dynamic parameter identiﬁcation and analysis of...

Dynamic Parameter Identification and Analysis of aPHANToMTM Haptic Device

Amir M. Tahmasebi1, Babak Taati2, Farid Mobasser2, and Keyvan Hashtrudi-Zaad2

1. School of Computing, Queen’s University, Kingston, ON, Canada2. Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON, Canada

[email protected]

Abstract— In this paper, the dynamics of a SensAble Tech-nologies PHANToM Premium 1.5 haptic device is experi-mentally identified and analyzed. Towards this purpose, thedynamic model derived in [1] is augmented with a frictionmodel and is linearly parameterized. The identified modelpredicts joint torques with over 95% accuracy and producesan inertia matrix that is confirmed to be positive-definitewithin the device workspace. In addition, user hand forceestimates with and without including the identified dynamicsare compared with the measured values. The experiments arealso conducted for other typical installation conditions of thedevice, such as with force sensor mounted at the end-effector,using gimbal and counter-balance weight, and upside-downinstallation of the device. The contribution of different dynamicterms such as inertial, Coriolis and centrifugal, gravitational,and Coulomb and viscous friction for different installationsare demonstrated and discussed. The identified dynamic modelcan be used for hand force estimation, accurate gravity counterbalancing for different installation conditions, and model-basedcontrol systems design for haptic simulation and teleoperationapplications.

I. I NTRODUCTION

PHANToM is a force feedback haptic device which wasdesigned by Massie and Salisbury in 1994 and has been com-mercialized by SensAble Technologies Inc. The PHANToMPremium 1.5 is a desktop tool that allows for the explorationof application areas requiring force feedback in three degree-of-freedom (3-DOF).

Although PHANToM has been widely used in haptic andtelerobotic applications [2–4], its functionality is not satisfac-tory for some high performance applications, partly becausethe electrical and software subsystems of the PHANToMhaptic interface are unknown. To obtain the full functionalityof the robot, an accurate dynamic model is the first demandof researchers [5]. Dynamic model design for simulation,control, and contact force observation purposes requires theidentification of the dynamic parameters of the manipulatormodel. Dynamic parameter identification of robotic manipu-lators has been investigated by researchers [1, 4, 6–11].

The first parameter identification approach is to disman-tle various components of a manipulator and to measureand/or calculate the inertial parameters [6–8]. Using com-puter Aided Design (CAD) models, inertial parameters ofvarious components (links, transmissions, and actuators)canbe calculated based on their geometry and the materialsused. This method is not easy to implement and there

might be difficulties in measuring some of the dynamicparameters. Cavusogluet al. [1] have previously calculateddynamic parameters of PHANToM based on several simpli-fying assumptions. However, this technique introduces someinaccuracies due to geometric simplifications in modelling.Moreover, complex dynamic effects such as joint frictionare not considered. Mayedaet al. proposed the SequentialIdentification Method (SIM) [6] and conducted studies ondynamic models with no redundant parameters [7]. Naka-muro et al. [8] also derived the dynamic models of closed-link manipulators.

Experimental identification of robot dynamics has beenreported for industrial manipulators such as excavators [9–11]. It has been shown that dynamics of manipulators canbe linearly parameterized and identified using Least Squaresmethod (LS) [12]. In this work, the dynamic parameter iden-tification of PHANToM Premium 1.5 is experimentally in-vestigated. Our proposed method uses the dynamic structurederived in [1]. The method avoids some of the assumptionsmade in [1] (e.g.uniformity of link densities, etc.) and can beapplied to some other models of PHANToM series devicessuch as PHANToM Premium 1.0 and 3.0. The method canalso be easily applied every time the dynamics of the deviceis modified. This happens frequently as researchers oftenuse robots in different configurations (e.g. upside-down) orinstall sensors and tools which changes mass, inertia, and thelengths of different segments of the robot, see Figure 1. Insuch cases, calculation-based methods for identification aretime consuming and are sometimes inaccurate, particularlyif the added tools do not have simple geometric shapes.

The sequence of contents in this paper is as follows: Thedynamic equations of PHANToM including friction effect arepresented and linearly parameterized in Section II. Dynamicparameters of PHANToM under different installations areexperimentally identified and verified in Section III. Inaddition, the contribution of each dynamic component isexperimentally demonstrated and discussed. Section IV usesthe identified dynamic model for the accurate estimationof hand forces. Section V draws conclusions and discussesfuture work.

II. PHANTOM DYNAMIC MODEL

PHANToM Premium 1.5 has three degrees of mobility (3joints) and provides three translational DOF at its end-point

(a) (b)

(c) (d)

Fig. 1. PHANToM Premium 1.5 in different typical installation conditions;(a) “Normal”, (b) using gimbal and counter-balance weight, (c) with forcesensor mounted at the end-effector, and (d) upside-down installation.

as shown in Figure 1(a). Figure 2 shows the schematics of thedevice with three motors and the corresponding joint angles,θ1,θ2, andθ3, and a Cartesian frame attached to the end pointof the manipulator.

Fig. 2. Schematics of PHANToM with motors, corresponding joint anglesand the End-Point (EP) Cartesian frame.

Using the Euler-Lagrange method, Cavusogluet al. [1]derived the following dynamic structure and equations ofmotion for PHANToM

τ = M(Θ)Θ + C(Θ, Θ)Θ + N(Θ) (1)

or

τ1

τ2

τ3

=

M11 0 00 M22 M23

0 M32 M33

θ1

θ2

θ3

+ (2)

C11 C12 C13

C21 0 C23

C31 C32 0

θ1

θ2

θ3

+

0N2

N3

whereM , C, andN represent the inertial matrix, Coriolisand centrifugal matrix, and gravitational vector, respectively,

defined in terms of the inertial and kinematic properties ofthe device individual segments [1]. Here,τ = [τ1 τ2 τ3]

T

andΘ = [θ1 θ2 θ3]T are the torque command voltage vector

sent to the amplifier box and the joint angle vector read bythe encoders, respectively. The reader should note that in [1],τ represents the vector of induced motor torques rather thanthe torque command voltage. As the electric dynamics ofthe motors and the amplifier box are assumed to be muchfaster than the mechanical dynamics of the motors and thelinkages, the torque command voltages are proportional tothe motor induced torques. Experimental results have shownthat actual motor torques can be found by scaling down thetorque command voltageτ by a factor ofα = 2.73. In thesequel, “torque” refers to the torque command voltage vector.

To identify the device dynamics, eq. (2) is linearly para-meterized as:

τ = Y(Θ, Θ, Θ)π (3)

whereY is the regressor matrix andπ is the vector of 8unknown parameters, defined as:

π=

[

πd

−−

πg

]

=

18(4Iayy+4Iazz+8Ibayy+Ibeyy+4Ibezz+4Icyy+4Iczz

+4Idfyy+4Idfzz+L21mc+L2

2ma+4L23mc+4L2

1ma)

18(4Ibeyy−4Ibezz+4Icyy−4Iczz+4L2

1ma+L21mc)

18(4Iayy−4Iazz+4Idfyy−4Idfzz−L2

2ma−4L23mc)

L1(L2ma+L3mc)

14(4Ibexx+4Icxx+4L2

1ma+L21mc)

14(4Iaxx+4Idfxx+L2

2ma+4L23mc)

−−−−−−−−−−−−−−−−−−−−−−−−−−−g2(2L1ma+2L5mbe+L1mc)

g2(L2ma+2L3mc−2L6mdf )

(4)

where πd and πg represent dynamic and gravitationalparameter vectors, respectively. The inertial and kinematicparametersL1, L2, L3, L5, L6, Iaxx, Iayy, Iazz, Icxx, Icyy,Iczz, Ibayy, Ibexx, Ibeyy, Ibezz, Idfxx, Idfyy, Idfzz, ma, mc,mbe, and mdf are defined in [1] andg is the accelerationgravity. The Y matrix is given in (5), wheresi, ci, sij ,cij , s2.i, and c2.i, i, j = 1, 2, 3, stand forsin(θi), cos(θi),sin(θi−θj), cos(θi−θj), sin(2θi), andcos(2θi), respectively.

A. Inclusion of Friction Model

The following classic model is used to include frictioneffect in the dynamic model of the device as:

τ f = τ fcsgn(Θ) + τ fvΘ (6)

or

τ f =

[

τf1

τf2

τf3

]

=

πfc1sgn(θ1) + πfv1 θ1



= Yfπf(7)

whereπfciand πfvi

are the Coulomb and viscous frictioncoefficients for joint “i”, and τ fc = diag(τfci

), τ fv =diag(τfvi

), i = 1, 2, 3. Yf andπf are defined as:

YT

=

[

YdT

−−

YgT

]

=

θ1 0 0

θ1c2.2−2θ1θ2s2c2−θ1θ2s2.2 θ21s2.2 0

θ1c2.3−2θ1θ3s3c3−θ1θ3s2.3 0 θ21s2.3

θ1c2s3−θ1θ2s2s3+θ1θ3c2c3 − 12

θ3s23+ 12

θ21s2s3+ 1

2θ23c23 − 1

2θ2s23−

12

θ21c2c3+ 1

2θ22c23

0 θ2 0

0 0 θ3

−−−−−−−−−− −−−−−−−−−− −−−−−−−−−−

0 c2 0

0 0 s3

(5)

Yf =

θ1 0 0 sgn(θ1) 0 0

0 θ2 0 0 sgn(θ2) 0

0 0 θ3 0 0 sgn(θ3)

(8)

πf = [πfv1πfv2

πfv3πfc1

πfc2πfc3

]T (9)

wheresgn denotes the signum function. Considering fric-tion effects in the dynamic model, the totalY andπ expandto:

π =

πd

−−

πg

−−

πf

(10)

and

Y[3×14] = [Yd[3×6]Yg[3×2]

Yf[3×6]] (11)

III. E XPERIMENTAL RESULTS

In this section, the results of experimental parameteridentification are discussed and PHANToM dynamics areanalyzed. The experimental setup consists of a PHANToMPremium 1.5, an ATI Nano-17TM force/torque sensor anda real-time open-architecture control system developed in-house for full functionality of the robot. The developedopen-architecture platform1 that utilizes PHANToM ampli-fier box uses a Quanser Q8TM data acquisition board and aWinConTM /RTXTM real-time system, which links well withMATLAB Real-Time WorkshopTM . The sensory informationprovided by the setup are the three motor angles read byencoders, and six end-point generalized forces provided bythe force sensor in three Cartesian directions. Data collec-tion and control processes run at the rate of 1kHz. Jointvelocities are estimated from joint angles by using a high-pass filter numerical differentiator. Numerical calculation ofjoint accelerations significantly amplifies the noise and isnotrecommended. Instead, a filtering technique proposed in [13]is used to eliminate the need for acceleration measurement.To this end, the system total dynamic model (3), (10), and(11) is passed through a strictly stable low-pass filter withtransfer function such asL(s) = ω

ω+s, ω > 0 to obtain

τL = YL(Θ, Θ)π (12)

whereYL(Θ, Θ) andτL are filteredY andτ . The regressormatrix YL is a function of only joint angleΘ and joint

1For more information, refer to http://www.quanser.com

velocity Θ, since the filtered acceleration can be writtenas a function of joint velocity and filtered velocity; thatis θiL = ω(θi − θiL), i = 1, 2, 3. The elements ofYL

are given in (13) where the subscript “L” means that theargument has passed through filterL(s). By designing thefilter such that its cut-off frequency lies between the systembandwidth and the noise frequency, it is possible to attenuatethe degrading effects of the input and measurement noise onthe identification performance.

For identification experiments, a simple PD controller forangular position tracking was designed using SimulinkTM .The desired joint trajectory inputs were chosen for higherlevel of system excitation [14] needed for better convergenceof the identified parameters to their true values [12]. Towardsthis end, joint trajectories were constructed from severalsinusoids with various frequencies and amplitudes for eachjoint such that the robot workspace was not violated. As thesampling frequency was 1kHz, the chosen sine frequencieswere well below the Nyquist rate500Hz.

The experiments were all conducted for a time durationof 40 seconds. Since the low pass filter was implementedusing a memory unit in the discrete time domain, the firstfew seconds of the filtered data were discarded to allowfor the output of the filter to converge. The first half ofthe collected data were utilized to identify the dynamicparameters. For cross validation, the estimated parameterswere then employed to predict joint torques with the secondhalf of the data. Since filtered values of torque and jointvelocities were used in the estimation process, the filteredtorques were compared with their predicted values.

A. Effect of Friction

In the first experiment, friction parameters were not in-cluded and only 8 dynamic parameters,πd and πg, wereidentified. Figure 3 compares the actual filtered torqueτL

with two estimated filtered torquesτL = YLπ using theidentified parameters and the measured parameters providedin [1]. The large errors between the actual and the estimatedfiltered torques for joints 1 and 2 were expected to representthe unaccounted friction in joints and the power transmissionsystem. For clarification, the filtered torque prediction errors,τL − τL, are plotted versus joint velocities in Figure 4. Asit can be observed, substantial friction exists in all joints,especially in joint 1.

Therefore, six additional friction parameters were includedin the dynamic model as mentioned in Section II-A and 14π parameters were identified in total. The 14 identified pa-rameters and the 8 parameters calculated from the measuredvalues in [1] are shown in the second and the third columns

YLT =

YdLT

−−

YgLT

−−

YfLT

=

ω(θ1−θ1L) 0 0

ω[θ1c2.2−{θ1c2.2}L] θ21s2.2 0

ω[θ1c2.3−{θ1c2.3}L] 0 θ21s2.3

ω[θ1c2s3−{θ1c2s3}L] − 12[ωθ3s23−{ωθ3s23+θ2θ3c23+θ2

1s2s3}L] − 1

2ωθ2s23+{ 1

2ωθ2s23+θ2

2c23−12

θ21c2c3−

12

θ2θ3c23}L

0 ω(θ2−θ2L) 0

0 0 ω(θ3−θ3L)

−−−−−−−−−− −−−−−−−−−−−−− −−−−−−−−−−−−−

0 c2 0

0 0 s3

−−−−−−−−−− −−−−−−−−−−−−− −−−−−−−−−−−−−

θ1L0 0

0 θ2L0

0 0 θ3L

{sgn(θ1)}L 0 0

0 {sgn(θ2)}L 0

0 0 {sgn(θ3)}L

(13)

0 1 2 3 4 5 6 7 8 9

−0.1

−0.05

0

0.05

0.1

Motor #1 torque: τ1

Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9−0.1

−0.05

0


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9−0.3

−0.2

−0.1

0

0.1


Time(s)

Tor

que

(N.m

)

actual τ est. τ using identified paramsest. τ using measured params from [1]

Fig. 3. Actual and estimatedτ ; the solid black line shows the real filteredtorque, the dotted red line shows the predicted filtered torque using estimatedπ parameters (withoutfriction in the dynamic model), and the dash-dot blueline shows the predicted filtered torque using values given in [1].

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2−0.1

−0.05

0

0.05

0.1

Prediction error: τ1 actual

− τ1 estimated

Tor

que

(N.m

)

−1.5 −1 −0.5 0 0.5 1 1.5−0.05

0

0.05Prediction error: τ

2 actual − τ

2 estimated

Tor

que

(N.m

)

−4 −3 −2 −1 0 1 2 3 4−0.05

0

0.05Prediction error: τ

3 actual − τ

3 estimated

Ang. Vel.(rad/s)

Tor

que

(N.m

)

Fig. 4. Torque estimation error versus joint angular velocity (withoutfriction in the dynamic model).

of Table I. The two parameter sets have the same signsand are relatively close, which to some extent validates theassumptions made in [1]. Figure 5 illustrates the estimatedtorques with identified parameters after including frictionin the model. It can be observed that the estimated torquefollows the actual value closely.

0 1 2 3 4 5 6 7 8 9−0.2

−0.1

0

0.1

0.2


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9−0.1

−0.05

0


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9−0.3

−0.2

−0.1

0

0.1


Time(s)

Tor

que

(N.m

)

τactual

τestimated

Fig. 5. Actual and estimatedτ using identifiedπ parameters (withfrictionin the dynamic model).

In order to grasp a better view on the effect of eachfriction term, Coulomb and viscous terms are illustratedseparately in Figure 6. The first joint has the most significantfriction among all three. The effect of Coulomb friction isunanimously higher than that of the viscous friction for suchspeed of motion.

B. Various Configurations

Four additional installation configurations were consideredfor the PHANToM as described below:

1) Gimbal and counter balance weight mounted (GC):The gimbal and the counter balance weight supplied by themanufacturer are mounted on the PHANToM for additionalpassive DOF as shown in Figure 1(b).

2) Force sensor mounted (FS):For Haptic applications,measured hand force can be used in the design of transparentcontroller (Figure 1(c)).

0 1 2 3 4 5 6 7 8 9−0.1

−0.05

0

0.05

0.1Friction in joint 1

Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9

0

0.05


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9

0

0.05


Time(s)

Tor

que

(N.m

)

Total FrictionViscousCoulomb

Fig. 6. Contribution of viscous and Coulomb friction terms in overallfriction, in all three joints.

π [1] Normal GC FS USD USD+GCπ1 0.0076 0.0039 0.0093 0.0028 0.0033 0.0083π2 0.0030 0.0037 0.0121 0.0059 0.0044 0.0090π3 -0.0011 -0.0011 -0.0032 -0.0021 -0.0014 -0.0020π4 0.0025 0.0019 0.0252 0.0082 0.0018 0.0251π5 0.0066 0.0057 0.0206 0.0095 0.0078 0.0174π6 0.0025 0.0026 0.0097 0.0031 0.0035 0.0086π7 -0.0445 -0.0525 0.0735 0.1279 0.0580 -0.0453π8 -0.2015 -0.3002 0.1270 -0.1886 0.2969 -0.3070π9 - -0.0057 -0.0074 -0.0025 -0.0037 -0.0003π10 - -0.0035 0.0003 -0.0009 -0.0004 0.0015π11 - -0.0005 0.0031 0.0012 0.0025 0.0020π12 - 0.0707 0.0716 0.0739 0.0712 0.0665π13 - 0.0251 0.0228 0.0255 0.0225 0.0199π14 - 0.0248 0.0247 0.0273 0.0221 0.0238

TABLE I

ESTIMATED π PARAMETERS OF DIFFERENT CONFIGURATIONS; GC:

GIMBAL + COUNTER BALANCE , FS: FORCESENSOR, USD:

UPSIDE-DOWN, USD + GC: UPSIDE-DOWN + GIMBAL + COUNTER

BALANCE .

3) Upside-down (USD):One of the most common con-figurations of PHANToM, especially for medical simulators,is to install PHANToM upside-down for better ergonomics.

4) Upside-down plus gimbal and counter balance weight(USD + GC): Figure 1(d), shows a PHANToM 1.5 used inan ultrasound training simulator developed by the authors[15]. For this particular application, the gimbal and thecounter balance weight supplied by the manufacturer aremounted on the device. Therefore, the dynamic parametersfor this configuration has also been identified.

C. Observation

The π parameters estimated for each configuration arelisted in Table I. Note that for all configurations, frictionwasincluded in the dynamic model. The variance of the estimateswere in the range of10−6 and10−9. Note that the dynamicparameters signifying the dynamics from motor torques to

joint angles can be found by dividing theπ parameters inTable I byα = 2.73. The followings can be observed fromTable I:

(1) π7 and π8 correspond to the gravitational effect.By adding the gimbal and counter balance weight, theseparameters become very small. This verifies that the counterbalance compensates well for the gravitational effect.

(2) Comparingπ1 to π6 in “Normal” and GC columnsshows that adding gimbal and counter balance weight addssubstantially to the device inertia.

(3) Comparing π1 to π8 parameters for Normal andUSD configurations shows that changing the PHANToMinstallation to upside-down does not change the dynamicparameters except for the sign of the gravitational parametersπ7 andπ8. This confirms the fact that in USD configuration,the arm moves downward when it is not activated. InNormal installation, the arm moves in opposite direction.

(4) By adding the gimbal and counter balance weightto the upside-down configuration,π7 and π8 change theirsigns. But the high absolute values imply that the counterbalance weight is not compensating satisfactorily for thegravitational terms. Therefore, either a new counter balanceweight needs to be designed or active control shouldcompensate for gravity in USD configuration.

(5) The gravitational parametersπ7 andπ8, change from-0.525, and -0.3002 to 0.1279 and -0.1886 for force sensormounted configuration. Reduction in absolute values impliesthat force sensor acts as a counter balance weight.

(6) The viscous parametersπ9−π11, are small confirmingthat there is no significant viscous friction in PHANToMjoints.

D. Validation

RMS Normal GC FS USD USD + GCτ1 1.53 2.42 2.91 1.89 3.70τ2 1.15 0.84 1.09 0.81 1.29τ3 0.10 5.02 1.70 0.21 2.88

TABLE II

RMS VALUES OF THE ACTUAL AND ESTIMATED TORQUE ERRORS IN

PERCENT FOR DIFFERENT CONFIGURATIONS; GC: GIMBAL + COUNTER

BALANCE , FS: FORCESENSOR, USD: UP-SIDE-DOWN, USD + GC:

UPSIDE-DOWN + GIMBAL + COUNTER BALANCE .

For the entire workspace of the robot and for all instal-lations, the estimate of inertia matrix were confirmed to bepositive definite with a minimum eigenvalue of1.8 × 10−3.

The RMS values [11] of the filtered torque estimationerrors for all configurations are listed in Table II. The GC andUSD + GC configurations have the most significant errorsamong all others. This can be due to the movement of thegimbal since it is not possible to rigidly fix the gimbal to the

robot arm while the arm is moving. Any small movement ofthe gimbal can noticeably change the dynamics of the robot.

E. Dynamic Dissection

In order to further analyze system dynamics, theestimatedπ parameters are used to calculate joints torquesand the corresponding contributions of inertia, Coriolis andcentrifugal, gravity and friction terms for each configuration.From Figures 7-11 that illustrate the contribution of theseterms for each configuration, the followings can be observedand concluded:

0 1 2 3 4 5 6 7 8 9 10

−0.1

−0.05

0

0.05

0.1


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10

−0.1

−0.05

0

0.05

0.1


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10−0.4

−0.2

0

0.2

0.4


Time(s)

Tor

que

(N.m

)

τCoriolis and CentrifugalGravityInertiaFriction

Fig. 7. Contribution of inertia, Coriolis and centrifugal,gravity, and frictionin joint torqueτ (Normal configuration).

0 1 2 3 4 5 6 7 8 9 10−0.4

−0.2

0

0.2

0.4


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10−0.5

0

0.5


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10−0.4

−0.2

0

0.2

0.4


Time(s)

Tor

que

(N.m

)


Fig. 8. Contribution of inertia, Coriolis and centrifugal,gravity, and frictionin joint torqueτ (gimbal and counter balance mounted).

(1) Joint 1: For all installations, the most significantcontribution comes from friction, and Coriolis and

0 1 2 3 4 5 6 7 8 9 10−0.2

−0.1

0

0.1

0.2


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10−0.2

−0.1

0

0.1

0.2


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10

−0.2

−0.1

0

0.1

0.2


Time(s)

Tor

que

(N.m

)


Fig. 9. Contribution of inertia, Coriolis and centrifugal,gravity, and frictionin joint torqueτ (Force sensor mounted).

0 1 2 3 4 5 6 7 8 9 10

−0.1

−0.05

0

0.05

0.1


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10−0.1

−0.05

0

0.05

0.1


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10

−0.2

−0.1

0

0.1

0.2


Time(s)

Tor

que

(N.m

)


Fig. 10. Contribution of inertia, Coriolis and centrifugal, gravity, andfriction in joint torqueτ (Upside-down configuration).

centrifugal terms.

(2) Joint 2: The main contribution comes from inertialterm and then Coriolis and centrifugal terms.

(3) Joint 3: In general, the contribution of gravity in torqueis the most significant in joint 3 compared to other two. ForNormal installation, adding extra mass such as force sensorcuts down the effect of gravity by half and adding gimbaland counter balance weight almost practically nulls the effectof gravity.

IV. FORCEESTIMATION

Haptic interfaces produce sense of contact between humanbody and virtual objects by displaying a bi-directional forcechannel. To design transparent controllers high bandwidthcontact forces need to be measured or estimated. Using an

0 1 2 3 4 5 6 7 8 9 10

−0.2

0

0.2


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10−0.5

0

0.5


Tor

que

(N.m

)

0 1 2 3 4 5 6 7 8 9 10

−0.5

0

0.5


Time(s)

Tor

que

(N.m

)


Fig. 11. Contribution of inertia, Coriolis and centrifugal, and gravity in totalamount ofτ (Upside-down configuration plus gimbal and counter balancemounted).

accurate estimate of PHANToM, hand forces are estimatedand compared to the output of an ATI Nano-17TM forcesensor, mounted at the End Point (EP) of the device as shownin Figure 1(c).

Using the device Jacobian provided in [1], the hand forcecan be estimated from system dynamics as:

Fext =1

α(Jp)

−T (τ − Yπ − Joτ ext) (14)

where

J =

Jp

−−

Jo

=

l1c2 + l2s3 0 00 l1c23 00 −l1s23 l2

−−− −−− −−−

0 0 −1c3 0 0s3 0 0

(15)

is the Jacobian in the EP frame (see Figure 2) andτ ext

is the external torque measured by the Nano-17 sensor. Notethat i) forces are scaled byα in order to accommodate thegain of electronics, and ii)Fext can be found without theneed forτ ext by using pseudo inverse ofJ. The measuredforces provided by the force sensor are also transformed intothe EP frame as well.

Figure 12 compares the actual force in Y direction to theestimated forces obtained with (eq. (14)) and without usingthe dynamic model (i.e. Fext = 1

α(Jp)

−T (τ − Joτ ext)). Asit can be seen, under dynamic condition especially whenchanging the direction of motion, force estimation withdynamic model produces slightly better results.

V. CONCLUSION AND FUTURE WORK

We have successfully identified the dynamics of a Sens-Able Technologies PHANToM Premium 1.5 using an ex-perimental method. The advantages of our method over the

2 4 6 8 10 12 14

−4

−3

−2

−1

0

1

2

3

Estimated force (Fy) in EP frame

For

ce(N

)

2 4 6 8 10 12 14−0.6

−0.4

−0.2

0

0.2

0.4

Error of force estimation in EP frame: with and without including dynamic model

Time(N)

For

ce(N

)

Err. est.: Fyext including dyn

− Fymeasured

Err. est.: Fyext without dyn

− Fymeasured

Measured ForceEstimated Force including DynamicsEstimated Force without Dynamics

Fig. 12. (a) Measured and estimated forces expressed in EP frame;Fy in y-direction of EP frame, and the corresponding error (b) including dynamics,and (c) without including dynamic model.

previously developed CAD-based method are the inclusionof an efficient yet simple friction model, the ease of use forhandling alterations to the device dynamics, and applicabilityto other models of Phantom Premium devices. Free motionexperimental results demonstrated noticable Coulomb fric-tion in all three joints, especially in joint 1. The haptic devicedynamics for different installation configurations, such aswith force/torque sensor, with gimbal and counter balanceweight, and upside-down, were also identified, validatedand analyzed. Estimated dynamic parameters were able topredict joint torques and human hand contact forces withover 95% accuracy. The identified dynamic model will beutilized in inverse dynamics based controllers for haptic andteleoperation applications.

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