Vision Assisted Con trol for Manipulation Using Virtual Fixtures Experimen ts at Macro and Micro Scales A
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Vision Assisted Con trol for Manipulation Using Virtual Fixtures Experimen ts at Macro and Micro Scales A

BettiniS LangA Ok am uraand GHager EngineeringResearc Cen ter forComputer In tegrated SurgicalSystems and ec hnology Departmen tofComputer Science The Johns Hopkins Univ ersit Abstract We pr esent the design and implementation of a vision ase system

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Vision Assisted Con trol for Manipulation Using Virtual Fixtures Experimen ts at Macro and Micro Scales A

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Presentation on theme: "Vision Assisted Con trol for Manipulation Using Virtual Fixtures Experimen ts at Macro and Micro Scales A"‚ÄĒ Presentation transcript:

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Vision Assisted Con trol for Manipulation Using Virtual Fixtures: Experimen ts at Macro and Micro Scales A. Bettini,S. Lang,A. Ok am uraand G.Hager EngineeringResearc Cen ter forComputer In tegrated SurgicalSystems and ec hnology Departmen tofComputer Science The Johns Hopkins Univ ersit Abstract We pr esent the design and implementation of a vision- ase system for micr on-sc ale, op er ative manipula- tion of a sur gic al to ol. The system is b ase donac ontr ol algorithm that implements br ad class of guidanc mo des al le virtual xtur es. virtual xtur e, like al xtur e,

limits the motion of a to ol to a pr escrib class or ange. The implemente system uses vision as sensor for pr oviding efer enc tr aje ctory, and the c ontr ol algorithm then pr ovides haptic fe db ack in- volving dir ct, shar manipulation of sur gic al to ol. We have teste this system on the JHU Ste ady Hand ob ot and pr ovide exp erimental r esults for p ath fol low- ing and ositioning on structur es at b oth macr osc opic and micr osc opic sc ales. In troduction Our recen ork in rob otically assisted micro- surgery has led us to consider metho ds that w ould al- lo wh umans and mac hines to

ol lab or ate on a complex, ph ysical manipulation task. e refer to suc h systems as Human-Mac hine Collab orativ Systems (HMCS). Broadly sp eaking, the goal of HMCS is to assist u- man op erators in the execution of manipulation tasks at the fringe of uman abilit while main taining ariable degree of op erator con trol. In con trast to tra- ditional teleop eration systems, the fo cus of HMCS is not to \remotize" h uman con trol, but rather to o er arying lev els of op erator assistance or p erformance enhancemen t dep ending on con textual factors. Virtual xtures [6, 7, ha b een recen tly dev

el- op ed as means of pro viding direct, ph ysical assis- tance. This pap er details the dev elopmen t and testing of complian t, vision-based virtual xture that ha emplo ed at b oth macroscopic and microscopic scales. In an immediate predecessor to this pap er [1 ], describ e con trol algorithms that can be used to create \hard" and \soft" virtual xtures for an ad- mittance con trol co op erativ e system, the JHU Steady Hand Rob ot [4 ,5 ,9]. e demonstrated that the use of vision-based virtual xtures signi can tly reduced p osi- tioning error and execution time in a macro-scale task. In this

pap er, extend [1 in o directions. First, e generalize our con trol algorithms to a broader class of ulti-step tasks. Second, pro vide quan titativ exp erimen tal data and system analysis for manipula- tion at scales an order of magnitude b elo w the results previously rep orted. Virtual Fixtures In our previous pap er [1 ], w e describ ed a basic con trol sc heme for aiding a user while follo wing a path or at- tempting to reac poin t. considered t yp es of virtual xtures: hard constrain ts, whic only per- mit a user to mo e along the reference path; and soft constrain ts, whic hallo wthe

user to deviate from the path. As sho wn b elo w, b oth classes of xtures can b e realized as a parametric v ariation on a single class of con trollers. e further note that mo ving to a sp eci c poin can be cast as mo ving along a path de ned the curren t p osition of to ol and the desired goal lo ca- tion. Th us, b y designing a general efer enc e dir ction xtur ,w e are able to accomplish all of our ob jectiv es. In this w ork, w etak e further adv an tage of the gener- alit of reference direction xtures extending our approac h to tasks with b oth path follo wing and p osi- tioning comp onen

ts. 2.1 Basic De nitions When the goal is to follo w a path, w e consider a refer- ence curv e describ ed b y a parametric expression: :[0 1] !< (1) In what follo ws, e assume that (1). The v ec- tor tangen t to the curv e in the direction of increasing parameter v alues is: )= ds (2) Giv en a p oin not on ,w e de ne the closest p oin on the curv eas ^ ) where (^ )) min [0 1] (3) 3354
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In the cases where ^ is not uniquely de ned, a further con tin uit y condition on (^ )guaran tees a correct map- ping from Cartesian space to parameter space during the motion. A preferred efer

enc edir ction, can b e de ned for eac h p oin 2< as )= (^ )) (^ )) (4) When the goal is to mo e to a sp eci c target p oin t, 2< ,w e assume that the desired path is a straigh line from the curren t p osition to It immediately follo ws that )= other w ise: (5) In practice, the singularit y at the target p oin t requires sp ecial handling. In the exp erimen tal section w eev al- uate four di eren t solutions to this problem. 2.2 Con trol La Let us no w consider as the op erational p oin of a rob ot that is directed b y a user. Direction is supplied the sensed forces applied to to ol handle.

Let represen these commanded forces in the rob ot base frame of reference. Lik ewise, con- sider and ) to b e expressed in the rob ot base frame. or rob ot position reference direction and measured ,w e mo del our problem as that of cre- ating virtual ontact bet een the to ol tip and the surrounding en vironmen t, whic h has anisotropic sti - ness prop erties according to the reference direction. In order to de ne this sti ness, e decomp ose the com- manded forces in to t o orthogonal comp onen ts, (6) The sti ness is then giv en co e∆cien ts: lo sti ness ( is de ned along while a high sti

ness ) is de ned in all directions orthogonal to it. With this decomp osition, can write elo cit la w for end-e ector motion as (7) where and are elo cit comp onen ts along the directions and resp ectiv ely Note that it is the atio of to that de nes the anisotrop of the con trol la w. Th us, y de ning the matrix ∆∆ e can deriv eav elo cit y command la was )) (8) is the 3 3iden tit y matrix, =1 =k is the orthog- onal compliance v alue, eha e xed =1, and ha ein tro duced a global scaling co e∆cien No w, e can separately tune the resp onsiv eness of the sys- tem using and set the \hardness" of

the virtual xture b y manipulating as follo ws: = 0 for hard virtual xturing, (0 1) for soft virtual xturing and = 1 for no virtual xturing (free motion). Using Equation 8, force exerted the user on the handle is transformed in to atool tip elo cit y ac- cording to its magnitude and direction, as if the force ere acting on the unconstrained to ol tip in con tact with the virtual en vironmen t. The anisotropic har- acteristics of the en vironmen are hanged according to simple rule: increasing (or reducing) in [0 1] increases (or reduces) the abilit yof the to ol to mo in directions orthogonal

to the reference direction. The lo op gain used in Equation can be de- comp osed in to t o terms: go erns the erall scaling b et een applied force and rob ot v elo c- it , while imp oses a maxim um norm, max for the elo cit yv ector according to kk (9) max max max (10) or p ositioning problems, the v elo cit y should b ecome zero when the target p oin is acquired. This can be ac hiev ed b yc ho osing max (11) where is a (0), monotonically non-decreasing func- tion suc that (0) 0. similar approac can be used in path follo wing problems as w ell, to reduce the maxim um v elo cit y in regions of

the path. Although the prop osed con troller is e ectiv in helping the user mo e in a sp eci ed direction, the de - nition of (Equation 4) only pro duces motion parallel to the reference curv e. In order to mo e the user bac to the curv e, w e mo dify the de nition of for the path follo wing case as follo ws: )=s ig num )) )+ (12) where is the Cartesian error )= (^ )) (13) is scalar gain (that eigh ts the attractiv e ect), and the ig num function allo ws the hoice of the righ direction for With this hange ust also add the condition that when set This ensures that the rob ot do es \push" the

user when it is a y from the reference tra jectory 2.3 More General ath De nition The structural in ariance of the con troller with resp ect to path follo wing or p ositioning suggests a generaliza- tion of the task de nition. The idea is to consider com bined task that rst in olv es follo wing giv en 3355
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path, and then requires p ositioning at a giv en target poin t. Suc h a reference path can b e formalized as fol- lo ws: A path equation ) (Equation 1). target poin lying along the path ( [0 1]). A spherical neigh b orho o d ) of radius ab out The sphere ) is a con troller

switc hing surface: outside ), the task is path follo wing problem, while inside ), it is a p ositioning problem. Con- sidering the same v alue of for b oth parts, the switc only in olv es a discon tin uit yinthe efer enc e dir ction xtur If the instan taneous rotation applied to the di- rection is to o high, it is p ossible to smo oth it in more than one sample instan t. In this w , tolerating a small error, smo oth motion is guaran teed. further generalization is still p ossible sub- stituting the condition (1) with lo oser one (1). This corresp onds to considering tasks com- p osed of a set

of link ed path follo wing problems. The reference direction virtual xture (Equation 4) is still ell-de ned, with exception of the non-di eren tiable path connection p oin ts. these poin ts, the curv tangen t (Equation 2) can b e ev aluated as the direction that is orthogonal to the minim um distance segmen (orien ted in the reference direction), and lies in the lo- cal osculating plane. This c hoice guaran tees a correct ev aluation of the reference direction ev erywhere in the path. Experimen ts eha e implemen ted the algorithms describ ed ab o e, and p erformed exp erimen ts demonstrating

the sys- tem's p erformance using reference direction virtual x- tures at the macro and micro scales. The same exp ert user p erformed all the exp erimen ts. 3.1 Exp erimen tal System The algorithms describ ed ab o ew ere implemen ted on the JHU Steady Hand Rob ot system (SHR) [5 ]. The rob ot w as equipp ed with a vision sensor and a force- sensing handle on the end e ector. ec hose to exe- cute t o-dimensional tasks (de ning a task plane), so only the rst t o translational join ts of the rob ot base ere used. p erformed exp erimen ts using CCD camera at the macro scale and a grin lens

endoscop e at the micro scale. The vision sensor alw ys view ed the task plane, allo wing reading of the motion refer- ences and real time displa y of task execution (Figure 1). On-screen displa of the task execution is useful for op erators at the macro scale, and essen tial at the micro scale, as it w ould b e imp ossible to complete the task using the nak ed ey e. Figure 1: The exp erimen tal setup of the JHU Steady Hand Rob ot when using virtual xtures to assist in path follo wing and p ositioning tasks: left, macro scale; righ t, micro scale. The cen ter of the image as graphically mark

ed, and users ere instructed to p erform path follo wing and p ositioning tasks relativ e to this mark. The sensor on the handle w as used to record user commands. The force sensor resolution is 12 mN and force v alues are expressed as m ultiples of this base unit. or the ositioning case, the task w as sp eci ed b de ning p osition in absolute rob ot co ordinates. In order to de ne the task for the user, visual cue (a blac mark on sheet of pap er) as created at the appropriate lo cation. or the ath fol lowing case, at macro scale, the path is furnished to b oth the system and the user prin

ting sine curv (35mm ampli- tude, 70mm elength, and 0.54mm width) on the task plane (in blac k on white pap er). t micro scale, it w as not p ossible to prin t a su∆cien tly smo oth curv e, so instead em bedded vy uman hair (ab out 80 m diameter) in glue on ello sheet of pap er. In the macro case, the camera w as p ositioned 200mm from the pap er, yielding a pixel fo otprin t of 0.066mm on the w orking surface. In the micro case, the endo- scop e as ab out 150 m ab o the orking surface, yielding a pixel fo otprin t of ab out 1 m (Figure 2). or the ositioning case, the con trol la w used a p

osi- tioning error measured from the rob ot enco ders while, for the ath fol lowing case, visual trac king (using the XVision system [3 ]) as used to sense (in real time) Figure 2: An endoscop e image of the 80 m -diameter uman hair used as the path in micro scale exp eri- men ts. 3356
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the lo cal p osition and tangen direction of the path. Subpixel in terp olation is used to increase the preci- sion of these measuremen ts. The vision and con trol subsystems executed on di eren PCs, and the data exc hange w as realized o er a lo cal net ork. The con trol system op erated at

100 Hz, using the most re- cen ta ailable data from the vision system and handle force sensor. The vision system recorded the direction and error estimates at eac sample time: the macro scale used 640 480 pixel images at 30Hz, while the micro scale used 320 240 pixel images at 60Hz. The motion w as scaled c ho osing 001 : k 001(1 + 0 003( k 2)) : (14) where is the norm of the Cartesian elo cit in mm/s. With this gain de nition, pushing ligh tly on the handle mo es it slo wly (up to mm=s whereas pushing hard on the handle quic kly increases elo c- it t the macro scale the v elo cit yw as

saturated at 10 mm=s while, at micro scale, at 2 mm=s (users nev er sa w the acceleration e ect). or the ath fol lowing case, the gain of the com- p ensation lo op (Equation 12) w as =0 08 at macro scale, and =0 03 at micro scale. or the osition- ing case, a circle of radius 10 mm is de ned, so that inside that the circle, the maxim um v elo cit y is reduced linearly to 0.1 mm/s, the nal v alue that is obtained at the target p oin t. Also, this case switc hes to a ne p ositioning sc heme when the distance from the target is less than 1 mm. 3.2 Results for the ath ollo wing Case t the macro

scale, the goal w as to follo w a reference path using four di eren compliance alues: (hard virtual xturing), =0 6 (soft virtual x- turing), and = 1 (no virtual xturing, free motion). In order to examine the e ect of di eren alues on user's abilit to generate motions not dictated y the virtual xture, an \a oidance region," a 10 mm radius circle, as added near the cen ter of the path. The circle as not part of the virtual xture, so the user had to deviate from the reference path in order to steer clear of it. The user as told to follo the path as closely as p ossible, and lea eitonlytoa oid the

area inside the circle (this is only p ossible when =0). In addition, the free motion exp erimen tw as executed wice: once while asking the user to follo the path as fast as when virtual xtures w ere presen t, and the other while trying to do the task as precisely as p ossible. Figure rep orts the error and elo cit pro les obtained for the compliance cases describ ed ab o e. able 1 summarizes the results. As exp ected, the case = 0 is the fastest and most precise, although part of the time reduction (ab out is simply due to shorter tra jectory in olv ed (the to ol do es not a oid the circle

but crosses it). The case =0 3 is still quite accurate, while the execution erage error execution obstacle (pixels) time (sec) oidance time (sec) 0.59 16.38 N/A 0.3 0.84 21.16 8.71 0.6 2.08 17.49 4.36 1 (fast) 7.06 19.55 4.58 1 (precise) 2.25 39.29 7.85 able 1: Error (excluding obstacle a oidance), execu- tion time, and obstacle a oidance time for an exp ert user under v arious compliance conditions at the macro scale. erage error (pixel) execution time (sec) 3.20 26.86 0.3 4.97 34.85 0.6 7.64 45.66 8.15 55.75 able 2: Error and execution time for an exp ert user under arious compliance

conditions at the mi- cro scale. time increases signi can tly due to the e ort in olv ed in shifting from the path to a oid the circle. The case =0 6 yielded a larger a erage error, but the lo er sti ness dropp ed the erage execution time and ob- ject oidance time. Finally the p erformance in the case (free motion) dep ended en tirely on the user's in ten tion. What is p erhaps most in teresting is that ev en a small degree of help =0 6) pro duces large reductions in error and time compared with the unassisted cases, while still lea ving the user in com- plete con trol. urthermore, ev en the

error for =0 is less than unassisted precise motion (whic h requires at wice the time). A similar approac h is tak en to demonstrate the sys- tem p erformance at micro scale, using uman hair for the path (Figure 4). The same four compliance conditions w ere used: =0 and 1. In this case, no oidance regions ere considered; the only requiremen tw as to follo w the path as quic kly and ac- curately as p ossible. able 2 summarizes the results, and Figure 5 sho ws the error and v elo cit y pro les. >F rom Figures and 5, it can be seen that uc of the trac king error o ccurs in regions where the rob

ot motors switc direction. The lo scale of op eration (p eak amplitude is ab out 20 m su ers from the ef- fects of the lo w-lev el PID serv o-con trollers that con trol the motors. Simply put, the abstraction of the rob ot as a kinematic device dev oid of dynamics is breaking do wn. Another problem w e exp erienced w as that the rob ot no longer app ears sti at this scale ev en ligh touc on the force handle in tro duces p erturba- tions in to the system. Still, apart from the p eaks due to switc hing, the erage error is 44 pixels, whic 3357
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10 Compliance values: C =1 & C =0

HARD VIRTUAL FIXTURING Error (pixel) 10 Compliance values: C =1 & C =0.3 SOFT VIRTUAL FIXTURING Error (pixel) 10 Compliance values: C =1 & C =0.6 SOFT VIRTUAL FIXTURING Error (pixel) 10 20 30 40 Compliance values: C =1 & C =1 (fast) FREE MOTION Error (pixel) 10 Compliance values: C =1 & C =1 (precise) FREE MOTION Error (pixel) 10 15 20 25 30 35 10 Velocity profiles (norm) mm/sec Time (sec) =1 (precise) =0 Figure 3: Error and v elo cit y pro les for the ath fol- lowing case at the macro scale with di eren t orthogo- nal compliance v alues. The o -scale errors corresp ond to times when the user

is purp osely a oiding a region of the path. corresp onds to less then 2 m This demonstrates ho the virtual xturing sc heme is e ectiv e in follo wing a path, ev en when external disturbances in tro duce unex- p ected errors. In comparison to the macro scale case, the execution time at the micro scale v aries far more signi can tly with orthogonal compliance. This is be- cause the user is only pro vided with narro view of the hair from the endoscop e (Figure 2). When the user attempts to increase the v elo cit , heorshedoes not ha wide enough view to plan future elo ci- ties/p osition tra

jectories and tends then to lea e the curv e. It is p ossible that adding an additional con trol term related to the curv ature of the line w ould impro this. 3.3 Results for the ositioning Case The ositioning case su ers from singularit y problems in the neigh b orho o d of the target poin t. in es- 15 20 25 30 −31 −30.8 −30.6 −30.4 −30.2 −30 −29.8 −29.6 −29.4 −29.2 −29 Cartesian position Y position (mm) X position (mm) Figure 4: Cartesian p ositions of user motion for com- pliance 0, where uman hair is used as the path. Sc

heme free hard virtual el Acc motion xture T(sec) 22.54 0.72 1.04 3.03 able 3: Execution times for four di eren ne posi- tioning sc hemes at the macro scale. tigated four sc hemes to use in this singularit y neigh- borhood ( ). The rst t ov ary the alue in creating free motion ( = 0) and a hard virtual xture 1). The last are elo cit and acceleration con trollers that autonomously mo e to the target p o- sition, regardless of force applied b y the user. o compare these sc hemes, w e executed the task of mo ving the rob ot from (0 0) to ( 35 mm; 0), with 1 (for all cases), of radius 1 mm, and a

p ositioning error tolerance of 5 m elo cit y reduction is disabled inside when using the autonomous sc hemes. Details of these con trollers can b e found in [2]. able summarizes the times in olv ed to reac the target after the con troller switc h. Figures 6 and 7 sho wthe Cartesian p ositions and the elo cit pro les for the four approac hes. The free motion sc heme requires a m uc h longer time to acquire the target poin t. Due to the elasticit of the rob ot arm and the bac klash of the gears, the same enco der p ositions corresp ond to di eren t end-e ector p ositions when the user v aries

the magnitude and di- rection of the applied force. When the con trol lo op is closed using enco der measuremen ts from the rob ot, the user is not able to determine the exact (enco der- based) rob ot p osition relativ to the target on the screen resulting in some random mo emen t at the end. In con trast, the hard virtual xturing sc heme is fast and e ectiv e, as it can exploit the maxim um possi- ble elo cit The hard constrain ts eep the user in 3358
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10 20 30 Compliance values: C =1 & C =0 HARD VIRTUAL FIXTURING Error (pixel) 10 20 30 Compliance values: C =1 & C =0.3 SOFT

VIRTUAL FIXTURING Error (pixel) 10 20 30 Compliance values: C =1 & C =0.6 SOFT VIRTUAL FIXTURING Error (pixel) 10 20 30 Compliance values: C =1 & C =1 FREE MOTION Error (pixel) 10 Compliance values: C =1 & C =0 HARD VIRTUAL FIXTURING (zoom) Error (pixel) 10 20 30 40 50 0.5 Velocity profiles (norm) mm/sec Time (sec) =1 =0 Figure 5: Error and v elo cit y pro les for the ath fol- lowing case at the micro scale for arious orthogonal compliance v alues. the righ t direction of motion, although what app ears on the screen is sligh tly di eren from the enco der- based p osition. urthermore, the elo

cit pro le for this sc heme do es not c hange discon tin uously at the in- stan tofswitc hing. The autonomous sc hemes are also e ectiv e, al- though they are somewhat slo er than the hard vir- tual xturing sc heme b ecause the v elo cit yisforcedto zero as the target is approac hed. In the v elo cit ycon- troller there is discon tin uit in the elo cit y pro le, but it is to o small to b e felt b y the user. The acceler- ation sc heme a oids an y discon tin uit yin the v elo cit pro le, ho ev er it is slo er than both hard virtual xturing and autonomous elo cit con trol. It is no- table that

the assistiv e, rather than the autonomous, sc hemes p erform the b est. It has b een sho wn that can acquire the exact target position using ne p ositioning, so no ob- serv e the p erformance for the ositioning case in en vi- ronmen ts c haracterized b y di eren t compliance prop- erties: (hard virtual xturing), 1.5 0.5 0.5 1.5 Y position Free motion 36 35 34 1.5 0.5 0.5 1.5 Hard virtual fixturing 36 35 34 1.5 0.5 0.5 1.5 X position Y position Autonomous velocity 36 35 34 1.5 0.5 0.5 1.5 X position Autonomous acceleration Figure 6: Detail of target acquisition using the four prop osed ne p

ositioning sc hemes at the macro scale. The circle indicates the switc hing surface. 0.1 0.4 T(sec) 8.93 9.51 9.98 11.02 able 4: Execution times for a p ositioning task at the macro scale using four di eren t compliance v alues. (soft virtual xturing), and = 1 (no virtual xtur- ing or free motion). hose constan lo op gain of 006 and the elo cit sc heme to obtain the target p osition. The elo cit slo do wn e ect, the switc hing sphere, the p ositioning error in the target, are all the same as in the previous set of exp erimen ts. The starting p osition is (35 0), the stopping p osition is ( 35

0)(bothinmm), and a 5 mm radius circle is at (0 0). The user w as told to mo e as straigh tas pos- sible to ard the target, a oiding the circle (if =0) and returning bac k on the old line of motion. Figures and sho the Cartesian p ositions and the elo c- it y pro les for the four compliance cases, and T able 4 summarizes the execution times. The execution time of this task increased sligh tly with the orthogonal compliance v alue (also in this case the tra jectory is shorter for = 0, reducing the time y ab out 0.55s). As exp ected, the di∆cult yinmo ving straigh tto ard the target increases

with the orthogo- nal compliance v alue, although the di∆cult yin going around obstacles decreases. The extreme case of hard virtual xturing, whic hmo es the rob ot rigidly along a straigh t line, do es not allo wan y obstacle a oidance. 3.4 Results for an Extended ask osho w the system b eha vior when executing a more general task comp osed of path follo wing part plus nal p ositioning at target p oin t, conducted the 3359
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10 mm/sec Free motion 10 mm/sec Hard virtual fixturing 10 mm/sec Autonomous velocity 10 15 20 25 10 mm/sec Time (sec) Autonomous acceleration Figure 7: elo

cit pro les for the four prop osed ne p ositioning sc hemes. The left and righ t dashed v erti- cal lines mark the switc hing and motion termination ev en ts, resp ectiv ely follo wing exp erimen t. instructed the user to fol- lo w half of the sin usoidal path and p osition the rob ot in Cartesian p osition (0,0) (appro ximately the cen ter of the path). The system w as set to switc h from the ath fol lowing con troller to the ositioning con troller as so on as the rob ot as within 10 mm of the tar- get. or the p ositioning part of the task, the settings ere iden tical to those describ ed in

the previous sec- tion. or b oth parts, a constan t orthogonal compliance alue ( =0 6) w as used. In Figures 10 and 11, the Cartesian p ositions and the elo cit pro le are sho wn. It is imp ortan to note that, in actualit ,nov elo cit y discon tin uities are presen t during the con troller switc h. The jump in the error diagram is due only to a c hange in error de ni- tion: the path-follo wing error (vision error, in pixels) is replaced b y p ositioning error (rob ot enco der error, in mm). Conclusion rom our initial results, it app ears that virtual xtures for path follo wing and p ositioning

tasks are sup erior to free motion in an admittance-con trol co op erativ e ma- nipulation en vironmen t. arying lev els of en vironmen compliance can pro vide the user with assistance that impro es path follo wing and p ositioning accuracy ,y et the freedom to a oid obstacles in the path. Lik ewise, limitations in absolute rob ot accuracy and rob ot dy- namic p erformance mak e soft virtual xtures an ideal means for guidance. On the one hand, they pro vide go o d high-lev el guidance, but at the same time allo user to \o erride" the system in situations where appropriate. One ey result of

this ork is that iden tical con- 40 30 20 10 10 20 30 40 Cartesian position Y position (mm) X position (mm) =0 =0.1 =0.4 =1 Figure 8: Cartesian p ositions for the ositioning case with di eren t orthogonal compliance v alues. The cir- cle surrounds the area that the user is required to a oid in the soft virtual xturing cases. trol la ws can b e used for at b oth the macro and micro scales, and for a wide v ariet y of guidance tasks. This is true ev en in situations where our mo del of the manipu- lator as an ideal, rigid, v elo cit y-con trolled device is no longer completely v alid. rom our

studies, it app ears that the user's reaction to di erence compliance v alues at b oth scales is similar, but the lev el of impro emen er freehand motion is more pronounced at micro- scopic scales for tasks that are more c hallenging for an unaided h uman user. are curren tly considering ho to apply these virtual xturing algorithms in the con text of vitreo- retinal ey surgery Comp ound tasks, suc as the path follo wing/p ositioning example presen ted in Sec- tion 3.4, will b e critical for practical applications. In related w ork, h uman comp ound task execution is b e- ing examined using

Hidden Mark Mo dels, so that con textually appropriate virtual xtures can be ap- plied. Comprehensiv e user studies are ongoing in b oth the macro and micro domains to quan tify p erformance enhancemen t (including execution time and error rate) and learning e ects. Ac kno wledgmen ts The authors gratefully ac kno wledge Ra jesh Kumar for his assistance in this w ork. ew ould also lik e to ac- kno wledge the help of Hong Zhang. Finally ,w e recog- nize the supp ort of the National Science oundation under gran ts #EEC9731478 and #I IS-0099770. References [1] A. Bettini, S. Lang, A. Ok am ura

and G. Hager. Vi- sion Assisted Con trol for Manipulation Using Virtual Fixtures. Pr c.oftheIntl.Conf.onIntelligentR ob ots andSystems , pp. 1171-1176, Maui (HI) Oct. 2001. 3360
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10 mm/sec Compliance values: C =1 & C =0 HARD VIRTUAL FIXTURING 10 mm/sec Compliance values: C =1 & C =0.1 SOFT VIRTUAL FIXTURING 10 mm/sec Compliance values: C =1 & C =0.4 SOFT VIRTUAL FIXTURING 10 10 mm/sec Time (sec) Compliance values: C =1 & C =1 FREE MOTION Figure 9: elo cit y pro les for the ositioning case with di eren t orthogonal compliance v alues. [2] A. Bettini. ask and Join tCon trol of

Human-Rob ot Collab orativ Systems. PhD Thesis, Dip artimento diInformatic aeSistemistic a,UniversitdiR oma"L Sapienza". , Dicem b er 2001. [3] G. D. Hager and K. ama. The \XVision" sys- tem: A general purp ose substrate for real-time vision applications. Comp. Vision, Image Understanding. 69(1):23-27, Jan uary 1998. [4] R. Kumar, T. Goradia, A. Barnes, P . Jensen, L. Whit- com b, D. Stoiano vici, L. Auer, and R. T ylor. erfor- mance of rob otic augmen tation in common dextrous surgical motions. Pr c. Me dic al Image Computing and Computer-Assiste Intervention pp. 1108-1115. Springer-V erlag,

1999. [5] R. Kumar, G. Hager, P . Jensen, and R.H.T ylor. An augmen tation system for ne manipulation. In Pr c. Me dic alImageComputingandComputerAssiste dIn- tervention , pp. 956-965. Springer-V erlag, 2000. [6] F. L. R.D. Ho e. Virtual xtures for rob otic endo- scopic surgery Biorob otics Lab oratory rep ort, Har- ard Univ., 2000. [7] L. Rosen berg. VirtualFixtur es PhD thesis, Dept. of Mec h. Eng., Stanford Univ., 1994. [8] Z. Stanisic, S. andeh, and E. Jac kson. Virtual xtures as an aid for teleop eration,. In 9thCanadian er onauticandSp ac eInst.Conf. , 1996. [9] R. T ylor, A. Barnes, R.

Kumar, P . Gupta, Z. W ang, . Jensen, L. Whitcom b, E. de Juan, D. Stoiano vici, and L. Ka oussi. ards a rob otic microsurgical as- sistan t. Int. Jnl. of ob otics ese ar ch 18(12):1201- 1210, 1999. 15 10 10 15 15 10 10 15 Cartesian position Y position (mm) X position (mm) Reference Path Robot trajectory Controller Switch Fine Positioning Switch Figure 10: Detail of the Cartesian p ositions in the switc bet een con trollers for the com bined task of path follo wing and p ositioning in the target. 10 15 Error profile pixel mm 10 12 10 12 Velocity profile mm/sec Tempo (sec) Figure 11: Error and

v elo cit y pro le for the com bined task of path follo wing and p ositioning in the target. The v ertical lines mark, from left to righ t, the con trol switc h time, the ne p ositioning switc htime, andthe motion termination time. 3361