Mechatronics 20 (2010) 767–777

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Mechatronics

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Haptic tele-operation system control design for the ultrasound task:A loop-shaping approach

C.J. Zandsteeg a,*, D.J.H. Bruijnen b, M.J.G. van de Molengraft a

a Eindhoven University of Technology, Department of Mechanical Engineering, Postbus 513, 5600 MB Eindhoven, The Netherlandsb Philips Applied Technologies, High Tech Campus 7, 5656 AE Eindhoven, The Netherlands

a r t i c l e i n f o

Keywords:Medical systems

Tele-operationControl system designHuman–machine interfaceControl applications

0957-4158/$ - see front matter � 2010 Published bydoi:10.1016/j.mechatronics.2010.02.007

* Corresponding author. Tel.: +30631042913.E-mail addresses: c.j.zandsteeg@tue.nl (C.J. Za

philips.com (D.J.H. Bruijnen).

a b s t r a c t

This paper introduces a step-by-step frequency domain loop-shaping procedure for tele-operation sys-tem controllers, in particular for the three-channel Environment Force Compensation (EFC) control archi-tecture. The framework is explained by designing a controller for a tele-operated 5-DOF probe forultrasound echo-cardiography. Models of the tele-operation system components are created and perfor-mance requirements are specified. A control design procedure is proposed using a generic tele-operationblock-scheme. In this procedure, the choice for the EFC control architecture is underpinned and guide-lines for the loop-shaping of this tele-operation controller for performance and stability robustness aregiven. The designed controllers are tuned using the introduced procedure. Passivity, performance and sta-bility robustness of the newly designed controller are evaluated using experiments.

� 2010 Published by Elsevier Ltd.

1. Introduction

Robotic tele-operation systems are used to replace or enhancemanual labor in many areas. Tele-operation enables indirectmanipulation of objects and is used in space exploration (nuclear)waste management and for surgical tasks. However, the absence offorce perception in tele-operation systems results in an increase ofthe task completion time [1] and higher contact forces [2] in com-parison with direct manipulation.

To enable force perception during indirect manipulation, tele-operation systems are equipped with one or more feedback chan-nel(s) to transfer information about the environment back to thehuman operator. This haptic tele-operation reveals areas for theapplication of tele-robotics, such as the ultrasound task in echo-cardiography, as discussed in this paper.

Echo-cardiography is utilized during minimal invasive heartsurgeries to provide images to the surgeon. Sonographers, whomanipulate the ultrasound probe, need force perception to dis-criminate tissue and bones to optimize the image quality. Theultrasound task is physically intensive, since the workspace be-tween the patient’s body and other equipment used is restricted.The poor ergonomics, combined with the duration of the surgery,often results in occupational injuries. Furthermore, X-ray imagingequipment is also used during the surgery. To reduce these occupa-tional- and X-ray-hazards for sonographers, a tele-operation sys-

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tem for the ultrasound task, with force feedback, is developed byPhilips Applied Technologies and Eindhoven University of Technol-ogy. An illustration of this Tele-Operated Ultrasound Probe (TOUP)is given in Fig. 1. Haptic tele-operation systems, such as TOUP, en-able perception of the environments impedance. Several chal-lenges are present in developing a tele-operation system for aspecific task. This paper focusses on the control design for stabilityrobustness and performance for tele-operation systems withouttime-delay in the communication channel. For this application,time-delay can be neglected because the master is connected tothe same control platform as the slave and the sampling frequencyis much higher than the control bandwidth.

The performance of haptic tele-operation systems is often ex-pressed as ‘transparency’, which is the ratio between the imped-ance felt by the operator and the actual environment impedance[3]. Other performance measures are: ‘fidelity’ [4], a measure forthe reflection of impedance changes, and ‘Z-width’ [5], a measurefor the range of possible perceived impedances by the operator.However, the latter only addresses the range of all possible per-ceived impedances and does not give information about the errorbetween the actual and the perceived impedance. Furthermore,‘fidelity’ only addresses the error between impedance changes.

Models for haptic tele-operation systems, which enable stabilityand performance analysis, are often derived using two-port net-work theory [6,3]. In a two-port network, the dynamical behaviorof the system is characterized by the ‘‘effort” and the ‘‘flow” atthe system ports, i.e. the operator and environment side. Formechanical systems, ‘‘effort” represents force and ‘‘flow” repre-sents velocity. A generic method to model the dynamical behavior

Fig. 1. 5-DOF tele-operated ultrasound probe for ultrasound echo-cardiography.

Fig. 2. Simplified representation of the control layout of TOUP including the master (left) and the slave (right).

768 C.J. Zandsteeg et al. / Mechatronics 20 (2010) 767–777

of linear tele-operation systems, is the hybrid matrix notation [6].This notation is the base for the general bilateral tele-operator sys-tem block-diagram as proposed in [3]. An extension to the block-diagram of Lawrence [3] is given in [7], where two (local) forcecontrollers are added. The extra controllers result in extra designfreedom, which enables ideal transparency while using only threecommunication channels.

The hybrid matrix notation is a powerful tool for control archi-tecture design. In the last decades numerous control architecturesare developed from this point of view. A recent overview of severalcontrol architectures using this notation is given in [8]. However,the current literature does not provide a clear framework for ro-bust, performance-driven, data-based controller design of tele-operation system controllers in the frequency domain.

A first frequency domain loop-shaping approach for control de-sign for a two-channel position–force architecture is introduced in[9]. In this approach, classical control theory can be used to enablea simultaneous increase in transparency and stability robustnessfor the force–position scheme with optional local force feedbackcontrol loops. This approach is extended to MIMO systems in[10]. In both papers an extra filter is placed in one of the commu-nication channels. The increment in performance and stabilityrobustness is achieved by shaping this extra filter, but the actualcontrol design of the several other controllers is not discussed. Fur-thermore, the results are based on ideal rigid body dynamics with-out mode-shapes.

This paper contributes to the haptic tele-operation systemcontrol design, by introducing a step by step, frequency domain,data-based, loop-shaping approach for use with well-known haptictele-operation system control architectures. The advantages of the

proposed framework are that no parametric model of the hardwareis necessary due to the data-based approach and classic loop-shap-ing techniques can be used to design for performance and stabilityrobustness. Hence, the modeling errors in the dynamics of masterand slave are reduced because all resonances are taken into ac-count in the control design. In contrast with the work in [9,10], thispaper discusses the control design of the complete tele-operationsystem controller and the experimental results are based at realsystem dynamics with resonances.

The approach is explained from a pragmatic point of view, thatis the application at the TOUP tele-operation system. The approachis illustrated by the flowchart in Fig. 3. The procedure begins byanalyzing the Frequency Response Functions (FRF) of the masterand the slave and by creating models of the environment (Section2). These FRF’s are used for further analysis. Furthermore, the per-formance requirement is specified a priori (Section 3). Then a con-trol architecture is selected. The control architecture selection isbased on the system dynamics, the system configuration and theperformance requirement.

An important step in the control design procedure proposed inthis paper is the simplification of the control problem by express-ing the system dynamics in terms of well-known closed loop trans-fer functions. The simplified control problem gives insight in theinfluence of the controller parameters at stability robustness andperformance, which enables intuitive control design using classicloop-shaping techniques. The selection of the control architectureand the control design method are discussed in Section 4. Further-more, an adapted tele-operation system block scheme is proposed,which is based on the block-scheme of Hashtrudi-Zaad and Salcu-dean [7].

Fig. 3. Flowchart containing the steps taken in the haptic tele-operator controldesign methodology.

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The designed controller is analyzed for stability in Section 5,where the system is analyzed for passivity and stability robustnessfor operator impedances. Finally, the performance of the system isanalyzed using theory and experiments in Sections 6 and 8. Despitethe fact that the control design methodology is elaborated usingthe EFC control architecture [7], the proposed control design proce-dure can also be used for the Shared Compliance Control (SCC)architecture [11] since its structure is similar to the EFC controller.Furthermore, this framework can also be inspiring for control de-sign for other control architectures that can be described by thegeneral tele-operation system block-scheme of Hashtrudi-Zaadand Salcudean [7].

2. Experimental modeling

A haptic tele-operation system consists of four dynamical sub-systems, which are the ‘‘Master”, the ‘‘Slave”, the ‘‘Environment”and the ‘‘Operator”. The operator interacts with the master, whilethe slave interacts with the environment. A tele-operation systemcontroller is placed in between, which virtually connects all sub-systems in the control loop. The first step in the design of this con-troller is to obtain the FRF’s and to analyze the dynamical behaviorof the subsystems in the tele-operation system to create insight inthe limitations by the hardware in the control design. The mea-sured FRF’s of the master and the slave, which are discussed in thissection, are used in the rest of the control design framework.

2.1. Master and slave

The master (Fig. 2) is the commercially available 6-DOF ForceDimension Omega.6 [12]. The three translational DOF’s, x; y andz, are constructed via a closed kinematic shape. Three rotations,Rx; Ry and Rz, are mounted on top of this structure. The positionin all directions is measured by encoders, while only the x; y andz directions are actuated. Therefore, the tele-operation system is

only bilaterally coupled in the three translational DOF’s. Further-more, Rz is not used in the tele-operation system.

In contrast to the master, the 5-DOF slave manipulator(x; y; z; Rx and Ry) is especially designed for the ultrasound task.The 5-DOF position is measured by encoders in all joints and alljoints are actuated. Furthermore, a 3-DOF force transducer isplaced close to the ultrasound probe and measures the forces inthe translational DOF’s, ðFx;y;zÞ. This enables the use of direct forcefeedback in the tele-operation system controller. The translationalDOF’s are bilaterally coupled with the DOF’s of the master, whilethe rotational DOF’s of the slave are in position control only.

Force feedback in the rotational degrees of freedom is not nec-essary for the ultrasound task, because the torques applied by theoperator are small. Lubricant is used between the probe and thehuman skin, which eliminates friction. An advantage of providingforce reflection in the translational DOFs only is that the force sen-sor can be placed anywhere near the ultrasound probe.

A simplified representation of the interaction between masterand slave in the haptic tele-operation subsystems is given inFig. 2. In this figure, the arrows represent multi-dimensional sig-nals communicated from one peripheral to another. Xmx;y;z ; Xsx;y;z

and Fx;y;z represent the measured position of the master, the mea-sured position of the slave and the measured force at the end-effec-tor of the slave, respectively, in x; y and z directions. Moreover,Cmx;y;z and Csx;y;z represent the force generated by the bilateral con-troller Cx;y;z in x; y and z, for the master and the slave, respectively.Likewise, XmRx;Ry and XsRx;Ry represent the orientation of the end-effector of the master and the slave, respectively, around Rx andRy. Furthermore, FcsRx;Ry , represents the force generated by the(non-bilateral) controller CRx;Ry.

Both, the master and the slave are non-linear robotic manipula-tors, since both inertia and gravity forces are function of the gener-alized coordinates. However, model based gravity compensation isapplied to compensate the static gravity forces. Furthermore, it isassumed that the change in inertia is also very small because theworkspace of both manipulators is small. Hence, it is assumed thatthe non-linearities are negligible and that both master and slaveare dominated by Linear Time-Invariant (LTI) dynamics. First, theassumption of linearity is validated for the master. Therefore, the3 � 3 MIMO FRF is measured in 27 evenly distributed operatingpoints within the used workspace of the manipulator. The FRF fromthe actuator force in [N], Fcmx;y;z , to the cartesian position of the end-effector in [m], Xmx;y;z , is measured in each operating point. The re-sults are illustrated in Fig. 4. It can be seen that the differences be-tween operating points are small for the diagonal terms, up to thefirst mode-shape at approximately 20 [Hz], in all directions. Thismode-shape is the decoupling of the end-effector, which causesnon-collocated actuation by the operator, while the actuators arecollocated. Below this frequency, rigid body dynamics are present.

Differences between operating points are noticed between theoff-diagonal terms in the FRF of the master. However, the off-diag-onal terms can be neglected if the system is decoupled. Theamount of coupling for the master is analyzed by computing theRelative Gain Array (RGA) [13]. The RGA addresses the dynamicalbehavior of each direction, when the controllers in the other direc-tions have infinite bandwidth. When the RGA of a system is uni-tary, each input only influences one output and decentralizedcontrol can be used to stabilize the system.

The RGA of the master is shown in Fig. 5. It can be seen that theRGA is nearly unitary up to the frequency of the first mode-shapeat 20 [Hz]. Hence, the diagonal terms dominate the dynamics ofthe master and the off-diagonal terms do not significantly contrib-ute to the dynamics of the diagonal terms. Therefore, decentralizedcontrol is allowed if the bandwidth is kept within the rigid bodydynamics. If so, the multi-DOF tele-operation system can be con-sidered as multiple SISO loops. A similar approach is used for the

−150

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de [d

B]X m

,y

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Fcm,z

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Fig. 4. MIMO frequency response function magnitude in multiple operating points of the master: cartesian space, inputs in [N] and outputs in [m].

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Fig. 5. RGA of the master in multiple operating points.

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slave manipulator. The 3 � 3 MIMO FRF from the actuator-force/torque, Fcsx;y;z , in [N] or [Nm] to the joint-position, Xsx;y;z , in [m] or[rad], is also measured in multiple operating points for the slave.The results are illustrated in Fig. 6. It shows that the differences be-tween the operating points are negligible in y direction. Hence, theassumption that the dynamics of the slave are dominated by lineardynamics holds for this direction. However, small but non-negligi-ble differences in magnitude between different operation pointsfor Xs;x and Xs;z are present. Therefore, the model in these directions

is based on the worst case system dynamics, i.e. the operatingpoint with the highest magnitude.

Differences between operating points are noticed between theoperating points in the off-diagonal terms of the FRF. To investigatethe contribution of the off-diagonal terms to the diagonal terms,the RGA is also computed for the slave. The RGA of the slave isshown in Fig. 7. It can be seen that the RGA of the slave is also uni-tary up to approximately 20 [Hz]. Hence, the off-diagonal termsalso do not contribute significantly to the dynamics of the diagonal

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Fig. 6. MIMO frequency response function magnitude in multiple operating points of the slave: Joint Space, Inputs in [N] and Outputs in [m] ðFcs;yÞ or Inputs in [Nm] andOutputs in [rad] ðFcs;x;zÞ.

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Fig. 7. RGA of the slave in multiple operating points.

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terms and decentralized control is allowed if the bandwidth is keptunder this frequency. The FRF’s in the other DOF’s, Rx and Ry, arenot shown in this paper. These DOF’s are not part of the bilaterallycoupled controller. Both DOF’s do not have significant couplingwith the other directions and the influence at the system dynamicscan be neglected.

Summarizing, the linearity assumption is validated for bothmaster and slave. Furthermore, the system can be considered asdecoupled for controller bandwidths below 20 Hz. Moreover, the

FRF’s obtained FRF’s of both the master and the slave as shownin Figs. 4 and 6, respectively, are used as a non-parametric modelin the control design procedure.

2.2. Environment

The slave interacts with the environment, which is the humantorso for the ultrasound task. The environment also influencesthe dynamics of the overall tele-operation system. It is assumed

772 C.J. Zandsteeg et al. / Mechatronics 20 (2010) 767–777

that the human torso consists of three different tissues: fat, muscleand the ribcage. Furthermore, it is assumed that the environmentis Linear and Time-Invariant (LTI) and that the tissues can be mod-eled as second-order impedances separately. The characteristicequation for second-order impedances is:

ZeðsÞ ¼ mes2 þ besþ ke; ð1Þ

where the mass, me, damping, be, and stiffness, ke, are obtained fromliterature for each tissue. The dynamical properties of each tissue,together with the references are given in Table 1.

2.3. Operator

The human operator interacts with the tele-operation systemand is also part of the system. Hence, the operator influences sta-bility. However, the dynamics of the human operator are very com-plex. It depends on the task and pose specified and may vary intime. When the operator is assumed to be passive, a sufficient cri-terium for stability of the tele-operation system in contact with aspecific environment is that the system without operator, in con-tact with the environment, is passive. This assumption reducesthe stability analysis to proving passivity of the tele-operation sys-tem without operator, in contact with the environment. To use thisproperty, the operator is assumed to be passive for the sequel.However, if passivity of the system without operator cannot beproven, it may be necessary to measure the operator impedance,which might be difficult.

3. Performance requirements

For the ultrasound task, stiffness perception is necessary forsuccessful task completion. The sonographer should be able to dis-criminate fat, muscle and the ribcage. Ribs decrease the quality ofthe ultrasound image. The sonographer uses the force feedback todetect ribs, covered in a (thin) layer of muscle and skin. Thereforethe system should enable reasonable stiffness perception of hardenvironments and especially discrimination between hard and softenvironments.

3.1. Transparency

Three performance measures are given in Section 1. ‘‘Transpar-ency” directly quantifies the ability of stiffness perception and isdefined as

Tp ¼Zto

Ze; ð2Þ

wherein Zto and Ze are the perceived impedance by the operator andthe impedance of the environment, respectively. Zto is the transferfunction from operator position/velocity to the force felt by theoperator.

In the literature, researchers often try to design controllers fortele-operation systems such that ideal transparency is obtained,Tp ¼ 1, for all frequencies. However, it is not possible to achieveperfect transparency under stability in practice. It is better to spec-ify the performance requirement necessary for the task first. Then,

Table 1Dynamical parameters for fat, muscle and the ribcage.

Tissue ke [N/m] be [Ns/m] me [kg]

Free motion 0 0 0Fat [14] 75 1 0Muscle [14] 500 3 0Ribcage [15] 7230 153 1

select a appropriate control architecture to attain this level oftransparency under stability, with the given hardware [3]. The hu-man limits in perception and motion can be used as guidelines tospecify this requirement.

3.2. Human performance and controller requirements

The human perception consists of two types of sensing [16].Kinesthetic Sensing incorporates the perception of body motionand low frequent force perception, which is used to examinemechanical properties of objects, like stiffness. The frequencyrange of Kinesthetic Sensing is [0,10–20] [Hz]. Cutaneous Sensingincorporates high frequent force information and is used for per-ception of roughness and structure of an object and for the sensa-tion high frequent vibrations. The frequency range of CutaneousSensing is [10–20,320] [Hz].

The frequency content of motion prescribed by the operator islimited. According to Hannaford [17], 99% of the frequency contentof accurate motion in surgical tasks is bounded by 2 [Hz]. Involun-tary motion, like tremor, contains mainly frequencies between 8and 10 [Hz] [16]. Hence, good position tracking up to 2 [Hz] is nec-essary, while frequencies above 8 [Hz] should be suppressed. Thiscan be achieved by limiting the maximum bandwidth of the posi-tion control loop of the slave. Consequently, the closed loop trans-fer-function becomes smaller than 1 for frequencies above thebandwidth. Hence, selecting a bandwidth lower than 8 Hz resultsin suppression of tremor. However, this is not an activesuppression.

Summarizing, the ultrasound task requires good force and posi-tion tracking up to 2 [Hz], which is equivalent to good transpar-ency up to 2 [Hz] ðZto=Ze � 1Þ. Furthermore, the bandwidth of thelocal position controller at the slave is limited to 6 [Hz], which en-ables good position tracking up to 2 [Hz] and attenuation oftremor.

4. Control design

4.1. Tele-operation system model

The next step in the control design is the modeling of the com-plete tele-operation system. A generic tele-operation system dia-gram is proposed in [7], which incorporates the system dynamicsof the master, the slave, the environment and the operator togetherwith the local controllers en controllers in the communicationchannel. However, non-collocated actuation by the human opera-tor cannot be described by this tele-operation system model. Itcan only represent equal dynamics for control and actuation bythe human operator. The Force Dimension Omega.6 is not rigiddue to the first mode-shape. This mode-shape causes differentdynamics for actuation by the human operator and for the actua-tors, which are used to control the master. The human operatoractuates via non-collocated dynamics, while the controller encoun-ters collocated dynamics. Hence, the model of Hashtrudi-Zaad andSalcudean [7] is not valid for TOUP, because non-collocateddynamics for human actuation characterize the dynamics of theForce Dimension Omega.6 (Section 2.1).

A new tele-operation model, based on the model proposed in[7], is proposed in Fig. 8. This tele-operation model incorporatesnon-collocated actuation by the operator. In this model, the imped-ances of the ‘‘Slave”, the ‘‘Operator” and the ‘‘Environment” arerepresented by Zs; Zh and Ze, respectively. Moreover, Zmc and Zmh

represent the collocated dynamics of the ‘‘Master” for controland the non-collocated dynamics for actuation by the human oper-ator, respectively. Local controllers, Cm; C6; Cs and C5, enable posi-tion and force control at the master and the slave side, respectively.

Fig. 8. Block diagram of a general bilateral controller incorporating non-collocatedoperator actuation (based on: [7]).

Fig. 9. Block diagram of the bilateral controller for the EFC control architecture. Thebold variables, Zmc and Zs , incorporate the optional compensation of dynamics ofmaster and slave, respectively. For TOUP Zmc ¼ Zs ¼ 0.

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In the communication channel, controllers C1; C2; C3 and C4 en-able and shape the position X and force F of the environment (sub-script e) and operator (subscript h), respectively. Furthermore, F�eand F�h represent the voluntary force input of the environmentand operator, respectively.

The notation used in Figs. 8 and 9 is equal to notation of Hasht-rudi-Zaad and Salcudean [7], which is unequal to the notation usedFig. 2. However, The position of the operator, Xh, and the position ofthe environment, Xe as used in Fig. 8 and 9 are equal to the positionof the master, Xmx;y;z , and the position of the slave, Xsx;y;z , as used inFig. 2, respectively. Furthermore, Fe is equal to the measured forceFx;y;z. Moreover, controllers C1; C2; C4; C5; Cs and Cm of Figs. 8 and9 are lumped in Cx;y;z in Fig. 2.

Because the haptic master is not equipped with a force trans-ducer (Section 2.1), the operator force, Fh, cannot be measured.Hence, the controllers C6 and C3 cannot be used in the haptictele-operation system controller of TOUP. Furthermore, it is de-sired to use a low bandwidth of 6 [Hz] for the slave position controlloop (Section 3). This low bandwidth results in large tracking errorsin contact with stiff environments, due to the environment forceFe. However, Fe can be counteracted, without influencing stabilityrobustness in contact, by using local force feedback at the slaveðC5 ¼ �1Þ, as proposed in [7,11]. When the impedance of Cs ismuch smaller than the environment impedance, this local forcefeedback results a significant increase in performance in compari-son with other control architectures that do not use the local forcefeedback controller C5, like the Position–Error and the Position–Force architecture. Therefore, the control architecture for TOUPshould feature C3 ¼ C6 ¼ 0 and C5 ¼ �1.

Three control architectures can be used which satisfy thisrequirement. That are the EFC, the SCC and the Force Reflectionwith Passivity II (FRP2) control architecture, which are discussedin [8]. However, it is claimed that the FRP2 architecture is not suit-able for stiffness perception [8]. Furthermore, the EFC architecture

is similar to the Shared Compliance Control (SCC) architecture forCm ¼ 0. Hence, it is chosen to design a controller for the EFC controlarchitecture, which may transform into the SCC architecture, whenthe optimal value for Cm in the control design is zero. This controlarchitecture is illustrated in Fig. 9.

4.2. Controller analysis and tuning

For the EFC control architecture, the local controllers are speci-fied as [7]

C1 ¼ Cs þ bZs ðC2;C3Þ ¼ ð1;0Þ;C4 ¼ �Cm � bZmc; ðC5;C6Þ ¼ ð�1;0Þ; ð3Þ

where bZmc and bZs are the terms that enable the optional compensa-tion of the dynamics of the master and the slave, respectively. Inpractice, the exact compensation of the dynamics of the masterand slave is not possible and estimates of Zmc and Zs are often used.Hence, to distinct these terms from the dynamics, they are indicatedby a caret.

Given the block diagram of Fig. 8 and (3), or Fig. 9 the perceivedimpedance by the operator, Zto ¼ Fh=Xh, for the EFC architecture isgiven by

Z�1to ¼

ZmcZ�1mh

Zcm þ ðZe � CmÞTs þW; ð4Þ

where Zcm ¼ Zmc þ Cm; Zcs ¼ Zs þ Cs and Ts ¼ CsZ�1cs represent the in-

verse process-sensitivity of the master, the inverse process-sensi-tivity of the slave, and the complementary sensitivity of the slave,which are all closed loop transfer functions of the corresponding lo-cal position control-loops of the master or the slave. Furthermore, Wcontains the terms which are depending on the compensation ofdynamics and is defined as

774 C.J. Zandsteeg et al. / Mechatronics 20 (2010) 767–777

W ¼

0 for C1 ¼ Cs^C4 ¼ �Cm;

ðCmCs � bZcmbZcsþ for C1 ¼ Cs þ bZs^

ZebZsÞZ�1

cs C4 ¼ �Cm � bZmc;

8>>>><>>>>:

ð5Þ

where bZcm ¼ Cm þ bZmc and bZcs ¼ Cs þ bZs are the estimated inverseprocess sensitivities of the master and the slave, which may be usedin controllers C4 and C1, respectively, as prescribed in (3).

Under assumption that exact compensation of dynamics can beapplied, i.e. bZmc ¼ Zmc and bZs ¼ Zs, Eq. (4) reduces to

Z�1to ¼

ZmcZ�1mh

Ze8x; ð6Þ

which is equal to ideal transparency up to the mode-shape in themaster dynamics. For a rigid body master, i.e. Zmc ¼ Zmh, (6) showsthat ideal transparency is obtained when the dynamics of Zmc arefully compensated.

In practice, (full) cancelation of the dynamics of master andslave is not possible due to sensor limitations. The dynamics aredominated by inertia. Often, only quantized position measure-ments are present in tele-operation systems, while accelerationis necessary for inertia compensation. Taking the second derivativeof quantized signals amplifies noise, which results in a low Signalto Noise Ratio (SNR) for small accelerations. During accurate tasks,like the ultrasound task, the operator accelerations are small.Hence, the control design is done without the compensation ofdynamics and Eq. (3) reduces to

C1 ¼ Cs; ðC2;C3Þ ¼ ð1;0Þ;C4 ¼ �Cm; ðC5;C6Þ ¼ ð�1; 0Þ; ð7Þ

which results in W ¼ 0 for (4).Under the assumption that F�e ¼ 0, the block diagram of Fig. 9

can be rearranged to the single negative feedback loop withloop-gain L ¼ ZhZ�1

to , as illustrated in Fig. 10.For W ¼ 0, (4) shows that the tunable parameters in the EFC

controller are reduced to Cm and Cs. Furthermore, jZmcj � jCmj atlow frequencies. Hence, Zcm � Cm for low frequencies. Moreover,Zmc ¼ Zmh up to the first mode-shape because collocated andnon-collocated dynamics are characterized by equal rigid bodydynamics. Hence, for low frequencies, (4) reduces to

Z�1to ¼

1ZeTs � CmðTs � 1Þ : ð8Þ

It is known that Ts � 1 up to the crossover frequency. The high-er Cs, the higher the crossover frequency of the slave’s local posi-tion control loop. Hence, (8) shows that optimal transparency isachieved when the impedance of Cs is maximized. Ideally, Zto

should be equal to Ze. Since Ts � 1 up to the crossover frequency,Cm should be minimized to optimize (8) for transparency. Hence,optimal performance is obtained for Cm ¼ 0, which is actually theShared Compliance Control architecture of Kim et al. [11], whichhas better performance than the EFC architecture, without com-pensation of dynamics.

On the other hand, for passivity and stability, Z�1to should be

bounded by the negative imaginary part of the Nyquist diagram.The advantage of EFC, in comparison with SCC, is that Cm addsdamping in the tele-operation system, which results in higher en-ergy-dissipation. Furthermore, increasing Cm decreases the gain of

Fig. 10. Negative feedback system.

Z�1to and phase advance of Cm adds phase to Z�1

to . Hence, for stabilityrobustness of the complete tele-operation system one should in-crease the impedance of Cm. Furthermore, extra damping in Cs intele-operation systems results in better contact stability in prac-tice. However, both measures result in a performance decrease.Hence, a trade-off between stability robustness and performanceshould be made in the control design and the values should be cho-sen such that all sub-systems are also stable.

These guidelines are now used for the control design of the localcontrollers in the EFC control architecture. For TOUP, the non-col-located actuation by the operator is characterized by a �360 [deg]phase after the first mode-shape. This phase behavior is also pres-ent in Z�1

to and may cause instability depending on the loop-gain.Increasing Cm decreases the magnitude of Z�1

to and increases stabil-ity robustness for high operator impedances. To maximize stabilityrobustness for high operator impedances, Cm is set to the maxi-mum value for which the local position control loop of the masteris stable. Furthermore, the impedance of Cs is set such the maxi-mum bandwidth of 6 [Hz], as stated in the performance require-ments, is achieved.

The controllers Cm and Cs are standard lead-controllers with asecond-order low-pass filter to attenuate the differentiator at highfrequencies. Hence, the expression for the controllers Cm and Cs ineach direction is as follows:

CðsÞ ¼ P1

2pfzþ 1

12pfpþ 1

11

ð2pflpÞ2þ 2b

2pflpþ 1

: ð9Þ

The resulting controller-parameters for the controller structuregiven in (9) are given in Table 2 for Cm and Cs in z direction, as anexample. The values for the other controllers are given in (7).

5. Stability analysis

In this section, the tele-operation system is analyzed for passiv-ity using the system models in z direction. Previously, the assump-tion has been made that the operator is passive. A feedbackconnection of two passive systems is passive [18]. Hence, if Z�1

to ispassive, the complete tele-operation system is passive when theoperator is passive.

A system GðsÞ is passive if its poles have positive real parts [18].Hence, a SISO system is positive real if ReðGðsÞÞP 0. Or equiva-lently, lays in the right half plane of the polar diagram. Thisrequirement is equivalent to 90 < \ðGðsÞÞ < �90 [deg]. Becausepassivity is based on effort (force) and flow (velocity), this criterionshifts to 0 < \ðGðsÞÞ < �180 [deg], for tele-operation systemswhich input is force and output is position. Hence, the passivityof the system without operator, Z�1

to , can be proven by investigatingits phase behavior. The FRF’s in z direction of Z�1

to are illustrated inFig. 11 for the designed controller and the environments specifiedin Table 1. It can be seen that the phase crosses �180 [deg] atapproximately 20 [Hz] for all environments. Hence, the system isnot passive. This is caused by the non-collocated dynamics in themaster for actuation by the operator. However, the system maybe stable for a limited set of operator impedances.

An attempt was made to measure the operator impedance. Thehuman operator dynamics are very complex and hard to measure.The operator impedance strongly depends on the task and pose of

Table 2Controller parameters in z direction.

P fz [Hz] fp [Hz] flp [Hz] b [–]

Cm;z 525 2.5 30 60 0.7Cs;z 6 2.25 30 100 0.7

100 101 102

−100

−50

0M

ag. [

dB]

100 101 102−180−90

090

180

Phas

e [D

eg]

Frequency [Hz]

Fig. 11. Z�1to in contact with environment in Z direction: fat (dotted), muscle

(dashed), ribcage (solid). Input: force [N], output: position [m].

100 101 102−50−25

02550

Mag

[dB]

100 101 102−180−90

090

180

Frequency [Hz]

Phas

e [D

eg]

Fig. 12. Calculated transparency in contact with fat (dotted), muscle (dashed) andthe ribcage (solid) in z direction. Input: [–], output [—].

C.J. Zandsteeg et al. / Mechatronics 20 (2010) 767–777 775

the forearm. Hence, the human operator impedance is highly non-linear. Linear operator measurement strategies did not provide areliable operator model for stability analysis. However, Fig. 11shows that the system without operator is stable. The Small Gaintheorem [13] states that the system is stable for kLk < 1. Hence,the system is stable for operator impedances which satisfykZhk < kjZtok. This shows that the system is stable for a limitedset of operator impedances. However, it cannot be proven thatthe operator impedance is within this set. Experimental evaluationof the designed controller (Section 7) shows that the system be-haves stable during the task, which suggests that the human oper-ator impedance is a subset of the allowed operator impedance.However, this can only be validated by measuring operator imped-ances for the ultrasound task specifically.

6. Performance analysis

In this section, the performance of the system is analyzed. It isknown that the EFC control architecture without compensation ofdynamics cannot achieve perfect transparency. However, it isimportant that both magnitude and phase of the measured trans-parency are near ideal transparency. Hence, a requirement for goodtransparency is defined in this paper in (10), which constrains boththe magnitude and phase error. The value for the magnitude erroris chosen such that the different tissues can easily be discrimi-nated. The value for the phase delay is defined to constrain thephase delay within a quarter period. This requirement is used inthe performance analysis:

� 3 ½dB� 6 ZtoðjxÞZeðjxÞ

�������� 6 3 ½dB� ^ . . .

� 45 ½deg� 6 \ ZtoðjxÞZeðjxÞ

� �6 45 ½deg�: ð10Þ

Fig. 12 shows the calculated transparency of the system for thedesigned controller, using the frequency response of the master,the slave and the environment. It can be seen that the systemhas good steady state performance, since the transparencyZto=Ze � 1 for low frequencies. The good steady state performanceresults in correct stiffness perception at low frequencies. Hence,the operator is able to discriminate the different environments.According to the performance definition, the achieved transpar-ency is 0.5 [Hz], 1 [Hz] and 6 [Hz] in contact with fat, muscle andthe ribcage, respectively. Unfortunately, the transparency require-ment of 2 [Hz] is not met for the soft environments. However, theoperator is also still able to distinguish ribs and tissues clearly be-tween 1 and 2 Hz, because the transparency error is not in the

same order of magnitude as the difference in impedance betweenthe tissues and the ribcage. In contact with muscle and fat, thetransparency-error for frequencies above 1 [Hz] is mainly causedby the high impedance of Cm. The high magnitude for Cm is neces-sary to suppress the first mode-shape of the master, which in-creases the stability robustness for high operator impedances.However, the operator is able to discriminate soft and hard envi-ronments and will be able to locate and avoid the ribs for optimalimage quality.

7. Experiments

In this section the designed controller is validated. To illustratethe actual transparency of the system for the newly designed con-troller, both position and force of the operator can be comparedwith the position en force of the environment. However, the Ome-ga.6 is not equipped with a force sensor as mentioned in Section2.1. Therefore, a 1-DOF force sensor is mounted at the haptic mas-ter to be able to evaluate the control design frameworkexperimentally.

It has been shown in Section 2 that the system is decoupled andthe SISO controllers are designed similarly for all directions. The re-sults in this section are discussed for the z direction only, as anexample for the other directions. The experimental evaluationsfor the x and y directions are not discussed, since it was hardly pos-sible to mount a force sensor in these directions. The dynamicalproperties of the environment during the experiments are compa-rable to the ribcage.

The measured position and force of the environment and theoperator in z direction are illustrated in Fig. 13 for voluntary oper-ator motion of approximately 1.5 [Hz]. As illustrated, the systembehaves stable and contact instability did not occur during theexperimental evaluation. Good force tracking is obtained, sinceFe � Fh. The force tracking error at 1.5 [Hz] is 0.5–0.75 [N]. How-ever, the position tracking is not ideal. The position tracking erroris 1 [mm], which is mainly caused by the coulomb friction presentin the gear and the bearings of the z-joint of the slave. The coulombfriction in combination with the low bandwidth of the local posi-tion controller of the slave, Cs, results in a error between the posi-tion of the master and the slave. The coulomb friction in the z-jointis approximately 0.75 [N] and is felt by the operator via the posi-tion controller in the master Cm. This is a property of the EFC con-trol architecture. The coulomb friction also influences the forcetracking performance. The force tracking error is approximately0.75–1 [N] at the peaks. The coulomb friction is not taken into ac-count in the linear system models and causes a difference with theexpected performance of Fig. 12. However, this is an hardware is-sue which should be resolved (see Section 9).

0 2 4 6 8 102468

10

Forc

e [N

]

Time [s]

0 2 4 6 8 104

5

6

7

8 x 10−3

Posi

tion

[m]

Fig. 13. Measured position, X, and force, F, of operator (solid) and environment(dash-dotted) for the EFC controller in contact with a stiff environment.

776 C.J. Zandsteeg et al. / Mechatronics 20 (2010) 767–777

To illustrate the performance difference between a controllerwithout local force feedback slave and the newly designed EFCcontroller, a second experiment is performed under the same con-ditions as the previous experiment, for a Position–Force controlarchitecture [3,8]. Therefore, C5 and Cm are both set to zero, whileC2 and Cs are equal to the previously designed EFC controller.

The result is shown in Fig. 14 for the position-force controller. Itcan be seen that the error between operator’s and environment’sposition is approximately 7 [mm], which is increased with a factor7 in comparison with position tracking of the EFC control architec-ture. The error in force tracking is approximately 0.35 [N], which isslightly better than the EFC-controller. According to Klomp [8], theposition tracking in free motion of the Position–Force architectureis better than the EFC controller without compensation of dynam-ics, since the dynamics of the slave are not felt. However, in contactwith an environment the EFC architecture is much more balancedin terms of Force and Position tracking as illustrated in Fig. 13.

8. Application

The TOUP haptic tele-operation system, including the controllerdesigned in this paper, is successfully tested by St. Thomas’ Hospi-

0 2 4 6 8 10

0

2

4

6

8

Forc

e [N

]

Time [s]

0 2 4 6 8 10−202468 x 10

Posi

tion

[m]

Fig. 14. Measured position, X, and force, F, of operator (solid) and environment(dash–dotted) for the force-position controller in contact with a stiff environment.

tal, London, UK. After a test-period by sonographers of St. Thomas’Hospital, TOUP has been successfully used in their Cathlab duringsurgeries. Fig. 15 shows the use of TOUP during this surgery. At thismoment the results of this test are analyzed for furtherdevelopment.

9. Summary, conclusions and recommendations

This paper provided a step-by-step, data-based, loop-shapingapproach in the frequency domain to tune the EFC control architec-ture for transparency and stability robustness under the assump-tion of no time-delay. This framework is applicable for realsystems due to the use of measured frequency responses. The pro-posed framework has been applied and the controller is imple-mented in the TOUP tele-operation system of Philips AppliedTechnologies and all steps necessary in the control design are dis-cussed. The result is a haptic tele-operation controller, tuned forperformance and stability robustness, based on the tele-operationsystem’s dynamics. The approach is summarized in the flowchartas illustrated in Fig. 3.

In this framework, classical control theory can be used in thecontrol design for passive and non-passive systems. For the lattercategory, a measurement strategy to obtain the operator imped-ance is necessary for stability analysis using necessary stability cri-terions like the Nyquist criterion. Measuring representative humanoperator impedances is very difficult. The framework can be usedto show that the system is stable for a certain range of operatorimpedances, without identifying the actual operator impedance.However, it is still recommended to further investigate the model-ing of the human operator to validate if the operator impedance ispart of this set.

Experimental evaluation pointed out that the tuned EFC con-troller reduces the position error with a factor 7 in comparisonwith the Position–Force architecture. However, the force trackingperformance of the EFC architecture is slightly decreased in com-parison with the Position–Force architecture due to the coulombfriction in the hardware. Nevertheless, the tuned EFC controlleroutperforms the Position–Force controller in terms of transparencyas shown in Section 7. However, fully transparent performance isnot achieved with TOUP. This cannot be addressed to control de-sign procedure, but is caused by the system dynamics and the fric-tion in the slave. To increase the transparency of the system, thecoulomb friction in the gears of the slave manipulator should beminimized.

Fig. 15. TOUP used in a surgery at St. Thomas’ Hospital.

C.J. Zandsteeg et al. / Mechatronics 20 (2010) 767–777 777

Furthermore, this approach gives insight in the bottlenecks inthe dynamics of the TOUP tele-operation system for both stabilityrobustness and performance. For better stability robustness, therotational DOF’s of the haptic master should be redesigned suchthat the end-effector of the master decouples at a higher fre-quency. The increased stability robustness can be used to decreasethe impedance of Cm, which will result in a significant decrease inthe transparency-error of the system for the soft environments, asshown in Section 4.

The framework can also be used for other control architecturesthan EFC. An experimental comparison of several control architec-tures in terms of performance and stability robustness againstoperator impedances, using the proposed framework, would bevery interesting.

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