biomedical paper - aminer · biomedical paper a six-degree-of ... over the last 2 decades, medical...

Biomedical Paper

A Six-Degree-of-Freedom Passive Arm with DynamicConstraints (PADyC) for Cardiac Surgery Application:

Preliminary ExperimentsOlivier Schneider, Ph.D., and Jocelyne Troccaz, Ph.D.

Laboratoire TIMC/IMAG, Faculte de Medecine, Universite Joseph Fourier, La Tronche, France

ABSTRACT The purpose of Computer-Assisted Surgery (CAS) is to help physicians and surgeonsplan and execute optimal strategies from multimodal image data. The execution of such plannedstrategies may be assisted by guidance systems. Some of these systems, called synergistic systems, arebased on the cooperation of a robotic device with a human operator. We have developed such asynergistic device: PADyC (Passive Arm with Dynamic Constraints). The basic principle of PADyCis to have a manually actuated arm that dynamically constrains the authorized motions of the surgicaltool held by the human operator during a planned task. Dynamic constraints are computed from thetask definition, and are implemented by a patented mechanical system. In this paper, we firstintroduce synergistic systems and then focus on modeling and algorithmic issues related to thedynamic constraints. Finally, we describe a 6-degree-of-freedom prototype robot designed for aclinical application (cardiac surgery) and report on preliminary experiments to date. The experimen-tal results are then discussed, and future work is proposed. Comp Aid Surg 6:340–351 (2001). ©2002Wiley-Liss, Inc.

Key words: medical robotics, man/robot cooperation, cardiac surgery, synergistic devices, computer-assisted surgery

INTRODUCTIONOver the last 2 decades, medical robotics hasevolved from the adaptation of industrial robots tomedical tasks to a specific domain of robotics re-quiring the development of innovative architecturesand control modes. Classical taxonomies distin-guish three types of guidance systems for comput-er-aided surgery: active, passive, and semiactivesystems. In this division, the degree of passivitycorresponds to the type of interaction between thehuman and the device.

1. Passive systems display information to thesurgeon about the position of the surgicaltool relative to anatomical data or to a pre-planned strategy, but the surgeon is totallyresponsible for the execution of the surgicalaction. Such a system is generally based onthe use of a localizer (an encoded mechan-ical arm or a device based on optical, mag-netic, or ultrasonic technologies), whichtracks the surgical instrument and other ob-

Address correspondence/reprint requests to: Jocelyne Troccaz, Ph.D., Laboratoire TIMC/IMAG, Faculte de Medecine,Domaine de la Merci, F-38706 La Tronche cedex, France; Telephone: �33 (0)4 76 54 95 08; Fax: �33 (0)4 76 54 95 55;E-mail: [email protected].

Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/igs.10020

Computer Aided Surgery 6:340–351 (2001)

©2002 Wiley-Liss, Inc.

jects of interest. References 1–3 present typ-ical examples of passive systems.

2. Active systems realize a part of the inter-vention autonomously. A robot may ma-chine a bone, or hold a sensor or surgicaltool, without the need for interaction withthe human operator, who generally super-vises the action. For examples, see refs. 4and 5.

3. A semiactive system involves a combinedaction with the human operator for the com-plete realization of the task. For example, amechanical guide positioned by a robot6,7 ormanually8,9 may align a linear drilling tra-jectory that the surgeon then executes.

This classification has some limitations. Ro-botic systems for telesurgery (such as that describedby Guthart and Salisbury10) are somewhat difficult toclassify in these three categories because the masterand slave manipulators involve different types of in-teraction. Moreover, the precise meaning of “semiac-tive” is quite variable in the community. Nevertheless,this existing classification is well known, and consti-tutes a good basis for discussion.

Each of these systems has its own advantagesand drawbacks, and the selection of which one touse is highly dependent on the application needs.11

Because our goal is to develop robotic systems thatenable tight cooperation between man and ma-chine, we focused on semiactive systems. Theseallow an ergonomic, direct, and accurate transfer ofthe surgical planning to the operating site. Never-theless, they are restricted to rather elementarytasks such as linear motions and planar cuts. More-over, this transfer is implemented using task-spe-cific hardware; this hardware may be considered asthe implementation of a mechanical constraint. Suchmechanical constraints need to be generalized andmade programmable. Therefore, we proposed the newconcept of synergistic devices. Synergistic devices areintended for direct physical guidance of a surgicaltool, a tool that is also held and controlled directly bya surgeon. The concrete objective is to build general-purpose mechanical devices designed to be held in thesurgeon’s hand, allowing him to feel the virtual worldof patient data (including safety regions around ana-tomical obstacles that are to be avoided) and surgicalstrategies while moving in the real world.

PRINCIPLES

Basic Principle of the SynergyThe basic principle of these devices is as follows.Both the surgeon and the synergistic device hold

the tool, apply forces to it and to each other, andimpart motions. Under computer control, the syn-ergistic device may allow the surgeon to have con-trol of some degrees of freedom (DOF) while thedevice controls the others. The system filters themotions proposed by the surgeon, keeping onlythose that are compatible with the surgical plan (seeFig. 1). For instance, during the preplanning stage,an orthopedic surgeon selects a cutting plane formachining a bone before implanting a knee pros-thesis. In such a case, the synergistic system guar-antees that the motions of the cutting tool arestrictly limited to the preplanned plane, while thesurgeon is in charge of the selection of motionswithin the plane. Such a system takes the bestadvantage of (1) the robot and its computer-basedmodel of the surgical action, and (2) the surgeonand his knowledge, sensing capabilities, and abilityto react to unexpected or nonmodeled events.

The principle of synergy is rather recent, al-though a somewhat similar system was proposedby Taylor et al.12 to improve the usability of apassive mechanical arm by means of particlebrakes. Synergistic systems have been imple-mented using several types of technologies. Acro-bot (Active Constraint Robot), an implicit force-controlled robot, is used for knee surgery.13,14 Thesurgeon guides the bone cutter while Acrobot guar-antees that the tool remains in the planned region.The system helps the surgeon by restraining hisability to move towards the forbidden region byprogressively increasing the resistance of the mo-tors. The motors and the operator are considered atthe same level in the control loop. Burghart et al.15

developed a similar approach using a force-con-trolled robot for craniofacial surgery. Whereasthese two systems are based on an active mecha-

Fig. 1. General principle of the PADyC system.

Schneider and Troccaz: PADyC for Cardiac Surgery 341

nism, P-TER,16 Cobot17,18 and PADyC are basedon passive joints. Cobot (Cooperative robot) isbased on nonholonomic elements allowing the cou-pling of DOFs. For instance, for a planar 3DOF(two translations and one rotation) Cobot, x, y, and� parameters are defined such that tg � � vy/vx,where vx and vy are the Cartesian velocities in theplane of motion. PADyC’s principles were intro-duced in ref. 19. The system is presented in fulldetail in the following sections.

Mechanical Architecture of a Single JointTo constrain the motion of the end-effector in theperformance of a given task, each joint of thePADyC has to be able to provide the four followingfunctions: (1) F1: motion authorized in the positivedirection only; (2) F2: motion authorized in thenegative direction only; (3) F3: motion authorizedin both directions; and (4) F4: no motion authorized.

These four functions are provided using apatented mechanism associated with each encodedjoint. The mechanism consists of two freewheelsmounted in opposite directions and associated withtwo motors. A freewheel is very similar to a con-ventional roller bearing, but it naturally providesthe basic function of unidirectional motion. Forinstance, as shown in Figure 2, let us consider thatthe internal part of the freewheel is fixed (�i

� � 0).If the operator imparts motion to the external partof the freewheel with velocity �user in the positivedirection, the motion will be blocked while themotion is free in the negative direction. If a motoris now associated with the internal part of the

freewheel and rotates with velocity �i�, then both

directions of motion are allowed but �user isbounded by �i

� in the positive direction.For one joint, each of the two freewheels is

associated with one clutching motor rotating in asingle direction. The velocities �i

� and �i� of the

two motors associated with the joint Ji are com-puter controlled. The operator moves the other partof the freewheel at velocity �user. Depending on thevalues of the relative velocities (�i

�,� � �user), themotion is blocked or authorized. Based on thismechanism, one can guarantee that, at each instant,the resulting velocity �i of the joint Ji is boundedby �i

� � �i � �i�.

This mechanism allows us to clutch or de-clutch the freewheels and to obtain the four func-tions F1 to F4 by a suitable choice of the �i

�,�

values:

F1: �i� � 0 � �i

� � 0

F2: �i� � 0 � �i

� � 0

F3: �i� � 0 � �i

� � 0

F4: �i� � 0 � �i

� � 0

The intrinsic safety of such a system is good. In-deed, the joint mechanical design integrates anotherset of freewheels and worm screws that respec-tively guarantee that the arm cannot move autono-mously, because the motors cannot drive the joints,and that the user cannot back-drive the motors.Moreover, the joints are naturally locked whenunpowered.

Task and Dynamic ConstraintsA surgical strategy is defined in terms of “taskconstraints.” These constraints are generally de-fined in the Cartesian space from multimodalitypatient data. Examples include a trajectory that hasto be executed relative to a given anatomical struc-ture, or a surgical tool that has to explore a pre-defined space while avoiding organs at risk. Theseconstraints apply to one or several control pointspositioned on the surgical tool or on the synergisticdevice. We have defined four programming modescorresponding to basic types of task constraints:

1. Free mode. In this mode, PADyC behavesas a mechanical localizer. No specific con-straint applies. The position of the surgicaltool is computed and recorded.

2. Position mode. PADyC helps the user tomove the tool towards a predefined position

Fig. 2. Freewheel mechanism.

342 Schneider and Troccaz: PADyC for Cardiac Surgery

and orientation. For instance, a bone frag-ment or a prosthesis component may bepositioned relative to bony structures ac-cording to a preplanning step.

3. Trajectory mode. This mode constrains themotion to follow a predefined trajectorywith a given accuracy. A biopsy trajectory,for example, will be executed in this way.

4. Region mode. The tool is free to move in agiven region of space, but cannot escapefrom that region. Motion inside the region istotally free and unconstrained. This allows asurgeon to stay in a region to remove sometissue (e.g., tumor resection or cavity prep-aration for prosthesis placement) or to guar-antee that some critical structures will beavoided.

More specialized modes have been defined:linear trajectory motion, planar region motion, andconical region motion. Combined modes can alsobe defined; for example, a position has to bereached while avoiding structures at risk.

The task is described in terms of these pro-gramming modes. Such a description may be gen-erated from the planning tools included in classicalCAS systems. For example, the shape of a 3Dregion in which the tool must remain is computedfrom anatomical data of the patient obtained beforethe intervention. In such a case, the 3D represen-tation of the region is the main parameter of themode.

A second set of constraints called “dynamicconstraints” results from the integration by the sys-tem of the task constraints and the current config-uration of the synergistic system. They are com-puted such that, at each instant, task constraints aresatisfied. The representation of dynamic constraintsdepends on the synergistic system. In the case ofCobot, for example, a dynamic constraint is anequation connecting joint variables. Because thePADyC joint mechanism has been designed so thateach joint velocity can be constrained in both di-rection and amplitude, dynamic constraints corre-spond to velocity orders. The high-level control ofPADyC is in charge of the translation of task con-straints to dynamic constraints. The following sec-tions describe these algorithms.

Modeling the Dynamic ConstraintsAs presented below, at each instant, each joint isconstrained to move in a given direction with abounded amplitude. The velocity window [�i

�,�i

�] associated with each joint Ji guarantees that,

during the next sampling period �t, the configura-tion of the robot belongs to a known hyper-paral-lelepiped parallel to the joint axes, called the win-dow of admissible configurations or WAC (see Fig.3). (In the following, for the sake of readability,illustrations will correspond to the case of a 2DOFPADyC.) For an n-joint robot, the WAC is definedas WAC(t) � (�q1

�, �q1�, �q2

�, �q2�, . . .,�qn

�,�qn

�).The constraint executed at instant t and avail-

able until t � �t may be described by the dynamicconstraint vector �(t) � (�1

�, �1�, �2

�, �2�, . . .,

�n�, �n

�), where �i�,� are the velocity orders to

be sent to the clutching motors of the joint Ji. Themajor control issue of PADyC concerns the deter-mination, from the current configuration of therobot and the preplanned task, of the vector ofdynamic constraint �(t) that has to be applied dur-ing the next sampling period to guarantee correctexecution of the task. This necessitates computa-tion of the WAC(t), from which �(t) is very easilydeduced: �(t) � WAC(t)/�t.

COMPUTING THE DYNAMICCONSTRAINTSThe low-level control of PADyC is very simple,because it relies on the execution of the velocityorders sent to the motors. Meanwhile, its high-levelcontrol requires a mapping of the geometric de-scription of the task from the Cartesian space whereit is generally defined to the joint space where theconstraints apply (see Fig. 4). This is a very well-known problem of robot motion planning for whichcomputational complexity is a critical issue. More-over, in our application, the task may vary withtime in some cases. For instance, a drilling trajec-tory in a vertebra will move as a function of themotions of this vertebra during surgery. Therefore,the computational cost of the algorithms used to

Fig. 3. Window of admissible configurations (a simpleexample).


map the Cartesian space to the joint space must bekept sufficiently low to allow real-time control. Inthe following, we introduce the principle of thesealgorithms for the position and region modes. Thefree mode control is rather trivial; the trajectorymode may be implemented either as a succession ofposition modes or as a region mode, which is builtfrom the planned trajectory and its associated tol-erance.

Position ModeLet us consider, for instance, that a configuration Qf

� (q1f, q2

f, . . ., qnf ) has to be reached in the position

mode, and that Qc � (q1c, q2

c, . . . , qnc) is the

current configuration at the instant t. To help theuser to reach Qf, WAC(t) is defined in the followingway (see Fig. 5):

if qif � qi

c � 0 then �qi� � 0 and �qi

� � qif � qi

c

else �qi� � qi

f � qic and �qi

� � 0

In this way, at each sampling period, the currentconfiguration is closer to the goal configuration.

Region ModeAs already stated, computing WAC(t) is more dif-ficult for trajectories or regions. A major difficultylies in representing in the joint space an object—forexample, a region—defined in the Cartesian space.The region may be, for example, the shape of acavity to be machined with the surgical tool. Toavoid this computation, we developed an approachinspired by the work of Barraquand and Latombe.20

It consists of replacing this 6D problem, i.e., com-puting the region in the joint space and deducingthe range of available positions and orientations ofthe surgical tool, by the combination of severalmuch simpler 3D problems: computing availablepositions of a set of k control points Pj located onthis tool. Thus, for each of the k control points Pj,a local WACj(t) is computed. To compute WACj(t)

at an instant t, when PADyC is in the configurationQc, the position of Pj is evaluated using the robotdirect kinematics model. A ball Bj(t) of admissiblepositions is determined locally in the Cartesian space,using a precomputed 3D chamfer distance map.Then, the algorithm determines a WACj(t) whoseimage in the Cartesian space, called WACj

cart(t), isincluded in the ball Bj(t). To speed up this process,we can use a linear approximation of WACj(t)because, as the sampling period �t is small, Bj(t) isalso small. Finally WAC(t) is simply defined as

WAC�t� �� j�1

kWACj�t�

The rationale is that the constraint is globally sat-isfied if it is locally satisfied by all the controlpoints. As WACs are very simple mathematicalobjects, their intersection is straightforward.

The specific modes are based on similar ap-proaches, but they allow for more rapid computa-tions than this general algorithm used for free-formregions or trajectories. Finally, the combinedmodes are implemented as a conjunction of con-straints, and therefore equivalently as an intersec-tion of WACs.

For more details about these methods, pleaserefer to refs. 21–23.

IMPLEMENTATION OF PADYC

Previous PrototypesSeveral prototypes of PADyC were realized andevaluated. The very first system was a Meccano™assembly (Fig. 6a), which allowed us to test thebasic design idea of a single joint equipped withtwo freewheels and two clutching motors. The sec-ond prototype was a single joint equipped with anencoder and two computer-controlled motors (Fig.6b). It allowed us to test the basic velocity control

Fig. 5. Position mode: computing WAC(t).

Fig. 4. PADyC control.


of a single joint. The third system was a planar2DOF prototype (Fig. 6c). As can be seen in theillustration, the end-effector is a pen, allowing us tovisualize executed motions and trajectories. Thefour basic modes were implemented on this proto-type, and successful experiments were run. A thirdaxis was later added to experiment with redun-dancy (Fig. 6d). These experiments are reported inrefs. 21 and 24.

A Six-Degree-of-Freedom Prototype:For What Purpose?Based on those previous developments, it was de-cided to develop a 6DOF PADyC on a more clin-ical basis. We selected one application where nei-ther traditional passive systems nor active robotsare fully satisfactory. Pericardial puncture, alsocalled pericardiocentesis, is a task well suited forthe clinical evaluation of PADyC. This procedureconsists of removing some pathological liquid fromthe pericardium using a needle. The percutaneousaccess to the effusion (a subcostal access throughthe skin) can only be performed when the effusionis large enough, typically more than 15 mm in thedirection of motion. This threshold is used to pre-vent the puncture needle from accidentally damag-ing the heart. The percutaneous procedure is almostblind for the surgeon, who cannot easily track theneedle on intraoperative echographic images. Thisis one reason why pericardial puncture is a difficultprocedure, with a failure rate of 20% and a 5% riskof puncture of the heart, which may lead to thedeath of the patient.25 When the effusion is toosmall for a safe percutaneous access, the cardiacsurgeon performs an open procedure, which is veryinvasive and traumatic. To decrease the thresholdof percutaneous puncture while allowing a safeprocedure, we developed the CASPER (ComputerASsisted PERicardial puncture) system.26 CASPER

is based on passive optical guidance. After an echo-graphic imaging procedure, a safe target positionand a safe trajectory are computed. During surgery,the position of the needle is tracked with the opticallocalizer and a user interface displays on a com-puter screen information about the current positionand orientation of the needle with respect to theplanned path, as shown in Figure 7. Animal exper-iments27 have shown that CASPER allows the sur-geon to safely puncture much smaller effusions.Although the system increases the accuracy of theprocedure, problems remain from an ergonomicpoint of view. The surgeon felt quite uncomfortablein maintaining a stable trajectory through the dif-ferent layers of soft tissue while controlling theneedle depth on a screen. In this clinical applica-tion, the distance of the needle tip to the heart is acritical parameter because the heart must beavoided at all costs. As safety is critical in thisapplication, we preferred to develop a synergisticsystem such as PADyC rather than introduce anactive robot.

In this PADyC-based version of CASPER,the feedback is basically haptic, so the use of ascreen is not strictly necessary. This should resultin a more comfortable use of the computer dataduring the intervention and in a more natural actionfor the surgeon, whose focus should be only on theneedle. As a result of better stability in the trajec-tory, accuracy and system usability should increase.

Architecture of the System

Based on the application specifications, a six-axisSCARA architecture was designed. As can be seenin Figure 8, the PADyC axes are: one verticaltranslation, three rotations around vertical axes, onerotation around a horizontal axis, a modular sixthjoint (see Fig. 8c), which can be either a rotation

Fig. 6. PADyC prototypes: (a) one axis (uncontrolled), (b) one axis, (c) two axes, (d) three axes. [Color figure can be viewedin the online issue, which is available at www.interscience.wiley.com]


axis or a translation axis. Figure 8a and b shows thetranslation module fixed on the robot.

The first joint is associated with a counter-weight to improve the system transparency by de-creasing the forces required to move the arm up-ward. Downward motions are made easier due togravity. The first three axes are equipped withmagnetic brakes. The resulting useful workspace ofthe end-effector may be approximated by a paral-lelepiped about 20 cm high with dimensions of30 30 cm.

The control system is implemented on anindustrial PC running the real-time operating sys-tem QNX. This operating system allows us to guar-antee a control loop rate of 100 Hz under anyconditions. High-level control algorithms are im-plemented in the C�� language.

The expected use of the PADyC-basedCASPER system is the following. It is very similarto the passive version of CASPER, presented in theprevious section, in terms of the surgical protocol.The six-axis device will replace the navigation sys-tem (i.e., the optical localizer and the display). Inthe first stage, the echographic probe is mounted onthe rotation module and attached to the robot’send-effector. The probe is used for image acquisi-

tion. After the planning phase, where the targetposition and approach trajectory are defined, theprobe module has to be removed from PADyC. Theneedle is then mounted on the translation modulethat replaces the rotation module. Then, the sur-geon, assisted by the robot, performs the pericardialpuncture. First, using the position mode, the needlehas to be aligned with the planned trajectory. Whenthe needle is in the correct approach configuration,the first five axes are kept in position, the clutchingmotors are stopped, and the brakes are activated.Then, using the translation module, the needle pro-gression toward the target point is executed using aposition mode on the sixth axis. Because the re-verse motion of the needle is not critical, the sixthaxis translation module is equipped with a singlefreewheel and its associated clutching motor. Motiontoward the target is velocity controlled; motion back-ward is free. Moreover, this allows the surgeon toremove the needle very rapidly if a problem arises.

EXPERIMENTS AND PRELIMINARYRESULTSThe system is not yet totally integrated with theapplication. Nevertheless, a number of tests havebeen performed to evaluate the basic properties of

Fig. 7. CASPER navigation system: (a) the guiding system; (b) the display before trajectory alignment; (c) the display duringneedle progression. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com]


the arm and the control algorithms. The experi-ments make use of an external measurement de-vice: a 6D optical localizer (Optotrak™, NorthernDigital, Inc., Ontario). Optotrak localizes infrareddiodes fixed to moving objects; this allows thetracking of several objects within a measurementvolume of 1 m3 with very good accuracy. [Moreprecisely, several tests (intrinsic accuracy, relativeaccuracy, etc.) were performed on 4 localizers.Maximum errors for Optotrak are most often lessthan 0.5 mm and 0.1 degrees.28] Two rigid bodiesconsisting of sets of five diodes were used. Onerigid body is attached to the robot base and corre-sponds to the absolute reference. The second rigidbody is placed on the end-effector. The 6D relativedisplacements of these rigid bodies are then re-corded.

Mechanical PropertiesThe aim of this first class of experiments is toobserve the behavior of the system under forceapplication. In these two tests, the system isstopped and no computer control is active.

Experiment A: RigidityThe protocol is as follows:

1. The system is positioned in a configurationwhere the arm is extended (this is the worstconfiguration for accumulating the errors);clutching motors are stopped; brakes areactive.

2. The initial position of a reference point onthe end-effector is recorded.

3. Calibrated forces of 0–3 kg are applied tothe end-effector, and 10 positions underforce application are recorded for eachrange of force intensity.

The results are shown in Figure 9. Note thatthe displacement of the reference point due to theelasticity of the robot may be rather important; upto about 1 cm for forces of 3 kg. This will bediscussed later.

Experiment B: RepeatabilityThis second test aims to determine the ability of thesystem to return to its initial position after force

Fig. 8. PADyC 6-axis prototype: (a) general sketch; (b) the prototype; (c) the 6th axis modules (translation or rotation).[Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com]


application. The protocol is rather similar to theprevious one:

1. The system is positioned in a configuration;clutching motors are stopped; brakes areactive.

2. The initial position is recorded.3. Arbitrary forces are applied to the end-ef-

fector, and the positions of the referencepoint (about 100) under force applicationare recorded.

4. The position after removing the force isrecorded.

Position dispersion (step 3) under force ap-plication confirms the results of the previous ex-periments: the position displacement in the verticaldirection is very much smaller than in the x and ydirections. The effect due to the force application islarger for y than for x because of the selectedconfiguration (arm extended in the x direction).

Repeatability is good, as can be seen in Table 1.The repeatability for the x and y axes also differsfrom that for the z axis.

A third test was conducted in which two rigidbodies were fixed on two successive links of therobot to detect backlash effects in the freewheels.The displacements obtained were too small relativeto the Optotrak accuracy to draw conclusions otherthan that these effects are smaller than the Optotrakaccuracy.

Evaluating the Programming ModesWe focused on the accuracy evaluation concerningthe position mode for the first five axes and for thesixth translation axis. In these experiments, theaxes are computer controlled.

Experiment A: Position Mode—First Five AxesThe protocol is as follows:

1. An arbitrary configuration is selected andrecorded (joint variables and Cartesian co-ordinates of the reference point).

2. The arm is moved far from this initial posi-tion to some other arbitrary position.

3. The position mode is used to return to therecorded configuration.

4. The reached position is recorded.5. Steps 2 to 5 are repeated 10 times.

The results are given in Table 2. The positionaccuracy is very good. Again, the x, y, and z axesare not equivalent. Mean errors for x, y, and z arerespectively 0.53, 0.54, and 0.09 mm. Standarddeviations for x, y, and z are, respectively, 0.31,0.34, and 0.09 mm. These measurements were alsoused for the evaluation of orientation errors. Roll,pitch, and yaw angles are given in Table 3. These

Fig. 9. Force/motion graph: the three curves representminimum, mean, and maximum values for a given range offorce intensity.

Table 1. Evaluation of Repeatability after Force Application

Test number

�x (mm) duringforce application

(100 measurements)

�y (mm) duringforce application

(100 measurements)

�z (mm) duringforce application

(100 measurements)Mean SD Mean SD Mean SD

1 1.94 1.92 3.47 4.08 0.65 0.552 1.44 1.43 1.6 2.18 0.37 0.383 1.86 1.65 2.2 1.77 0.61 0.534 1.13 0.78 1.08 0.95 0.70 0.525 0.95 0.88 2.18 2.37 0.50 0.47

Repeatability(for the five positions)

�x (mm) afterforce application �y (mm) �z (mm) �d

Mean 0.38 0.53 0.16 0.70SD 0.34 0.47 0.18 0.57

SD � Standard deviation.


orientation errors most probably come from axes 4and 5. This should be confirmed by further exper-iments.

Experiment B: Position Mode—Sixth AxisThe protocol consists of the following steps:

1. An arbitrary configuration is selected for thearm; the first five axes are stopped and thebrakes are active.

2. A goal position is selected for the needle.3. The goal position is reached under computer

control.4. The reached position of the needle is re-

corded.5. Steps 2 to 5 are repeated 10 times.

The results are given in Table 4. Mean errorsfor x, y, and z are respectively 0.09, 0.1, and 0.09mm. Standard deviations for x, y, and z are respec-tively 0.08, 0.1, and 0.02 mm.

The other modes were tested and are workingsatisfactorily from the algorithmic point of view.For these other modes, the robot behaves correctlyon a qualitative level, even if some tasks may besimpler than others. For example, in the planarregion mode, the orientation of the plane in therobot reference frame may lead to a more or lesseasy interaction with the user. However, no quan-

titative evaluation has been performed yet; such anevaluation is necessary for further progress withthat prototype and its application.

DISCUSSION

In this paper we have introduced the principle ofsynergistic systems, described the algorithmic andcontrol issues, and presented a 6DOF PADyC pro-totype, as well as preliminary experiments per-formed with this system.

● On a purely algorithmic level, all modes havebeen successfully tested. Moreover, the sys-tem allows for a good interaction with the userwhen using the different modes. However, asnoted previously, a complete quantitativeevaluation of the modes is necessary and isplanned for the coming months.

● The first set of quantitative tests concerningthe two position modes (first five axes andsixth axis) involved in the CASPER applica-tion are satisfactory. The different behaviorsof the x, y, and z axes are due to the selectedarchitecture. Vertical accuracy is much betterthan x and y accuracy, but a position can stillbe reached with very good accuracy that iscompatible with the clinical specifications.

● However, concerning the application, two is-sues have to be discussed. The first is relatedto robot calibration. In this initial stage ofdevelopment, we used a simple model of thearm, based on measurements performed bythe manufacturer, in which the joints are con-sidered to be perfectly parallel or perpendic-ular. This model is reasonably accurate. More-over, the quantitative evaluation we describedin the previous section did not require the useof the kinematic model of the arm, and thus

Table 2. Evaluation of Accuracy in the Position Mode Applied to the First Five Axes

Test number

�x (mm) after positionmode (five axes)

(10 measurements)

�y (mm) after positionmode (five axes)

(10 measurements)

�z (mm) after positionmode (five axes)


1 0.52 0.33 0.55 0.41 0.02 0.042 0.49 0.32 0.59 0.31 0.08 0.083 0.57 0.36 0.47 0.38 0.19 0.07

Global accuracy in theposition mode(for the three tests) �x (mm) �y (mm) �z(mm)

Mean 0.53 0.54 0.09SD 0.31 0.34 0.09


Table 3. Evaluation of Orientation Accuracyin the Position Mode Applied to theFirst Five Axes

Orientation accuracyin the position mode

Roll errorangle

(x axis)

Pitch errorangle

(y axis)

Yaw errorangle

(z axis)Mean 0.71 0.76 1Standard deviation 0.41 0.44 0.51


we did not introduce any additional errorsbecause of this simple model. However, fur-ther developments will require the selection ofa more complex model and the identificationof its parameters through calibration proce-dures. The second issue also concerns accu-racy. Modes were tested independently withno cumulative effects. If we consider thepuncture application where a position modefor the sixth axis follows a position mode forthe first five axes, the orientation accuracy isnot so satisfactory. For example, if the firstfive axes are positioned with an error of 1°, atranslation of axis 6 of about 15 cm, which isreasonable for the puncture application, couldresult in a position error of about 2.5 mm atthe target. The reasons for the orientation in-accuracy must be studied carefully, and couldlead to some modifications of the mechanicaldesign.

● Experiments also demonstrated that the rigid-ity of the system is not yet very satisfactory.We can make two remarks on this: first, thetests have been performed in a very unfavor-able configuration compared to typical config-urations used for the application. Second, theforces used for these experiments were largerthan what is typical for clinical actions such aspuncturing. However, some other clinical ap-plications that require larger force intensities,such as drilling of bones, could not be exe-cuted safely with this current version ofPADyC. In light of this, the PADyC structurehas to be made more rigid.

Despite some limitations in the present sys-tem, the general behaviour of PADyC is very prom-ising, and efforts will be made to ensure its clinicalapplicability and usability. Several tasks are

planned for the future: (a) the quantitative evalua-tion of the PADyC 6DOF prototype is to be con-tinued; (b) the mechanical behavior of PADyC hasto be improved (most likely by miniaturizing thesystem and redesigning the links) to increase rigid-ity and reduce orientation errors; and (c) integrationwith the CASPER application and its evaluation interms of clinical usability is to be continued.

ACKNOWLEDGMENT

We thank Dr. Olivier Chavanon and Pr. DominiqueBlin for their active participation during the clinicalspecification stage, and the Sinters company for therealization of the prototype.

REFERENCES

1. Mosges R, et al. Computer assisted surgery. An inno-vative surgical technique in clinical routine. In: LemkeHU, editor: Computer Assisted Radiology (CAR’89).Berlin: Springer-Verlag, 1989. p 413–415.

2. Lavallee S, Sautot P, Troccaz J, Cinquin P, Merloz P.Computer Assisted Spine Surgery: a technique foraccurate transpedicular screw fixation using CT dataand a 3D optical localizer. In: Proceedings of the FirstInternational Symposium on Medical Robotics andComputer Assisted Surgery (MRCAS’94), Pittsburgh,1994. p 315–322.

3. Grimson W, Ettinger G, White S, Gleason P. Evalu-ating and validating an automated registration systemfor enhanced reality visualization in surgery. In: Pro-ceedings of CVRMed’95. Lecture Notes in ComputerScience 905. Berlin: Springer, 1995.

4. Taylor RH, et al. A robotic system for cementless totalhip replacement surgery in dogs. In: Proceedings ofthe Second IARP Workshop on Medical and Health-care Robotics, Newcastle, England, September 1989.p 79–89.

5. Paul H, Bargar W, Mittlestadt B, Musit B, Taylor R,Kazanzides P, Williamson B, Hanson W. Develop-

Table 4. Evaluation of Accuracy in the Position Mode Applied to the Sixth Axis

Test number

�x (mm) after positionmode (sixth axis)

(10 measurements)

�y (mm) after positionmode (sixth axis)

(10 measurements)

�z (mm) after positionmode (sixth axis)


1 0.05 0.05 0.22 0.08 0.09 0.032 0.14 0.07 0.06 0.05 0.1 03 0.08 0.04 0.04 0.05 0.1 0

Global accuracy inthe position mode(for the three tests) �x (mm) �y (mm) �z (mm)

Mean 0.09 0.1 0.09SD 0.08 0.1 0.02



ment of a surgical robot for cementless total hip ar-throplasty. Clin Orthop Rel Res 1992;285:57–66.

6. Lavallee S, et al. Image guided robot: a clinical appli-cation in stereotactic neurosurgery. In: Proceedings ofthe IEEE International Conference on Robotics andAutomation, Nice, 1992. p 618–625.

7. Gotte H, Roth M, Brack C, Gosse F. A new less-invasive approach to knee surgery using a vision-guided manipulator. In: Proceedings of the IARPWorkshop on Medical Robots, Vienna, Austria, 1996.p 99–107.

8. Radermacher K, Staudte HW, Rau G. Computer as-sisted orthopaedic surgery by means of individualtemplates—aspects and analysis of potential applica-tions. In: Proceedings of MRCAS’94, Pittsburgh,Pennsylvania. p 42–48.

9. Fortin T, Coudert JL, Champleboux G, Sautot P, La-vallee S. Computer-assisted dental implant surgeryusing computed tomography. J Image Guid Surg1995;1:53–58.

10. Guthart GS, Salisbury JK. The Intuitive™ telesurgerysystem: overview and application. In: Proceedings ofthe IEEE Robotics and Automation Conference, SanFrancisco, April 2000.

11. Troccaz J, Peshkin M, Davies B. Guiding systems forComputer-Assisted Surgery (CAS): introducing syn-ergistic devices and discussing the different ap-proaches. Med Image Anal 1998;2(2):101–119.

12. Taylor RH, et al. A model-based optimal planning andexecution system with active sensing and passive ma-nipulation for augmentation of human precision incomputer-integrated surgery. In: Proceedings of theSecond International Conference on Experimental Ro-botics, Toulouse, France, 1991.

13. Davies B, Harris S, Jakopec M, Cobb J. A novelhands-on robot for knee replacement surgery. In: Pro-ceedings of the Third Annual North American Pro-gram on Computer Assisted Orthopaedic Surgery(CAOS USA ’99), Pittsburgh, Pennsylvania, June1999. p 70-74.

14. Harris S, Jakopec M, Cobb J, Davies BL. Intra-oper-ative application of a robotic knee surgery system. In:Taylor C, Colchester A, editors: Proceedings of theSecond International Conference on Medical ImageComputing and Computer-Assisted Intervention(MICCAI’99), Cambridge, England, September 1999.Lecture Notes in Computer Science 1679. Berlin:Springer, 1999. p 1116–1124.

15. Burghart C, Keitel J, Hassfeld S, Rembold U. WoermH. Robot controlled osteotomy in craniofacial surgery.In: Proceedings of the 1st International Workshop onHaptic Devices in Medical Applications, Paris, 1999.

16. Davis H, Book W. Torque control of a redundantlyactuated passive manipulator. In: Proceedings of theAACC Conference, 1997.

17. Colgate JE, Peshkin M, Moore C. Passive robots andhaptic displays based on nonholonomic elements. In:Proceedings of the IEEE International Conference onRobotics and Automation, 1996.

18. Peshkin MA, Colgate JE, Wannasuphoprasi W. Non-holonomic haptic displays. In: Proceedings of theIEEE International Conference on Robotics and Au-tomation, 1996.

19. Troccaz J, Lavallee S, Hellion E. PADyC: a passivearm with dynamic constraints. In: Proceedings of theInternational Conference on Advanced Robotics(ICAR’93), Tokyo, Japan, 1993. p 361–366.

20. Barraquand J, Latombe JC. Robot motion planning: adistributed representation approach. Technical reportSTAN-CS-89-1257. Stanford University, RoboticsLaboratory, Computer Science Department, 1989.

21. Delnondedieu Y. Un robot a securite passive en re-ponse aux problemes de securite et d’ergonomie enrobotique medicale. Ph.D. thesis, Institut National Poly-technique de Grenoble, TIMC laboratory, Grenoble,1997.

22. Troccaz J, Delnondedieu Y. Synergistic robots forsurgery: an algorithmic view of the approach. In:Agarwal P, Kavraki L, Mason M, editors: Robotics:the algorithmic perspective. Proceedings of the Work-shop on the Algorithmic Foundations of Robotics(WAFR’98), Houston, 1998. Natick, MS: AK Peters,1998.

23. Schneider O. Robot a securite passive: application a laponction pericardique. Ph.D. thesis, Institut NationalPolytechnique de Grenoble, TIMC laboratory, Grenoble,2001.

24. Troccaz J, Delnondedieu Y. Semi-active guiding sys-tems in surgery. A two-DOF prototype of the passivearm with dynamic constraints (PADyC). Mechatronics1996;6(4):399–421.

25. Kirkland L, Taylor R. Pericardiocentesis. Crit CareClin 1992;8:699–712.

26. Chavanon O, Barbe C, Troccaz J, Carrat L, Ribuot C,Blin D. Computer assisted pericardial puncture: workin progress. Comp Aid Surg 1998;2(6):356–364.

27. Chavanon O, Carrat L, Pasqualini C, Dubois E, BlinD, Troccaz J. Computer-guided pericardiocentesis:experimental results and clinical perspectives. Herz2000;25(8):761–768.

28. Chassat F, Lavallee S. Experimental protocol for ac-curacy evaluation of 6-D localizers for Computer In-tegrated Surgery: Application to four optical localiz-ers. In: Wells WM, Colchester A, Delp S, editors:Proceedings of the First International Conference onMedical Image Computing and Computer-Assisted In-tervention (MICCAI’98), Cambridge, MA, October1998. Lecture Notes in Computer Science 1496. Ber-lin: Springer, 1998. p 277–285.


biomedical paper - aminer · biomedical paper a six-degree-of ... over the last 2 decades, medical...

Documents