Improving Position Precision of a Servo-Controlled Elastic CableDriven Surgical Robot Using Unscented Kalman Filter

Mohammad Haghighipanah1, Yangming Li1, Muneaki Miyasaka2, and Blake Hannaford3

Abstract— Cable driven power transmission is popular inmany manipulator applications including medical arms. Inspite of advantages obtained by removing motors from themechanism, cable transmission introduces higher non-linearityand more uncertainties such as cable stretch and cable coupling.In order to improve the control precision and robustnessof the Raven-II surgical robot, particularly for automationapplications, the Unscented Kalman Filter (UKF) was adoptedfor state estimation. The UKF estimated state variables of theRaven-II dynamic model from sensor data. The dual UKF wasused offline to estimate cable coupling parameters. The experi-mental results showed that the proposed method improved jointposition estimation precision and the estimation consistency,especially on the more elastic links. The improvements for links2 and 3 of the Raven were 36.76%, and 62.99%, respectively.For link 1 the improvement was 1.43% because the transmissionis very stiff.

Index Terms— surgical robots, cable driven mechanism, flex-ible manipulators, Unscented Kalman Filter.

I. INTRODUCTION

In a robot with cable driven power transmission, motorscan be mounted on the base of the robot, resulting in lowermass and inertia on the arms [1]. Moreover, since motorsare not mounted on the joints, these manipulators are morecompact. In surgical robotics, compact design and low inertiaare requirements and consequently many advanced surgicalrobots such as da Vinci R© [2] and Raven-II R© [3] are cabledriven systems. However, a drawback of cable transmissionis that the cables are elastic and flexible. Furthermore cableproperties change over time due to cable stretch and creep(a property of cables in which they slowly lengthen underlong term load). Cable dynamic properties such as stiffnessand internal damping are known to vary as a function oftension [4], [5]. These changes may cause deformation whichseparates motor position from joint position. Furthermorein remotely mounted actuator systems, the motion of oneactuator (depending on the mechanical design) may causejoint motion in another link [6]. In a cable driven robot thisis called cable coupling effect. With time, variation in cabletension changes the cable coupling parameters. Furthermore,by not compensating the effect of cable coupling a significantstress can be applied on cables which reduces the lifetimeof cables. Therefore being able to estimate these parameters

1Mohammad Haghighipanah (mpanah@uw.edu) and Yangming Li(ymli81@uw.edu) Department of Electrical Engineering

2Muneaki Miyasaka (muneaki@uw.edu) Department of MechanicalEngineering.

3Blake Hannaford (blake@u.washington.edu) Departments ofElectrical Engineering, Mechanical Engineering, and Surgery

University of Washington, Seattle, WA 98195, USA

online can improve not only the precision of robots but alsoincreases the lifetime of cables.

Most medical manipulators are closed-loop servo-controlled mechanisms. Closed loop control requires theprecise measurements of each joint. The most commonapproach is to use an optical encoder on the shaft of eachmotor and use deterministic forward kinematics to calculatejoint position. However this method assumes the drive train isinfinitely stiff and has no backlash. Adding additional opticalsensors directly on each joint is expensive and requires addi-tional wiring. Moreover in surgical robots, the use of an end-effector sensor may be difficult or costly due to sterilizationrequirements [4]. In Raven-II, all the encoders are mountedon the motors, and joint position is calculated solely based onMotor Position Sensing (MPS). Although cable stretch errorsare not generally perceptible in teleoperation, to exploreautomation of surgical tasks, more precise joint positionestimation is required. The Extended Kalman Filter (EKF)is widely used for state estimation of non-linear systems.However, the EKF uses the Taylor series to approximatelylinearize the system which is a source of errors. Moreover,its linearization step requires computing the derivative ofthe non-linear system. For such non-linear systems, Julieret, al.[7] proposed the Unscented Kalman Filter (UKF). TheUKF uses a deterministic sampling technique to computesigma points without a need for derivatives. The mean andcovariance of these sigma points describes the predicted state[8]. The UKF is simpler to implement and it is accurateto at least second order. As the non-linearity of the systemincreases, the UKF performs better than EKF [7]. TheUnscented Kalman Filter was used in [5] to estimate statesand parameters of one degree-of-freedom (DOF) cable driventest panel. It was shown that angle estimates were robustto variation of parameters, whereas velocity estimates werenot. However, state and parameter estimation of a multi-DOFserial chain robot were not investigated. In [1] the UKF stateestimation on an approximate model of a multi-DOF serialchain robot was applied on a simulated Raven. In simulationsthe UKF provided better estimates of joint angle in thepresence of cable deformation. A limitation of this work wasthat each link was approximately modeled as an independentlink. Cable coupling and the dynamic effects of multiplelinks on each other was not studied. The contributions ofthis paper are 1) Implementing the UKF in the real-timecontroller of an actual serial multi-DOF cable driven surgicalrobot and 2) estimating cable coupling parameters with theUKF to more precisely estimate joint positions. We firstidentify the cable coupling parameters off-line and then

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experimentally study whether or not increased accuracy injoint position measurement can be achieved using the UKFwithout joint sensors (although accurate joint sensors havebeen installed for validation in this study). The question willbe studied experimentally on the first three DOF of Raven-II. The proposed method can be applied to any cable drivenmechanism with a similar cable dynamics.

In this work, Raven-II was used to investigate the ef-fectiveness and robustness of the UKF to estimate jointstates of a cable driven power transmissions based only onmeasurements at the driving motors. The paper is organizedas follows. System modeling of a serial manipulator withelastic transmission and motor dynamics is explained inSection II. Methods for state and parameter estimation arecovered in Section III. Experimental methods are describedin section IV and Results and Discussion and Conclusionsare in Sections V through VII.

II. SYSTEM MODELING

A. Model

In this section, a dynamic model for a cable drivenmanipulator similar to [1] and [5] is presented. The generalform of the dynamic equation of a serial manipulator can beexpressed similar to [9] as:

ql = Il−1 [Γ− FH (ql, ql)] (1)

FH (ql, ql) = FC (ql, ql) + FG + diag (sign(ql))Fcl

+diag (ql)Fvl + JTFen (2)

Where: Il is Inertia matrix; J is Jacobian; FC are Coriolisand centrifugal; FG is Gravitational force; ql, ql, ql are Jointposition, velocity and acceleration, respectively; Fcl, Fvl arecoulomb and viscous friction, respectively; Γ, Fen are jointtorque and external torque, respectively.

The above model assumes the torque is directly appliedon the joints of the robot. However, in a cable driven mech-anisms, the applied torques in the motors are transformed bygears and transmitted through cables to the joints. Althoughin real systems cables are running through several idlerpulleys, we model each motor as 1) connected to a gearbox,2) the gearbox is connected to a motor capstan and 3) poweris transmitted from motor capstan to the joint via one cablewith nonlinear (exponential) tension-strain relationship, asshown in Fig. 1. With this simplification, similar to [1] thedynamics for each motor and transmission can be representedas: qm = (1/Im)(τ − τm − τrn) (3)

τm = τcmsign( ˙qm) + τvm ˙qm (4)τrn = rmcγ/N (5)

γ = ke(eqmcrmc−qlrl − eqlrl−qmcrmc)

+2be( ˙qmcrmc − qlrl)(6)

Γ = rlγ (7)

Where: qm, qm, qm: are motor position, velocity and accel-eration, respectively; ke, be: are cable stiffness and damping;τcm, τvm: are motor coulomb and viscous friction; rmc, rl:are capstan radius of motor and link, respectively; N, Im: are

the gear ratio and motor inertia of the motors, respectively;τ,Γ: are torques on motor and joint, respectively.

Fig. 1. Schematic drawing of a generic cable driven system. Motor shaftis connected to a gearbox and capstan is fixed on the gearbox shaft.

B. Inverse/Forward Dynamics

Inverse dynamics is used to compute torque needed for agiven joint motion. The inverse dynamics is computed usingthe Recursive Newton Euler algorithm. Forward dynamicsis used to compute acceleration given an applied torque.Our implementations of forward and inverse dynamics inthis paper are based on [9]. There are three main steps tocalculate the forward dynamics of the system given in (1).

1) Set joint acceleration to zero to calculate Coriolis, cen-trifugal, and gravity torques. When joint accelerationis zero, FH (ql, ql) is equal to Γ.

2) Set joint velocity, gravity, and coulomb friction to zero,and set joint acceleration to ui which is a unit basisvector with one in the ith row. Then, the ith column ofthe inertia matrix Ili is equal to the torque calculatedby inverse dynamics (Ili = Γ).

3) After calculating the FH and Il, joint acceleration canbe calculated from (1).

C. Hardware

The generic dynamic model of (1) has been applied tothe Raven-II experimental research platform. Raven-II hastwo cable driven arms with 7 DOF per arm. Its first threeDOF are dedicated to translational moves and the last fourdedicated to tool motion and orientation. The motors aremounted on the base of the robot and the encoders aremounted directly on the motors. The first three DOF useMaxon RE40 brushed DC motors with encoders (AvagoTechnologies, model number HEDM-5540, 4000 counts perrevolution). All the joints have a cable run from the motor tothe joint and back to the motor. Because of the motor gearratios, mechanism kinematics, cable pulley ratios, and cablecoupling the motor angles are related to joint angles by:qm1

qm2

qm3

=

tr1 0 0C01tr2 tr2 0C02tr3 C12tr3 tr3

ql1ql2ql3

(8)

Where,tr1 = (rl1/rm1)N1

tr2 = (rl2/rm2)N2

tr3 = N3/rm3

(9)

and ql1 , ql2 , ql3 are the joint positions for Joint 1, 2, and 3,respectively.rl1 = 63.095mm, and rl2 = 56.298mm are the pulley

radii of link 1 and 2. rm1 = rm2 = rm3 = 5.675mm are thepulley radii of motor capstan for link 1, 2, and 3, respectively.

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N1 = N2 = N3 = 12.25 is the gear box ratio for all motors.C01 = 0.14545, C02 = 0.007797, C12 = 0.008077 are thecable coupling terms of link 0 to 1, link 0 to 2 and link 1 to2, respectively. These values were derived from the geometryof link design.

D. Parameter Identification

To be able to simulate a robot using Eqn. (1), initial inertiamatrices, mass, and Center of Mass (COM) of the systemlinks must be identified. CAD models were used to determinethese parameters for the first three links of Raven-II (Fig. 2).

III. METHODSA. State Estimation

The system states for Raven-II are motor angle, motorvelocity, joint angle, and joint velocity for each link; the ob-servations come from the optical encoders directly mountedon the motor shafts. Thus, the value of the joint angle needsto be estimated. In this paper, the square root form of theUnscented Kalman Filter (srUKF) is used for state estimation[10]. The srUKF has improved numerical properties overstandard UKF and it guarantees positive-semi-definiteness ofthe state covariance [11].

To apply srUKF the state space form of the Raven isrequired which can be described as:

x = f(x,u)

y = Hx(10)

Where x and H are system states and the observation,receptively. The system states and observations for the firstthree links are defined as:xi :=

[qmi qmi

qli qli], i = 1, .., 3

x =[x1 x2 x3

]Thi :=

[1 0 0 0

],H = blkdiag(

[h1, h2, h3

])

(11)

Where i is the link number. The system inputs, u, areapplied torques at the motors and the measurements aremotor positions. The differential equation can be discretizedfor numerical integration using the fourth order ExplicitRunga Kutta method.

The system parameters which cannot be obtained fromthe CAD model are: Spring constant (ke), Damping constant(be), Coulomb and Viscous friction of the motor side (τcm,τvm) and the joint side (Fcl, Fvl). Furthermore, these pa-rameters depend on cable tension. The following calculationswere used to derive nominal parameter values with which toinitialize the UKF parameter estimation.

These parameters are empirically approximated as shownin Table I. With an external torque (τext), dynamic model ofjust a motor can be represented as:

qmIm = τ − τcmsign(qm)− τvmqm + τext (12)

We applied a weight statically to a lever arm on the motorshaft and gradually increased it until the motor started toturn. At the time the motor starts to turn, Eqn.(12) becomesas follows and the Coulomb motor friction was obtained.

τcm = τext (13)

A known weight was applied to a string wound around thecapstan so that motor turned at a steady state velocity (qm,ss).This case, Eqn.(12) reduces to Eqn.(14) and viscous frictionwas calculated.

τvm =−τcmsign(qm,ss) + τext

qm,ss(14)

For inertia of the motor, we applied a constant input torquethat could induce non-zero motor acceleration. Using τcmand τvm, the input motor torque, and the measured motorvelocity and acceleration, Eqn.(15) yields the inertia of themotor.

Im =τ − τcmsign(qm)− τvmqm

qm(15)

Fcl is the lumped sum of the pulley and joint Coulombfriction. We experimentally measured the Coulomb frictionalforce of the pulley when applying average tension. Wealso estimated Coulomb joint friction based on the averagenormal force on the joint shaft and the coefficient of frictionfor steel on steel with lubrication. The estimated value ofFvl was selected to be about two orders of magnitude lowerof Fcl [5].

The value of ke was estimated by applying loads on asample cable and recording the stretch. be is calculated froman experiment in which a load is released and the decay ofsubsequent oscillations in length was measured by a laserdistance sensor.

TABLE IUNKNOWN PARAMETERS OF THE SYSTEM. THESE PARAMETERS WERE

EMPIRICALLY MEASURED.

Symbol Value Value Value Unit(link 1) (link 2) (link 3)

Fcl 0.505 0.49 0.53 Nm, NFvl 0.00505 0.0049 0.0053 Nms/rad, Ns/mke 720e3 88e3 9.25e3 N/mbe 4000 1380 400 Ns/mτcm 8.11e-2 4.11e-2 5.11e-2 Nmτvm 1.9e-4 1.8e-4 7.1e-4 Nms/radIm 2.847e-4 2.847e-4 2.847e-4 kgm2

B. Cable Coupling Parameter Estimation

To estimate cable coupling parameters the dual UKF wasused. In the dual UKF, a separate state-space representa-tion is used for states and parameters[12]. The state spacerepresentation for state is same as Eqn.(11) except for theobservation both motor sensors and attached joint sensorswere used offline, which makes hi 2x4 matrix. The statespace representation for the weights is given by:

wk+1 = wk + rk (16)dk = G(xk,wk) + ek (17)

Where, wk is the stationary process with identity statetransition matrix which represents the unknown parameters,G(xk,wk) is a nonlinear mapping that is parameterized bythe vector w. rk is the process noise, ek is the error ofthe machine, and dk is the desired output from nonlinearobservation on wk[13].

srUKF was implemented in C++ and was used to estimatethe system states online and cable coupling parametersoffline. The main objective of the UKF in this work is to

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Fig. 2. CAD models of the Raven for first three joints. CAD derived mass of links 1, 2, and 3 are 0.503Kg, 0.753Kg, and 0.407Kg, respectively.

better estimate joint angles of the first three Raven axesonline. Thus, to verify the effectiveness of the UKF in findingthe true state of the joint angles, the joints were instrumentedwith additional optical encoders (Avago Technologies, modelnumber AEDA-3300, 80000 counts per revolution, first twojoints and linear optical encoder MicroE Systems, modelnumber Mercury II 1600, resolution 5 µm, for the thirdprismatic joint) (Fig. 3) and their output was recorded forcomparison with the estimated joint angles.

To initialize the value of its motor encoders, the robotundergoes a process known as “homing”. During “homing”,each joint rotates until it reaches physical joint limits. At thisposition, the encoders are initialized. Both the motor positionsensors and attached joint position sensors are synchronizedand initialized during homing.

To test the algorithm, a sinusoidal desired trajectory wascreated for each joint. A PD controller based on feedbackfrom the motor encoder drove the motor to follow the inputtrajectory. Since the main objective of this paper is to studythe state estimation performance of the UKF and not the PDcontroller, the feedback input of the controller is the motorposition, not the UKF estimated states or the joint encoders.Furthermore, accurate tracking by the PD controller is notrequired because the UKF is tasked with estimating actualjoint trajectories.

To study the robustness of the state estimation, the UKFwas tested under two different cable tensions (Table II). Inaddition, in a real world scenario, when the robot picks up anobject, the system dynamics change. To test the robustnessof the system under varying loads, the robot picked up anobject weighing (100 g) under High tension.

The srUKF algorithm, Raven forward/inverse dynamics,and Raven control software were implemented in C++ andcommunicated with each other using “topics” of the RoboticOperating System (ROS)[14] for real time communications.From the Raven control software, a node called “r2control”publishes states of the robot in real time through a topiccalled “ravenstates”, and the UKF subscribes to the sametopic to receive joint states and torques. The computerrunning the square root UKF is Linux ubuntu 12.10 64-bitsystem with Intel Core i5-3330 processor and 8GB of RAM.

IV. EXPERIMENT PROCEDURE

In Raven-II, the tensions can be altered by screw adjustersfor each axis. However currently, it is not possible to measure

Fig. 3. Optical incremental encoders are mounted directly on each jointto measure the actual joint position for validation. Their value was usedonly for validation and not used in the controller or the UKF online stateestimation.

the tension of the cables precisely. Thus, the High andLow tensions were roughly approximated by trial and errormeasurements on an off-robot pulley-board system. Table IIshows the approximate tension values for each link.

In the first set of experiments, cable coupling parameterestimation was performed offline to estimate cable couplingparameters for High and Low tensions using the sametrajectory. The estimated parameters were used online forstate estimation.

Next, the following three experiments were performedto investigate the UKF state estimation performance androbustness.

Joint High (Kg.) Low (Kg.)1 5.2 2.82 4.4 1.83 4.2 1.4

TABLE IIMEASURED CABLE TENSIONS OF EACH JOINT.

A. High Tension Performance

• The cable tension of each link was set to the High value.• The accuracy of joint position estimation during the

sinusoidal trajectory was measured and compared withand without the use of the UKF.

B. Low Tension Performance

• The steps in experiment A were repeated under Lowtension.

Experiments A and B allow evaluation of how well theUKF estimates joint position under variations in cable ten-sion. Another parameter which can be easily altered is link

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Fig. 4. Offline Cable Coupling parameter estimation for High and Lowtensions.

mass. In Experiment C, we study the robustness to changesin mass.

C. Robustness to Added Mass

• The cable tension was set to the High value.• Robot picked up a 100 g object and the steps in

experiments A were repeated. 100 g was chosen becausein surgery usually the loads on the graspers are muchless than 100 g.

In these experiments a Proportional Derivative (PD) con-troller on Raven-II was used to make each link approximatelyfollow a desired sinusoid trajectory with frequencies 0.3424Hz for Joint 1, 0.3852 Hz for Joint 2, and 0.4565 Hz for Joint3. These frequencies were chosen from recorded trajectoriesof subjects performing the Fundamentals of LaparoscopicSurgery (FLS) [15] block transfer task. The feedback inputof the PD controller was only the motor position.

The input of the system dynamics that is used in the UKFwas the generated torque from the PD controller and onlymotor positions were used as the observation for the UKFonline state estimation. In the UKF, α defines the spread ofthe sigma points around mean and is set to a small value (1e-3), κ is a secondary scaling parameter and is usually set to0, and β is used to incorporate the prior use of a distribution.For Gaussian distribution optimal β value is 2 [12]. In thispaper the process noise covariance Rv and the measurementcovariance Rn are used to control the convergence of theUKF and they do not represent the real noise in the system.For further detail see [7],[8].

V. RESULTS

Cable coupling parameter estimation for High and Lowtensions were estimated offline. The results are shown inFig. 4. Data collected in Experiment A (High tension) isplotted in Fig. 5 which shows the estimated angular positionwith and without the use of the UKF. The reference truevalue from the attached optical encoders were also plottedto demonstrate the true joint values. Fig. 6 shows the sameresults collected in Experiment B (Low tension).

Data were also recorded from Experiment C (Fig. 7) forposition of Joint 1 through 3.

Fig. 8. Error statistics for position estimation of joint 1-3 for all theexperiments; High Tension, A; Low Tension, B; Robustness to Added Mass,C.

TABLE IIIRMS AND PEAK POSITION ESTIMATION ERRORS FOR EXPERIMENTS

A-C. RESULTS WITH GREATER THAN 15% DIFFERENCE ARE SHOWN IN

BOLD.

RMS Error Peak ErrorExp. Joint UKF Non UKF UKF Non UKF Unit

A 1 1.3830 1.4070 2.5619 2.4281 Deg.2 1.9394 3.6137 5.3315 5.6128 Deg.3 0.0929 0.2647 0.2634 0.3538 cm

B 1 1.1945 1.2070 2.5367 2.2899 Deg.2 1.2417 1.3023 3.0223 3.3524 Deg.3 0.0927 0.2437 0.2907 0.3593 cm

C 1 1.3063 1.3263 2.6769 2.3506 Deg.2 1.8245 2.9990 4.6896 4.8877 Deg.3 0.0927 0.2437 0.2608 0.3422 cm

The RMS estimation errors for joint position of all thejoints under both tension conditions were calculated withand without the use of the UKF as:

RMS = (1/n)

n∑i=1

|(xest − xtrue)| (18)

The RMS and peak errors for joints 1-3 are shown in TableIII.

The percent improvement of the UKF position estima-tion relative to motor measurements can be computed byEqn.(19). The average RMS position errors and percentimprovement of the three experiments for joints 1-3 areshown in Table IV.

%Imp. = 100×(NonUKFest−UKFest)/NonUKFest (19)

TABLE IVAVERAGE POSITION ERRORS AND IMPROVEMENT OF ALL THE

EXPERIMENTS

Joint Avg. Avg. % Improvement(Unit) UKF RMS Non UKF RMS

1 (Deg) 1.2946 1.3134 1.4342 (Deg) 1.6685 2.6383 36.763 (cm) 0.0928 0.2507 62.99

To visualize the error and uncertainty, error bars for allthe joint positions experiments A-C are shown in Fig.8.

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Fig. 5. Actual, kinematic estimation, and UKF estimation comparison in experiment A. First row shows joint trajectories for joints 1, 2 and 3 respectively;second row shows corresponding error histogram for joint 1, 2 and 3 respectively.

Fig. 6. Actual, kinematic estimation, and UKF estimation comparison in experiment B. First row shows joint trajectories for joints 1, 2 and 3 respectively;second row shows corresponding error histogram for joint 1, 2 and 3 respectively.

Fig. 7. Actual, kinematic estimation and UKF estimation comparison in experiment C. First row shows joint trajectories for joints 1, 2 and 3 respectively;second row shows corresponding error histogram for joint 1, 2 and 3 respectively.

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VI. DISCUSSIONThe UKF performance was evaluated on Raven but we

believe that this work can be extended to any cable drivenmechanism. The cable coupling parameters were estimatedutilizing the UKF dual parameter and state estimation offline.The observation vector for offline parameter estimation con-tained both the motor angles and the joint angles. In theexperiments online, the UKF outputs and Raven kinematicsoutput without the use of the UKF were compared withinstalled joint sensors output. The joint sensor outputs wereconsidered as the true value because they are mounteddirectly on each joint axis.

From Fig. 4 all the three cable coupling parameters underboth High and Low tensions converged in from 60-500iterations. The C01 which is the cable coupling terms oflink 0 to 1 converges in about 60 seconds of robot operationwhereas C02 and C12, the cable coupling terms of link 0 to2 and link 1 to 2, converged at a much slower speed.

Table III shows the joint position estimation performanceof the UKF for all the three joints. The table shows thatthe UKF joint position estimation performed better and hadbetter RMS error values for all three joints in all cases. Also,the UKF peak error for Joint 2 and 3 was better in all thecases. The joint position estimation of the UKF for Joint1 was similar to the Raven kinematics output because thelength of the cable for Joint 1 is only 5.6 cm, which makesthe transmission very stiff, therefore the cable deformationfor Joint 1 negligible. Clearly the UKF will not providemore information if the transmission from motor to joint ishighly stiff. When the dynamics of the system is perturbed bychanging the cable tension or end-effector inertia, the errorsin the UKF estimation are still small compared to the errorswithout the UKF.

From the error bars in Fig. 8, the UKF position estimationis more stable and consistent for joint 2 and 3, whichindicates better robustness. In a surgical robot, not onlyprecision but also robustness is important. The robustness ismore pronounced in Joint 3, which further indicates that asthe link transmission elasticity increases the simple forwardkinematic method is not sufficient to estimate states andmore sophisticated state estimation method is beneficial.Also, from Table IV it can be seen the percent improvementincreases as elasticity increases.

VII. CONCLUSION & FUTURE WORKThis paper applied the Unscented Kalman Filter to esti-

mate the states of a serial cable driven mechanism usingonly motor angles on an experimental surgical robot platform(Raven-II) and also investigated the possibility of estimat-ing cable coupling parameters with the UKF. Through theexperimental results, it was verified that the UKF positionestimation outperforms motor measurements plus kinematicson both precision and robustness. Also, as the transmissionstiffness decreases, the use of the UKF is more necessary.Also, the robustness experiments suggest that the UKF isrobust to meaningful loads that can be added to the tip ofthe robot.

The future work will include using a camera to increasethe accuracy and performance of the robot. A visual markerwill be placed on the end-effector and by utilizing the inversekinematics, the end-effector position will be added as anadditional observation vector to the UKF.

ACKNOWLEDGMENT

We would like to thank the Korean Institute of Science andTechnology (KIST, Dr. Hujoon project), and the NationalScience Foundation (grant number 1227406) under a sub-contract from Stanford University, and National Institutes ofHealth (grant number 5R21EB016122-02). Also, the authorswould like to thank Biorobotics lab, University of Washing-ton and the reviewers.

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