the relationship f t f n,where is the oeffiient of frition and f n is the normal fore applied to the objet. The stati and kineti oeffiients of frition are assumed to be equal. Defining the frition angle = tan,1, the total ontat fore must lie on or inside the one of vetors whih interset the ontat and make an angle with the ontat normal. If the ontat is sliding, the fore felt by the objet lies on the boundary of the frition one maximally opposing the motion of the objet relative to the ontating surfae. B. Notation Thefollowing notation will be usedthroughoutthe paper(see fig.1): ^n ontat normal unit vetor (into the objet) angle of the pushed edge (9 degrees lokwise of the angle of ^n) angle of motion of the pusher d ontat loation along the pushed edge of the objet (d = at the point on the edge losest to the CM, and d is positive to the right of the ray from this point to the CM) l distane from the pushed edge to the CM r radius of the disk pusher frition oeffiient between the pusher and objet s frition oeffiient between the objet and support Bold letters are vetors, and unit vetors are apped with a irumflex, as in ^n. We will denote linear veloities (v x;v y) as v, generalized veloities (v x;v y;!) as q, linear fores (f x;f y) as f, and generalized fores (f x;f y;m) as p. All -vetors should be regarded as vetors in 3-spae with zero third omponents. Angular

2 r n^ α φ d < l CM Fig. 1. Pushing system notation. veloities and moments may be written in boldfae as vetors with the first two omponents zero. II. MECHANICS OF PUSHING In this setion we review the mehanis of pushing and develop a model of the motion of a pushed objet. This model may be used in the design of a pushing ontroller. A. The Voting Theorem Mason [6] analyzed the mehanis of quasi-stati pushing operations given a known pusher objet ontatpoint, ontatnormal, pushing diretion,, and CM of the objet. The analysis results in a simple method for determining the sense of rotation of a pushed objet, whih we will refer to as the voting theorem: Construt three rays at the ontat point: the two frition one limits and the ray of the pusher motion. Eah ray that passesto the left of the CM votesfor lokwiserotation, and eah ray that passes to the right votes for ounterlokwise rotation. The votes are tallied and the majority determines the rotation sense. If two or three rays pass through the CM, or one ray passes through the CM and the other two vote oppositely, the objet will translate along the ray from the ontat to the CM. 1 Atually, this result uses the enter of frition (CF), not the CM. The CF is loated at the entroid of the support frition distribution multiplied by the pressure distribution. For the ase of a uniform s, however, the CF is simply the projetion of the CM to the support plane. In this paper we assume a uniform s. If this assumption is violated, CF should be substituted where CM appears. The power of the voting theorem omes from its insensitivity to the form of the pressure distribution. The pressure distribution between an objet and support is usually unknown and possibly hanging due to mirosopi variations in the support surfae. Although the exat motion of a pushed objet depends on the form of the pressure distribution, Mason showed that the rotation sense depends only on the loation of the CM. We an apply the voting theorem to determine the set of pushing ontats from whih an objet an be translated. The possible translational pushing ontats are obtained by drawing the frition one at the CM and extending the one until it intersets the pushed edge. For a ray of pushing through the CM, translation ours in the diretion of the push for ontats inside the projeted frition one, i.e.,, l d l. Contats to the left of the frition one result in 1 If the objet s support is onfined to a line segment perpendiular to the pushing diretion, the objet may rotate [6, 1]. θ lokwise rotation regardless of the push diretion. Similarly, ontats to the right of the frition one result in ounterlokwise rotation. B. Limit Surfaes Whereas the CM is suffiient for determining the rotation sense of a pushed objet, the pressure distribution of the objet must be onsidered to find the exat motion. The quasi-stati relationship between the instantaneous veloity of a sliding objet and the support fritional fore is governed by a losed, onvex, origin-enlosing limit surfae in (f x;f y;m) spae [1]. For a given referene point, the limit surfae is the boundary of the sum (respetively integral) of the fritional fores and moments that eah of the objet s individual support points (resp. differential elements of support area) an apply to the support plane. The limit surfae in (f x;f y;m) spae enloses the set of generalized fores p whih may be statially applied to the slider. The limit surfae of a sliding objet is analogous to the frition one for a single ontat. Any applied fore p inside the limit surfae is ompletely resisted by the support frition, and the objet will not move. If p extends outside the limit surfae, stati equilibrium is violated and the objet will aelerate. During quasi-stati motion of the objet, p lies on the limit surfae and the diretion of the objet s veloity is given by the unit vetor ^q normal to the surfae at p in (v x;v y;!) spae, whih is aligned with the (f x;f y;m) spae. (See [1] for further details.) The shape of the limit surfae is determined by the pressure distribution, and s simply sales the limit surfae. Thus, if the pressure distribution is known, the relationship between applied fores and objet motions is ompletely desribed by the limit surfae. In general, the pressure distribution is unknown and possibly hangingas the objetmoves. For this reason, we will developa model using an approximation to the atual limit surfae. The limit surfae will be modeled as an ellipsoid in fore-moment spae [11, 1, 13]. The proedure to find the ellipsoid is similar to that in [13]: 1. Choose the CM as the referene point about whih moments are measured. Find the maximum fritional moment m max, resulting from a pure rotation aboutthe referene point: m max = s Z jxjp(x)da (1) A where A is the support region, da is a differential element of area of A, x is the position of da,andp(x) is the pressure at x. This defines two ellipsoid endpoints: (; ; m max).. Find the maximum fritional fore (pure translation): fx f max = sf n () where f n is the normal support fore. 3. The approximating ellipsoid is given by the equation: f max + fy f max + m = 1 (3) m max The alulation of m max requires a known pressure distribution p(x). To aount for the unknown pressure distribution, the pushing ontroller should be designed to be robust for limit surfaes with a range of values of m max. If the objet s support pressure is onentrated near the boundaries of the objet, m max is large and the resulting limit surfae is elongatedalongthe m-axis. The motion We assume the CM is oinident with the enter of twist [1]. A pure rotation about the enter of twist orresponds to a pure moment.

3 m.1.5 p ^q f y 1.. irle of radius f max f x Fig.. Ellipsoidal limit surfae. p is the generalized applied fore and ^q is the assoiated generalized veloity unit vetor. of the pushed objet tends to be largely translational. If the objet s support pressure is onentrated near the CM, m max is small and the limit surfae is relatively flat. The objet s motion tends to be mostly rotational. An example ellipsoidal limit surfae is shown in fig.. The m = ross-setion of the ellipsoid is a irle of radius f max. In order to translate the objet, a fore f max must be applied through the CM in the diretion of the desired translation. In addition, positive moment orresponds to ounterlokwise rotation, and negative moment orresponds to lokwise rotation. These properties of the ellipsoid are onsistent with the voting theorem. For the ellipsoid model, the translational veloity v of the CM is always parallel to the applied linear fore f. If a pure moment is applied, the objet will rotate about the CM. The ellipsoid approximation to the limit surfae satisfies the voting theorem and gives a nonlinear losed-form relationship between fores and veloities. The auray of the approximation depends on the partiular pressure distribution; see Setion V for an example. C. Equations of Motion Defining the parameter = m max=f max (with units of length), the relative values of the omponents of q (defined at the CM) for an applied fore p are derived from the ellipsoid equation: v x! v y! = f x m = f y m The magnitude of the applied fore jpj is given by (3) and jqj is determined by the veloity of the pusher. The objet s veloity must be just suffiient to move out of the way of the advaning pusher. Equations (4) and (5) relate applied fores to objet veloities. It remains to find the objet s motion in response to a position-ontrolled push. The method for doing this is taken from [6]: 1. The origin is loated at the CM and the pushing ontat is loated at x =(x;y ). The pusher veloity at the ontat is denoted v p =(vpx;v py), and the resulting veloity of the objet at the ontat is written v o =(vox;v oy).. Find the unit generalized veloities ^q l =(vlx;v ly;! l) and ^qr = (v rx;v ry;! r) resulting from fores at the left and right edge of the frition one, respetively. The orresponding veloities at the ontat point x are v l = (vlx,! ly ;v ly +!lx ) and v r =(vrx,! ry ;v ry +!rx ). These two veloity vetors form the boundary of the motion one [6]. Any fore applied at x inside the frition one results in a veloity v o whih is a positive linear ombination of v l and v r (i.e., inside the motion one). (4) (5) Fig. 3. Motion ones for a square objet using the ellipsoidal limit surfae approximation and m max alulated using a uniform pressure distribution. Contats are sampled along the bottom edge with different values of.for =, the motion one redues to a ray, and for = 1, the interior angle of the motion one is 18 degrees. The motion ones in this figure imply two nonintuitive effets: 1) Infinite frition does not neessarily imply stiking ontat during pushing. The ray of pushing may lie outside the 18 degree motion one. ) Vetors in the motion one with a negative omponent in the diretion of the ontat normal imply that it is possible to pull the objet by applying a fore inside the frition one. 3. If the pusher veloity v p is ontained within the motion one, stiking ontat ours (v o = v p). If v p is to the left of the motion one, the pusher slides to the left with respet to the objet, resulting in an applied fore at the left edge of the frition one. The objet veloity at the ontat therefore lies on the left edge of the motion one. If v p is to the right of the motion one, the pusher slides to the right with respet to the objet, and v o lies on the right edge of the motion one. See fig. 3. This proedure is applied using the ellipsoidal limit surfae model. 1) Objet Motion During Stiking Contat: When v p is inside the motion one, two onstraints on the objet s veloity q =(v x;v y;!) are given by v o = v p. Sine the line of applied fore f must pass through the ontat, this defines a onstraint on the applied moment, m = x f. These three onstraints may be written v x = vpx +!y (6) v y = vpy,!x (7) m = x f y, y f x (8) Remembering that f is parallel to v, we solve for q using (4) and (5): v x = ( + x )v px + xy v py + x + y v y = x y v px +( + y )v py + x + y (9) (1) xvy, yvx! = (11) ) Objet Motion During Slipping Contat: When v p is outside the motion one, the ontat is slipping and v o lies on one of the motion one boundaries. The slipping veloity v slip is along the ontat tangent, and v o and v slip must satisfy v o + v slip = v p (1) as in fig. 4. In order to treat both slipping diretions simultaneously, we denote the boundary of the motion one under onsideration v b and the orresponding generalized veloity ^q b. For ontat normal ^n we define the saling fator =(v p ^n)=(v b ^n). The motion of the

4 v l v o = n^ κ v r v r v slip v p Fig. 4. v o and v slip for v p to the right of the motion one. objet during slipping ontat is given by the following equations: v o = vb (13) v slip = vp, v o (14) q = ^q b (15) 3) Contat Veloity: The veloity of the ontat along the pushed edge has two omponents: slipping and rolling. The ontat veloity d_ is given by _ d = v slip ^t,!r (16) where ^t is the unit tangent vetor in the diretion of inreasing d. III. ACTIVE SENSING In addition to manipulation, a pushing ontrol system may be used for ative sensing. Sensory modalities whih projet a signal (e.g., light striping, radar, laser range finding) or use strategies to guide the aquisition of data (e.g., tatile probing, ative vision) are ommonly labeled ative sensing. In this paper, however, ative sensing refers to the proess of exploiting task mehanis by performing an ation or set of ations in order to hange the system state to a known smaller set of possible resulting states. The voting theorem onstrains the CM of the objet to lie on the ray of pushing during a finite length translation.with this knowledge of the task mehanis, we onlude that if our pushing ontrol system an ahieve stable translation by pushing, the CM of the objet must lie on the ray of pushing. This onstraint on the loation of the CM may be used in the following ways. 1) With the aid of a vision system, the loation of the CM of an unknown objet an be determined by establishing stable translational pushing at two or more ontat points. The CM lies at the intersetion of the rays of pushing. ) If the shape and CM of the objetare known, and the unertainty in initial position and orientation is bounded so that the pushed edge is known, the pushing ontroller an remove unertainty in the objet loation. The problem is that d annot be diretly sensed. If the objet is translating, however, d is onstant and is uniquely determined by the angle of pushing with respet to the edge: d =( l= tan(, ) if, <= l= tan( +, ) if, = (17) where l is given by the objet model. The sensed value of and the estimated value of d ompletely determine the position and orientation of the objet with respet to the pusher. IV. CONTROL ALGORITHM The onfiguration of the objet is ontrollable (i.e., the objet an be pushed to any position and orientation) by pushing an edge if at least two nonollinear ^q vetors, at least one of whih has a nonzero! omponent,an be obtained by pushing the edge. Suffiient onditions for the ontrollability of the objet onfiguration are 1) the edge has nonzero length or a nonzero oeffiient of frition (and is not a point at the CM), and ) the support pressure is bounded everywhere, i.e., the limit surfae is not flat at any point. In determining the form of a pushing ontrol law, we must onsider the nonholonomi onstraints on the motion of the objet arising from the point ontat with the pusher. The possible objet veloities are onstrained by funtions of and d. One onsequene of this fat is that it is impossible to design a ontroller to push the objet to a desired onfiguration using a smooth feedbak funtion of the system state. (See, for example, [14].) A method for determining bounds on the possible pushed objet trajetories, independentof the ontrol law, is presented in [15]. In this work, we fous on designing a ontrol system to ahieve stable translation of the pushed objet, whih allows ative sensing of the CM as desribed in Setion III. The disrete version of the ontrol law an be written (k) =(k, 1) +k p[(k), d] +kd[(k), (k, 1)] (18) where (k) is the ommanded push angle, (k) is the sensed ontat orientation, d is the desired ontat orientation, and k p and k d are the proportional and derivative gains, respetively. The goal of this simple linear ontroller is to stabilize the ontat orientation to a onstant d, whih results in objet translation (provided translation is possible). This ontrol sheme does not permit speifiation of a desired translation diretion. In general the translation diretion is not independent of the ontat orientation. For the ase =, for example, the only possible translation diretion is in the diretion of the ontat normal. V. SIMULATION AND EXPERIMENT A. Experimental Setup For our experiments we used a miniaturized version of the optial waveguide tatile sensor desribed in [16] mounted on one finger of the three-fingered hand developed at MEL [17]. The finger is mounted horizontally above the support plane, and the first of the three finger joints is fixed. The final two joints are used for planar finger tip motions. The finger is shown in a typial onfiguration in fig. 5. The finger tip is hemispherial and the tatile sensor returns two angles, the azimuth and the elevation of the ontat point. The projetion of the hemisphere to the support plane is semiirular, allowing us to treat the finger as a disk, as only the hemispherial portion of the finger tip will ontat the objet. The elevation of the ontat point and the finger joint angles are used to determine the ontat normal in the plane of motion. Theradius of the tatile sensoris 16 mm, inluding a.5 mm spaing between the rubber overing and the optial waveguide. During ontat, the rubber over diretly ontats the optial waveguide, giving the finger tip an effetive radius of 13.5 mm. The finger is mounted above a onveyor belt whih moves the support at a onstant veloity in the,y diretion. The quasi-stati mehanis of pushing are the same as for the finger moving with a onstant veloity v y in the +y diretion. The finger tip generates the speifiedpush angle ( <<; in pratie, we use 33 o <<147 o )

5 y x stroke onveyor veloity 13.5 mm 6 mm 74 mm = min = max = max = min Fig. 7. Simulated objet trajetories for open-loop pushing. m fixed Fig. 5. Experimental setup. Contat Orientation (degrees) 3 1 Desired Contat Orientation kp =.5, kd = 1 kp =.5, kd = 5 kp =.5, kd = 1 m max atual limit surfae, uniform pressure distribution ellipsoid model timesteps f max Fig. 6. Uniform pressure limit surfae and the ellipsoid model in the f x = plane. The figure is symmetri about the f y and m axes, and v x = for fores in the f x = plane. by moving with veloity v x = vy= tan. 3 As a result of using the onveyor belt, the length of onstant time pushes varies with and is equal to v yt= sin, wheret is the duration of the push. Due to the quasi-stati nature of the system, it is the length of eah push, not the sampling rate, whih determines whether or not the system an be ontrolled. In our experiments, the onstant onveyor speed is 5 mm/s and the sampling rate is 1 Hz. This results in a push length of between.5 mm and.9 mm, depending on. The objet to be manipulated is a 5 m x 4.75 m retangular steel blok with a CM at the enter. The 5 m edge is pushed and l = :375 m. The oeffiient of frition between the finger and the blok is very high; for simulation purposes, we assume = 1. B. Simulation In order to better understand the pushing model developed in Setion II, we wrote a simulation of the derived equations of motion. The simulation may be used to determine appropriate ontrol gains. The retangular objet is modeled using three different values for : max = 3:45 m, uni = 1:87 m, and min = :67 m. max is found by assuming that the support is onentrated at the orners and uni is found by assuming a uniform support distribution. (Fig. 6 shows the f x = plane of the atual and modeled limit surfaes for a uniform pressure distribution.) In priniple, min ould be zero if there is only a single point of support at the CM. In this ase, the limit 3 We simply ontrol the x veloity of the pole of the finger tip. This results in added linear veloity omponents at other points on the finger tip due to rotation of the finger tip. These veloities are relatively small, and ontat is usually near the pole of the finger tip, so we ignore them. f y - -3 Fig. 8. Simulated step response for ()= o, d()=,:6 m. surfae is onfined to the m = plane and there is no quasi-stati solution to the motion of the objet. Instead, we hose min for the ase of uniformly distributed support in a irle of radius 1 m about the CM. Fig. 7 shows the simulated trajetories of the retangular objet for = 9 o, initial orientation () = o, initial ontat d() =,:5m and four ombinations of and. Fifty pushes are simulated between eah snapshot. Simulations indiate that the ontrol law (18), with a proper hoie of ontrol gains (in partiular, k p, k d ), is effetive for a wide range of objets,, and initial onditions. The ontat slips and rolls to a point from whih the objet an be translated. Fig. 8 shows the system response for three different ombinations of k p and k d (for and measured in radians) for the retangular objet with = uni, () = o, d() =,:6m,() =9 o,and d =,1 o. C. Experimental Results We experimented with several different ombinations of k p and k d (for and measured in radians) and empirially determined that k p = :5, kd = 5: gave the best performane. Fig. 9 shows an example time history of the system for these gain settings and d =,1 o. The thin line represents and the thik line represents,9 o. After 173 timesteps (17.3 s or 8.65 m pushing in +y), stays within three degrees of d. After 4 timesteps,,1:4 o,8:9 o and 8: o 85:8 o. The objet is essentially translating. During this period the minimum value of, is 9:6 o and the maximum value is 95: o. Plugging these values and l into (17), we determine bounds

6 degrees 3 1 Contat Orientation Desired Contat Orientation Push Angle - 9 degrees VI. CONCLUSIONS This work demonstrates through simulation and experimentation the feasibility of manipulation and ative sensing by pushing using only tatile feedbak. To inrease the utility of a pushing ontroller, other ontrol algorithms, inluding nonsmooth feedbak laws, should be studied timesteps ACKNOWLEDGMENTS We thank the U.S. NSF and the STA of Japan for making this ollaboration possible, and the members of the Cybernetis and Biorobotis Divisions at MEL and the Manipulation Lab at CMU for support and helpful omments Fig. 9. Experimental results for the retangular objet. Contat Orientation (degrees) timesteps Fig. 1. Experimental results for the disk, d = o. on d during this time: :3 m d.1 m. By ative sensing the possible values of d have been redued from,:5m d.5 m. We tried the same ontrol law for a non-polygonal objet: a steel disk of radius.85 m with a CM at the enter. The results for d = o are shown in fig. 1. After 11 timesteps, the ontat orientation is maintained within one degree of d. D. Disussion The ontroller works enouragingly well in these examples. Our implementation of the pushing ontroller is limited, however, by a relatively small finger workspae, oasional sensor error, and limits on detetable ontat orientations due to the sensor design. These fators restrit the range of stabilizable initial system states. The simulation suggests that larger values of k p and k d give better system response, but large experimental gains resulted in instability. The primary reason for this is that the simulation assumes perfet pusher position ontrol. A more preise system model would inlude a model of the response of the robot finger. REFERENCES [1] S. Akella and M. T. Mason, Posing polygonal objets in the plane by pushing, in IEEE InternationalConfereneon RobotisandAutomation, pp. 55 6, 199. [] Z. Balorda, Reduing unertainty of objets by robot pushing, in IEEE International Conferene on Robotis and Automation, pp , 199. [3] R. C. Brost, Automati grasp planning in the presene of unertainty, International Journal of Robotis Researh, vol. 7, pp. 3 17, Feb [4] R.C.Brost,Analysis and Planning of Planar Manipulation Tasks. PhD thesis, Carnegie Mellon University, Shool of Computer Siene, Jan [5] K. Y. Goldberg, Stohasti Plans for Roboti Manipulation. PhD thesis, Carnegie Mellon University, Shool of Computer Siene, Aug [6] M. T. Mason, Mehanis and planning of manipulator pushing operations, International Journal of Robotis Researh, vol. 5, pp , Fall [7] M. A. Peshkin and A. C. Sanderson, Planning roboti manipulation strategies for workpiees that slide, IEEE Journal of Robotis and Automation, vol. 4, pp , Ot [8] F. Gandolfo, M. Tistarelli, and G. Sandini, Visual monitoring of robot ations, in IEEE/RSJ International Conferene on Intelligent Robots and Systems, pp , [9] M. Inaba and H. Inoue, Vision-based robot programming, in International Symposium on Robotis Researh, [1] S. Goyal, A. Ruina, andj. Papadopoulos, Planar sliding with dryfrition. Part 1. Limit surfae and moment funtion, Wear, vol. 143, pp , [11] R. D. Howe, I. Kao, and M. R. Cutkosky, The sliding of robot fingers under ombinedtorsion and shear loading, in IEEE International Conferene on Robotis and Automation, pp , [1] I. Kao and M. R. Cutkosky, Quasistati manipulation with ompliane and sliding, Center for Design Researh Tehnial Report , Stanford University, International Journal of Robotis Researh, in press. [13] S. H. Lee and M. R. Cutkosky, Fixture planning with frition. ASME Journal of Engineering for Industry, in press. [14] A. M. Bloh and N. H. MClamroh, Control of mehanial systems with lassial nonholonomionstraints, in IEEE International Conferene on Deision and Control, pp. 1 5, [15] K. M. Lynh, The mehanis of fine manipulation by pushing, in IEEE International Conferene on Robotis and Automation, pp , 199. [16] N. Nakao, M. Kaneko, N. Suzuki, and K. Tanie, A finger shaped tatile sensor using an optial waveguide, in Confereneof the IEEE Industrial Eletronis Soiety, pp. 3 35, 199.

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