Abstract—Precision, robustness, dexterity, and intel-ligence are the design indices for current generationsurgical robotics. To augment the required precision anddexterity into normal microsurgical work-flow, handheldrobotic instruments are developed to compensate phys-iological tremor in real time. The hardware (sensors andactuators) and software (causal linear filters) employed fortremor identification and filtering introduces time-varyingunknown phase delay that adversely affects the deviceperformance. The current techniques that focus on three-dimensions (3-D) tip position control involves modelingand canceling the tremor in three axes (x-, y-, and z-axes)separately. Our analysis with the tremor recorded fromsurgeons and novice subjects shows that there existssignificant correlation in tremor across the dimensions.Based on this, a new multidimensional modeling approachbased on extreme learning machines is proposed in thispaper to correct the phase delay and to accurately model3-D tremor simultaneously. Proposed method is evaluatedthrough both simulations and experiments. Comparisonwith the state-of-the art techniques highlight the suitabilityand better performance of the proposed approach fortremor compensation in handheld surgical robotics.
Index Terms—Extreme learning machines (ELMs), hand-held robotics, multidimensional modeling, physiologicaltremor.
Manuscript received January 3, 2016; revised March 23, 2016 and May16, 2016; accepted May 18, 2016. Date of publication August 2, 2016;date of current version January 10, 2017. This work was supported bythe Basic Science Research Program through the National ResearchFoundation of Korea funded by the Ministry of Education, Science andTechnology under Grant NRF-2014R1A1A2A10056145. (Correspondingauthor: Kalyana C. Veluvolu)
S. Tatinati is with the School of Electronics Engineering, College ofIT Engineering, Kyungpook National University, Daegu 702-701, SouthKorea (e-mail: [email protected]).
K. Nazarpour is with the School of Electrical and Electronic Enineeringand the Institute of Neuroscience, Newcastle University, Newcastle, NE17RU, U.K.
W. T. Ang is with the School of Mechanical and Aerospace Engi-neering, Nanyang Technological University, Singapore 639798 (e-mail:[email protected]).
K. C. Veluvolu is with the School of Electronics Engineering, College ofIT Engineering, Kyungpook National University, Daegu 702-701, SouthKorea, and also with the School of Mechanical and Aerospace Engi-neering, Nanyang Technological University, Singapore 639798 (e-mail:[email protected]).
Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIE.2016.2597119
I. INTRODUCTION
PHYSIOLOGICAL tremor is a major impediment to per-form delicate and fine motor tasks, such as microsurgery
[1], [2]. In microsurgical procedures, the surgeons hand motionmust be precise at the magnitude smaller than few microme-ters (10 μm) [1]. Even under normal conditions, physiologicaltremor exists in normal human motions to some degree withamplitude of approximately 100 μm [2], [3], and it adverselyaffects the outcome of the microsurgery. Consequently, surgicalrobots are being developed to provide surgeons with the requiredprecision and dexterity to execute the microsurgical proceduressuccessfully. Over the past two decades, the surgical roboticshave evolved from autonomous robots to teleoperating robotsand now to handheld robotic instruments [4], [5]. For these sur-gical robotic instruments, precision, dexterity, and intelligenceform the design indices.
The advent of handheld instruments has created an oppor-tunity to augment the required precision and dexterity into thenormal surgical work flow by compensating the tremulous mo-tion [6], [7]. The working principle of typical handheld instru-ments is simple as shown in Fig. 1 and it involves subsequentexecution of following three steps:
1) sensing its own motion;2) filtering the involuntary motion from the sensed motion;3) actuating the surgical end effectors (instrument tip) based
on the filtered involuntary motions to compensate for theerroneous motions.
To possess the advantages of being compact, multidimen-sional freedom as a conventional surgical instrument, andless obstructive to manipulate, the handheld instruments areembodied with miniature microelectromechanical systems(MEMS)-based inertial sensors to sense its own motion inthree-dimensions (sensing unit) and piezo-electric actuators tomanipulate the instrument end effector (compensation unit),as shown in Fig. 1 [6], [7]. The intelligence to identify, filter,and accurately model the involuntary motions from the wholesensed motion is provided by the adaptive signal modeling unit(modeling unit) [7], [8]. Furthermore, this unit generates thecontrol signal for the three-dimensional (3-D) tip motion tocompensate tremor (compensating unit) based on the modeledtremor motion. For effective tremor compensation, all the abovethree stages have to be executed in one cycle (sample period) [7].
1646 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 2, FEBRUARY 2017
Fig. 1. Active physiological tremor compensation and effect of phasedelay. (a) Phase delay at various stage in a typical handheld instrument.(b) End compensation of physiological tremor (ideal case). (c) Phasedelay effect on end compensation.
The voluntary hand motions during microsurgery are oftensuperimposed with the involuntary motions such as physiologi-cal tremor, drift, noise and chorea, etc. The meticulous nature ofthe microsurgical procedures restricts the voluntary movementsto low-frequency components, i.e., less than 2 Hz [9]. Conse-quently, frequency selective linear filters have been employedto filter tremulous motion [10]. These linear filters serves alsoin removing the notorious numerical-integration drift due todouble-integration and other unwanted noise/drift that comesfrom the sensing unit while converting the sensed motion inthe acceleration domain to position domain, as shown in Fig. 1.As physiological tremor lies in band of 6 to 14 Hz, the inherentphase lag as small as 10◦ (20 ms) can generate an out-of-phasecontrol signal for compensation unit and this exacerbates the tipmotion at the instrument end effector rather than compensatingit. To illustrate the effect of a phase delay on the instrument’s tipposition control, comparison between the corrected tip obtainedwith actual tremulous motion and delayed tremulous motion(obtained as described in Section II) for a typical trial is shownin Fig. 1(c). The experiments conducted with handheld instru-ment (Micro) showed that the phase delay of liner filtering stagelimited the compensation accuracy to only 20% and also desta-bilized the eye-had feedback loop [11].
Various factors such as causality, resolution and responsetime of sensors, phase delay, and drift also effect the real-timeperformance [7], [10]. It is now evident that the phase lag is thesingle major factor that adversely effects the end compensation
accuracy [8]. In the sensing unit shown in Fig. 1, the presence ofan on-board low-pass filter in accelerometers introduces a phasedelay of 3 ms. An additional delay of 1 ms is identified as theresponse time for piezo-electric actuators. As the bandpass filteremployed in the modeling unit introduces frequency dependent(unknown) delay of 12–16 ms, a total delay in the range of16–20 ms is unavoidable from sensing to compensation in thesehandheld instruments.
Adaptive filtering techniques that rely on truncated Fourierseries (weighted Fourier linear combiner (WFLC) and band-limited multiple Fourier linear combiner (BMFLC) [12]–[15])have been popular to model the tremulous motion without anyphase delay. Recently, in [15], a quaternion version of WFLC(QWFLC) has been developed to model the tremulous motion inquaternion domain and empirically proven to be more effectivethan the real domain WFLC. Further, the method QWFLC alsodemonstrated the effectiveness of multi-dimensional couplingin accurate modeling of tremor compared to uni-dimensionalWFLC. Although, these methods accurately model the tremu-lous motion, the study in [10] demonstrated that the unknownphase-delay introduced by the pre-filtering stage adversely af-fects the final outcome. Consequently, the design indices for theadaptive tremor modeling algorithms are:
1) accurate tremor modeling;2) unknown phase-delay correction; and3) less computational complexity.
To this end, autoregressive methods [16], BMFLC, and leastsquares support vector machines (MWLS-SVM) [17] methodsare customized to perform a multistep prediction of the physio-logical tremor to counter the known and unknown phase delays.Among the existing methods, MWLS-SVM manages to meetall the indices, there is, however, much scope for improvementin terms of accurate modeling of unknown phase delay andreducing the computational complexity. To date, all these ex-isting methods consider the sensed motion in three-dimensionsas three independent signals. To achieve the 3-D tremor esti-mation and compensation, the adaptive filtering method mustbe applied to all the three axes separately. Hence, a multidi-mensional approach that can better utilize the information fromcross channels to counter the unknown phase delay and providemore accurate 3-D tremor is required.
Several popular signal processing methods like support vec-tor machines (SVM) have been extended to multidimensionalframework from the original single-dimensional (1-D) frame-work [18]. The improved multidimensional framework, how-ever, might suffer from either loss of generality or significantincrease in computational complexity due to the lack of multidi-mensional modeling scheme in its cost function [19], [20]. It hasbeen empirically proved that innate structure of single hiddenlayer feedforward networks (SLFN) can provide multidimen-sional modeling simultaneously where each output node canserve as the modeled output for each dimension [21]. Extremelearning machines (ELMs) is one of the effective learning pro-cedure to learn the SLFN parameters and has been successfullyapplied in solving regression, function estimation, and multi-class classification problems [19], [21], [22]. Further, it is es-tablished that the ELM has a better generalization performanceand less computational complexity [19]–[21].
TATINATI et al.: MULTIDIMENSIONAL MODELING OF PHYSIOLOGICAL TREMOR FOR ACTIVE COMPENSATION IN HANDHELD SURGICAL ROBOTICS 1647
Fig. 2. Proposed unified approach for 3-D tremor modeling.(a) Pro-posed multidimensional (3-D) approach for delay correction,(b) Offlinetraining for nonlinear mapping identification.
Motivated by this, in this paper, we developed a unified mul-tidimensional modeling approach with the ELM, which is capa-ble of integrating the cross-dimension couplings, and simultane-ously solve the phase delay correction and thereby provide moreaccurate 3-D tremor modeling with less computational complex-ity. The cost function of the conventional ELM does not havethe multidimensional form. Consequently, it provides unequalpenalty for all dimensions and it might affect the multidimen-sional modeling performance. To address this issues, a robustmultidimensional ELM (md-RELM) that provides equal penaltyfor all dimensions is developed in this paper. Further, to adaptto the nonstationary characteristics of a tremor, we also proposean online sequential update for the md-RELM (OS-mdRELM).To quantify the suitability of the proposed multidimensionaltechnique for tremor modeling, analysis was conducted on thetremor data collected from microsurgeons and novice subjects.The proposed technique is also validated experimentally withhandheld robotic instrument (iTrem). Results showed that theproposed multidimensional paradigm significantly improves thetremor modeling accuracy compared to the state-of-the-art mod-eling techniques.
In Section II, the proposed multidimensional tremor modelingapproach with several ELM variants are discussed. Section IIIpresents the performance evaluation of the proposed methodswith tremor data. Discussions, future work, and conclusions areprovided in Sections IV and V, respectively.
II. METHODS AND MATERIALS
The main objective of this study is to develop a unifiedframework that can effectively solve the phase delay correctionand provide more accurate 3-D tremor estimation. In whatfollows, we shall discuss on how these challenges are addressedin this paper:
1) Phase Delay Correction: Unknown and time-varyingfrequency-dependent delay in the range of 16 to 20 ms is in-evitable due to the presence of various linear filters at differ-ent stages in the signal processing chain. This delay correc-tion problem is considered as a classical learning problem ofestimating an unknown relation between the elements of an in-put space (S ∈ Rm ) and elements of an outer space (T ∈ Rn ),as shown in Fig. 2(b). The elements of input space are thephase-distorted tremulous motion components obtained afterconventional bandpass filter and the elements of output spaceare the actual tremulous motion components obtained with azero-phase bandpass filter. In this study, we adopt the ELM toidentify a generalized and accurate inverse-mapping nonlinearfunction (β(·)) such that β(s ∈ S) ≈ t ∈ T .
2) 3-D Tremor Modeling: By the very nature, the 1-D model-ing techniques lack the structure to utilize the cross-dimensionalcoupling information. By its inherent structure, the learningmethod ELM is capable of integrating the cross-dimension cou-plings. To simultaneously also solve the phase delay correctionwith the inverse-mapping function, a robust multidimensionalmodeling based on ELM is developed.
3) Computational Complexity: The innate structure of theELM facilitates modeling of a tremor in three dimensions si-multaneously. Therefore, the computational power required toachieve a 3-D tremor modeling can be significantly reducedwith the proposed multidimensional approach compared to thatof conventional 1-D approach. Furthermore, it has been rigor-ously proved that the computational requirement of ELM is verysmall compared to other popular machine learning techniquessuch as SVM [19], [21].
In the following section, we first discuss the proposed multidi-mensional learning techniques based on ELM for the 3-D tremormodeling. Conventional ELM can be trained to perform multi-dimensional modeling of tremulous motion. However, the out-put layer weights of the trained network lacks the technique touniformly penalize the cross-dimension couplings of all dimen-sions [19]. Further, the cross-dimension coupling might containoutliers or irrelevant information for modeling [20]. To addressthese issues, we customized the ELM and its cost function tosuit to our 3-D tremor estimation problem and named it as md-RELM. As the physiological tremor is nonstationary in nature,to adapt the regularized ELM output weights over the time, wealso developed the online sequential learning technique for md-RELM, named as OS-mdRELM. In what follows, both thesetechniques are discussed.
A. Robust Multidimensional ELM
For a set of N independently and identically distributedsamples S = {(si , ti)|si ∈ Rm , ti ∈ Rn ; i = 1, . . . , N} withS = [s1 , . . . , sN ] as input vector, T = [t1 , . . . , tN ] as its cor-responding target vector. With the randomly initialized inputweights w, hidden layer bias b and the computed output layerweights β, and sigmoid activation function, the multidimen-sional output with conventional ELM can be given as
ok = f(sk ) =L∑
i=1
βgi(wisk + bi). (1)
1648 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 2, FEBRUARY 2017
The output weight matrix (β) can be obtained with
β = G†T (2)
where G† is Moore–Penrose generalized matrix inversion of G.For more detailed description about ELM, refer to [21].
The md-RELM is structurally similar to the conventionalELM except the cost function. The regularized cost function ofthe ELM which provides equal penalty for all dimensions canbe formulated as
minβ, ε
n∑
j=1
12‖βj‖2 +
n∑
j=1
12cj
N∑
i=1
λij‖εij‖2
subject to tij − βjg(si) = εij , i = 1, . . . , N (3)
where λj = diag{λi1 , . . . , λin} represents the robust weight pa-rameters and obtained as
λij =
⎧⎪⎨
⎪⎩
1 |εij/s| ≤ c1 ;c2 −|ε i j /s|
c2 −c1c1 ≤ |εij/s| ≤ c2 ;
10−4 |εij/s| > c2
with s = IQR(si )2×0.6745 , IQR defines the interquartile range, c1 = 2.5,
and c2 = 3 and c = [c1 , . . . , cn ] represents the regularizationparameter.
Based on the Karush–Kuhn–Tuker (KKT) theorem, trainingthe ELM is equivalent of solving the following dual optimizationproblem, which can be given as
LD =n∑
j=1
12||βj ||2 +
n∑
j=1
12cj
N∑
i=1
λij ||εij ||2
−n∑
j=1
N∑
i=1
αij(εij − tij + βjg(si)) (4)
where αij ; i = 1, . . . , N and j = 1, . . . , n represents theLagrangian parameters. By solving the KKT optimality con-ditions, we can get an estimate of output weights
βj =(
Icj
+ GT λjG)−1
GT λjtj. (5)
The output of the mdRELM with the estimated output weightsfrom the regularized cost function can be given as
ok = f(sk ) =n∑
j=1
L∑
i=1
βj gi(wisk + bi). (6)
B. Online Sequential md-RELM
For an initial training dataset S0 = {si , ti}Ni=1 , the initial
Fig. 3. Functional block diagram representation for OS-mdRELMimplementation.
{si , ti}N +n0i=N +1 . Then, the output weights can be computed as
β(1) = K−1(1)
(G(0)
G(1)
)T(λ(0) 0
0 λ(1)
)(T(0)
T(1)
)(8)
where
K(1) =
⎛
⎝I
c+
(G(0)
G(1)
)T(λ(0) 0
0 λ(1)
)(G(0)
G(1)
)⎞
⎠ .
By considering K−1(k) = P(k) , we can generalize the relation-
ship between β(k+1) and β(k) as [23]
β(k+1) = β(k) − P(k+1)GT(k+1) λ(k+1)
×(β(k)G(k+1) − T(k+1)
)
(9)
where
P(k+1) = P(k) − P(k)GT(k+1)
(λ−1(k+1)
+G(k+1)P(k)GT(k+1)
)−1G(k+1)P(k). (10)
The output of the OS-mdRELM can be given as
ok = f(sk ) =n∑
j=1
L∑
k=1
β(k+1),jg(sk ). (11)
C. Implementation of Multidimensional Tremor ModelingApproach
Functional block diagram representation for the proposedmultidimensional approach (OS-mdRELM) is depicted inFig. 3. In what follows, the step by step procedure for the 3-Destimation is itemized:
1) Identification of Nonlinear Inverse-Mapping Function(β(k)): To identify accurate yet generalized mapping, the firstN samples of both delayed tremor motion and actual tremor
TATINATI et al.: MULTIDIMENSIONAL MODELING OF PHYSIOLOGICAL TREMOR FOR ACTIVE COMPENSATION IN HANDHELD SURGICAL ROBOTICS 1649
motion in 3-D are considered for the offline training, as shownin Fig. 2(b). In this training procedure, first the input vector isformulated in the embedded space constructed based on Taken’sembedded theory [24], [25]. For a 3-D modeling of tremor, theembedded space is formulated with the delayed x-, y-, and z-axes. If a two-dimensional (2-D) modeling is considered, thenthe embedded space can be formulated with two delayed axesi.e., x-, and z-axes or y- and z-axes. From this embedded space,md-RELM learns the nonlinear inverse-mapping function (β)by utilizing the existence of cross-dimension coupling and with(5), as shown in Fig. 2(b).
2) Updating the Nonlinear Inverse-Mapping Function(β(k+n)): The nonlinear mapping obtained with md-RELM canbe updated in real time with the arrival of every new sample byits online sequential learning approach (OS-mdRELM). First,upon arrival of the new sample for whole motion, the trainingdatabase will be updated with the recent N samples by simplydiscarding the oldest sample in the data, as shown in Fig. 3. Forexample, assume that the training database has N samples, i.e.,from p to p + N and the arrived new sample is p + N + n, thenthe training database will update to the recent N sample, i.e.,from p + n to p + N + n. With the updated database and from(10) and (9), the multidimensional nonlinear mapping will beupdated to β(k+n) . The phase delay correction will be carried outwith (11). For OS-mdRLEM, this procedure will be repeated forevery arrived new sample and accordingly the multidimensionalmapping will be updated.
Finally, the tremor compensation framework with handheldinstruments is modified by incorporating the “multidimen-sional modeling block” (comprises of the nonlinear inverse-mapping function (β(k))) after the bandpass filtering, as shownin Fig. 2(a). As a result, the phase delay induced by the filteringstage will be corrected and accurate 3-D tremor estimation canbe obtained.
III. RESULTS
In this section, we first provide the details of a physiologicaltremor data collected from microsurgeons and novice subjects.Later, the multidimensional correlation analysis and the com-parison analysis are discussed, followed by the experimentalvalidation of the proposed method.
A. Physiological Tremor Data Collection
Physiological tremor recordings were performed through themicro motion sensing system (M2S2) and a sensorized styluswith reflector ball at its tip [26]. M2S2 provides a measurementin a 10 × 10 × 10 mm3 workspace, with a resolution of 0.7 μmand minimum accuracy of 98% [7]. The 3-D displacement ofthe reflector ball is calculated by using reflected infrared raysfrom the ball and the photo sensitive diodes. For more detailsabout the design and data acquisition with M2S2, please referto [7], [26]. Two typical microsurigcal tasks are performed byfive surgeons and five novice subjects [26]:
1) Pointing Task: In this task, two dots were displayed on themonitor screen. One dot is white in color and fixed, whilethe another dot is orange in color and will move according
to the user’s tool tip movement. The subjects were instructed tokeep the orange dot overlapping the white dot for 30 s.
2) Tracing task: At the beginning of this task, a circle with4 mm diameter was displayed on the monitor screen. The sub-jects were instructed to trace the circumference of the circle inclockwise direction as accurately as possible for 30 s with thespeed that is realistic for surgical manipulation tasks.
Each task was performed with three magnifications: 1×, 10×,and 20×, and with grip force of 1 to 2 N. Sampling frequencyof 250 Hz was employed. For more information about magnifi-cation and force conditions, see [26].
B. Performance Indices
Let sx = [sx(1), . . . , sx(k)], sy = [sy (1), . . . , sy (k)], andsz = [sz (1), . . . , sz (k)] represent the tremor signal of lengthk in x-, y-, and z-axes, respectively. In this study, the couplingbetween the tremor signal characteristics measured in multidi-mensions simultaneously is identified with correlation coeffi-cients [24] and mutual information [25].
1) Correlation Coefficient: The correlation coefficient (ρ)between any two axes can be defined as
ρxy =∑N
i=1(sx(i) − μsx)(sy (i) − μsy
)√∑N
i=1(sx(i) − μsx)2∑N
i=1(sy (i) − μsy)2
(12)
where μsx= 1
N
∑Ni=1 sx(i) and μsy
= 1N
∑Ni=1 sy (i) repre-
sent the mean values of sx and sy .2) Mutual Information: The mutual information between any
two axes can be defined asI(sx ; sy ) = H(sx) + H(sy ) − H(sx ; sy ) (13)
where H(sx) and H(sy ) are the entropies of sx and sy , re-spectively, and H(sx ; sy ) represents the joint differential ofsx and sy . If sx and sy are Gaussian random variables withvariances σ2
x and σ2y , then H(sx) = 1
2 [1 + log(2πσ2x)] and
H(sx ; sy ) = 1 + log(2π) + 12 log(σ2
xσ2y (1 − ρ2)).
3) Accuracy: The tremor modeling performance of all meth-ods is quantified by using %Accuracy, defined as
%Accuracy =RMS(s) − RMS(e)
RMS(s)× 100 (14)
where RMS(s) =√
(∑k=m
k=1 (sk )2/m) with m is the number ofsamples, sk is the input signal at instant k, and e is the obtainedestimation error with a method.
C. Cross-Dimensional Coupling Analysis
The tremor data is preprocessed to analyze the cross-dimensions coupling. This preprocessing is an offline procedureand its main objective is to accurately separate the tremulous mo-tion from the voluntary motions and other low-frequency com-ponents in the whole sensed motion. To this end, we employeda zero-phase third-order Butterworth bandpass filter with passband of 6 to 20 Hz. The processed tremor data was shortened to29 s to remove the transient effect due to the prefiltering stage.
The correlation coefficients readily evaluates the linear rela-tionship **across the channels. With the correlation coefficients[defined in (12)], we found that the tremor measurements in x-,
1650 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 2, FEBRUARY 2017
Fig. 4. Correlation coefficients obtained for Subject #1.
Fig. 5. Cross-dimensional coupling analysis over all subjects and trials.(a) Correlation coefficients. (b) Mutual information.
y-, and z-axes are not independent time series and there existsa cross-dimensional correlation. For illustration, the correlationobtained between x–y-axes, x–z-axes, and y–z-axes for subject#1 are shown in Fig. 4. For this subject, correlation coefficients0.9, 0.65, and 0.86 are obtained for x–y-axes, x–z-axes, and y–z-axes, respectively, for tracing task, whereas for the pointing taskthe correlation coefficients are 0.5, 0.43, and 0.36 for x–y-axes,x–z-axes, and y–z-axes, respectively. For all subjects and trials,statistical results shown in Fig. 5(a) reveal that there exists asignificant level of cross-dimensions correlation.
As tracing task involves more control, larger correlation intremor amplitude can be observed as compared to pointing task.To further evaluate the arbitrary coupling in cross dimensions,we analyzed the mutual information. This measure takes thenonlinear dependencies into consideration and, then, evaluatesthe arbitrary coupling across the dimensions. Furthermore, thismeasure is also independent to the transformations acting onthe dimensions. The mutual information obtained across thedimensions on the whole dataset is shown in Fig. 5(b). Resultsshow that a normalized coupling of 0.35 and 0.29 exists betweenx–y-axes and x–z-axes, respectively. These results are in linewith the results obtained with the correlation coefficients.
D. Optimal Parameter Selection
The hyperparameters of md-RELM that require optimal ini-tialization are:
Fig. 6. Optimal parameter selection for md-RELM (a) grid search for Land m and (b) optimal parameter for c.
1) number of hidden neurons (L) in the hidden layer;2) the embedded dimensions (m);3) regularization constant (c).
To identify the optimal initialization, we randomly chose tentrials per task. In each trial, first 4 s data (1000 samples) isconsidered as a training dataset and the rest 25 s as the testingdataset. We conducted a grid search on the chosen 20 trialswith wide range of values for number of hidden neurons as1 ≤ L ≤ 1000, the embedded dimensions as 1 ≤ m ≤ 100, andregularization constant as 100 ≤ c ≤ 1010 .
The md-RELM was trained (as shown in Fig. 2) with allpossible combinations of L,m, and c on the training dataset ofeach trial. The obtained nonlinear mapping with each combina-tion was later employed for modeling the testing data. For eachcombination, the RMS of an estimation error obtained accord-ing to (14) is computed. The triplet (L,m, c) that provides theleast RMS of estimation error was considered as the optimalparameter set for initialization. For illustration, the grid searchconducted on a single trial with c = [103 , 103 , 103] for com-plete (L,m) is shown in Fig. 6(a). The RMS of error obtainedfor various selections of c in the chosen range also shown inFig. 6(b). For this particular trial, the identified optimal initial-ization was L = 171, m = 69, and c = [103 , 103 , 103]. Similaranalysis for all trials does not show significant variations in theidentified parameter set. Thus, for all subjects, we choose pa-rameters as L = 171, m = 69, and c = [103 , 103 , 103]. Sameparameters were selected for conventional ELM. For the case ofMWLS-SVM, we employed the parameter set reported in [17].
E. Comparison Analysis
In this section, comparisons analysis was conducted on atremor dataset among 1) ELM (1-D), 2) md-ELM, 3) md-RELM, 4) OS-mdRELM, and 5) MWLSSVM (1-D).
The procedure employed to validate each method is shown inFig. 7. In this procedure, the 3-D motion acquired with M2S2system was provided to third-order Butterworth bandpass fil-ter with pass band of 6 to 20 Hz. As discussed earlier, thisfiltering stage introduces frequency-dependent unknown phasedelay into the procedure. The phase-distorted tremulous mo-tion is provided to the devised phase-delay correction block toobtain in-phase tremulous motion. A zero-phase bandpass fil-ter with same specifications as above employed bandpass filterwas employed to obtain the motion without any phase delay.
TATINATI et al.: MULTIDIMENSIONAL MODELING OF PHYSIOLOGICAL TREMOR FOR ACTIVE COMPENSATION IN HANDHELD SURGICAL ROBOTICS 1651
Fig. 7. Phase delay correction.
Fig. 8. (a) Surgeon #1 (pointing task) (b) estimation error with ELM(c) estimation error with md-ELM (d) estimation error with md-RELM(e) estimation error with OS-mdRELM.
This motion was employed as the ground truth to compare theperformance of the phase-delay corrections, as shown in Fig. 7.
The multidimensional-based phase-delay correction modelwith md-RELM was obtained with the training dataset (first 4 s),as shown in Fig. 2. The parameters of md-RELM model wereinitialized as detailed in Section III-C. The output weights ob-tained with the training dataset for md-RELM were maintainedthroughout the testing dataset. For the case of OS-mdELM, thephase-delay correction model updates at every available newsample to adapt to the time-varying phase-delay characteristics,as detailed in Section II-B.
The actual tremor motion in z-axis and estimation errors ob-tained with all methods on Surgeon #1 (pointing task) are pro-vided in Fig. 8 for illustration. The estimation error obtainedwith the 1-D ELM in Fig. 8(c) and multidimensional ELM inFig. 8(d), highlights the influence of cross-dimension couplingin improving the performance. Further, the proposed md-RELMand OS-mdRELM demonstrate better performance compared tomd-ELM and 1-D ELM.
Fig. 9. Performance analysis of all methods.
Fig. 10. Performance analysis of OS-mdRELM for all dimensions.
To further quantify the performance of multidimensional ap-proach, task-wise analysis was conducted on the whole database.As subjects require more control, they displayed huge variationsin tremor amplitude while performing tracing task compared tothe pointing task. Hence, the analysis was conducted separatelyfor the two tasks. As the pointing task is less complex com-pared to the tracing task, %accuracy obtained for pointing taskis higher than the %accuracy obtained with the tracing task, asshown in Fig. 9. Over all subjects, multidimensional approachimproved the tremulous motion filtering accuracy significantly.Among the methods, OS-mdRELM showed least estimationerror. For pointing task, OS-mdRELM provided an average%accuracy of 83.87 ± 1.93% compared to 72.17 ± 6.07% and69.74 ± 11.32% obtained with md-RELM and md-ELM, re-spectively. On average of 9% improvement was obtained withthe proposed multidimensional approach compared to the bestexisting 1-D approach MWLS-SVM.
To further highlight the improvement in modeling accuracydue to the incorporation of cross-dimensional coupling, a com-parison analysis with OS-mdRELM is conducted for 1-D, 2-D,and 3-D. For an analysis, estimation of z-axis is chosen as theoutput, whereas the input spaces are sz (i), sx,z (i) or sy ,z (i), andsx,y ,z (i) for 1-D, 2-D, and 3-D, respectively. Results obtainedfor all subjects are shown in Fig. 10. An improvement of 3%accuracy can be seen in 3-D compared to 2-D for both the tasks.This also supports our hypothesis that the cross-dimensionalcoupling improves the modeling accuracy.
F. Computation Complexity
Computational complexity plays a vital role in minimizing thedelay in a real-time implementation. The number of operations
1652 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 2, FEBRUARY 2017
TABLE ICOMPUTATIONAL COMPLEXITY
Method Parameters Operations(O(·))
MWLSSVM [17] N = 1000 3 ×O(N 3 )MS-BMFLC-KF [10] n = 140 3 ×O(n3 )md-ELM [21] L = 171 O(L3 )md-RELM L = 171, n = 3 O(L3 )OS-mdRELM L = 171, n = 3 O(L3 ) + O(3L)
Fig. 11. Experimental setup.
required for various existing methods and proposed methodsare compared in Table I. Analysis shows that proposed methodscomputational complexity is similar compared to adaptive signalprocessing methods such as BMFLC-KF and significantly lesscompared to existing methods.
G. Experimental Validation
The experimental setup devised to validate the proposed mul-tidimensional approach is shown in Fig. 11. In this setup, thesurgical instrument was fixed on an antivibration table with anangle of 45◦. The subjects were asked to sit on a chair in acomfortable position and, then, rest their hand until wrist onthe table, as shown in Fig. 11. The subjects were provided withthe handheld instrument (iTrem) and informed to hold the tipof handheld instrument at the tip of the clamped surgical in-strument for 50 s. While performing the task, subjects wereprovided with a visual feedback through a table top opticalsurgical microscope (Leica M651 MSD, Leica MicrosystemsGmbH, Germany) with a built-in coaxial illuminator, as shownin Fig. 11. The magnification of the achromatic objective lens ofthe microscope is 25 and its focal length is 200 mm. For betterview of the task performed, a zoom portion to the instrumenttips is also shown in Fig. 11. The performed task was similar tothe pointing task and a typical task in microsurgical procedures.
The handheld instrument (iTrem2) is housed with four dual-axis digital miniature MEMS accelerometers (ADIS 16003,Analog Devices, USA). The accelerometer measurements areacquired by the embedded microcontroller (AT89 C51CC03,Atmel, USA) on board iTrem2 at the sampling frequency of333 Hz. The real-time communication between iTrem2 and
Fig. 12. Experimental procedure for estimation of tremulous motion.
the real-time Labview environment was achieved by using thecontroller-area network interface with a bandwidth of 500 kb/s.With a quadratic function, the acquired voltage readings fromthe accelerometer were converted to acceleration and, then, con-verted into position domain with numerical integration in Lab-View environment [7]. The iTrem2 comprises of a visual servocontrol integrated with inertial sensing to fulfill the need for hardreal timeliness in a microsurgery (accurate sensing) [27]. Thevision subsystem has a mono-vision camera mounted on the mi-croscope which is located at a fixed position in the workspace.The camera gives the tool tip position information in x- andy-axis; it lacks the depth information (z-axis). Thus, the setupis limited to two-DOF in-plane movement with the instrumentaligned with the microscope reference frame. For more detailsrefer to [7], [27].
The procedure employed to evaluate the suitability of pro-posed multidimensional approach for a tremor compensation isshown in Fig. 12. This approach is implemented as detailed inFig. 3. The whole motion converted to position domain is pro-vided to a bandpass filtering stage and, then, the proposed phasedelay correction block, as shown in Fig. 12. The phase delay cor-rection block is formulated according to the procedure detailedin Section II. To evaluate the performance of the phase delaycorrection block, a zero-phase bandpass filter was employed toprovide the actual tremulous motion in offline (considered asground truth). Further to account for the on-board first-orderlow-pass filter in accelerometers (RC circuit with C = 10 μFand R = 40 kΩ) and actuator delays, 4 ms delay block is alsoadded to the signal as shown in Fig. 12. With the actual tremu-lous motion obtained in offline, estimation error was computed,as shown in Fig. 12.
Experiments were conducted with three subjects and threetrials per each subject. Parameters and initial conditions forreal-time experiments are similar to the simulation experiments.In [17], MWLS-SVM provided better performance compared toexisting methods for a multistep prediction. Further based on our
TATINATI et al.: MULTIDIMENSIONAL MODELING OF PHYSIOLOGICAL TREMOR FOR ACTIVE COMPENSATION IN HANDHELD SURGICAL ROBOTICS 1653
Fig. 13. Experimental validation of OS-mdRELM. (a) Tremor motionestimation in x-axis. (b) Tremor motion estimation in y-axis.
study in earlier section, we infer that md-RELM provides betterperformance compared to conventional ELM. Hence, for exper-imental validation, we only choose OS-mdRELM, md-RELM,and MWLS-SVM methods. For illustration, the estimation errorobtained with OS-mdRELM and the estimation error due to thephase delay for subject #1 are shown in Fig. 13. An %accuracyof 81%, 78%, and 74% were obtained with OS-mdRELM, md-RELM, and MWLS-SVM, respectively. Overall for three sub-jects data, an average %accuracy of 79 ± 1.23% was obtainedwith OS-mdRELM, whereas 75 ± 1.56% and 71 ± 1.89% wereobtained with md-RELM and MWLS-SVM, respectively. Fur-thermore, OS-mdRELM provided better performance comparedto all other method for all subjects and all trials.
IV. DISCUSSION
The 3-D tremor estimation methods have been developed asa part of our continuing research to improve the performanceof handheld instruments. Correlation (linear relationship) andmutual information (nonlinear) are employed to analyze theexistence of cross-dimensional coupling in tremor measure-ments. To utilize this cross-dimensional coupling information,
embedded space with appropriate embedding dimensions (m =69) and proper delay (τ = 1) has been constructed with the dataobtained from all three dimensions. The developed multidimen-sional modeling methods are trained in this embedded space tolearn the nonlinear mapping that best represents the phase delaycharacteristics of a bandpass filter, as shown in Fig. 2(b). It hasbeen already established that if two time series are correlated,then the information of one time series is included in the dy-namics of other time series. Consequently, the embedded spaceconstructed with both time series better represents the geometryof time series rather than one time series alone [24], [25]. Thereduction in the prediction error with multidimensional methodshighlight that there exists correlation across the dimensions andthe ELM has been successful in learning that. Furthermore,the proposed multidimensional modeling approaches are lesscomputationally complex than other existing 1-D methods andare more suitable for active compensation in robotic systems.
Existing works on the handheld tremor compensation sug-gests that a final compensation of 70% is desirable for micro-surgery to improve the surgeon’s performance [7], [8]. Analysisshowed that the loss in the end compensation accuracy was moredue to the phase delay, integration drift, and other sensor noises.The proposed multidimensional approach improved the accu-racy by nearly 10% compared to the existing methods. With thisimprovement, we foresee that the final compensation accuracywill be also improved during instrument trials that are plannedwith micro surgeons in the future.
The handheld instrument (iTrem2) employed in this study hasa specially designed all-accelerometer inertial measurement unitto provide the instrument tool tip position in three-DOF accord-ing to the fixed microscope reference frame [27]. Based on thesemeasurements, the proposed multidimensional method has beencustomized to perform 3-D tremor prediction. However, othervariants of handheld instruments, for example Micron [11] andsteady hand [28], have incorporated six-DOF (position and ori-entation) sensing units. Compared to six-DOF sensing unit, thethree-DOF sensing-based modeling lacks the information aboutthe orientation. In recent work [29], it has been claimed thatjoint angle of wrist affects the physiological tremor. Thus, withsix-DOF modeling, the tremor modeling accuracy will be fur-ther improved. With the innate parallel processing structure ofELMs, the proposed multidimensional modeling (three-DOF)can be extended to six-DOF modeling for other variants ofhandheld instruments. However, the success of this extension tosix-DOF depends on accurate identification of the dependencyacross the six dimensions and the formulated of embedded spacefor learning.
Furthermore, to date, 3-D tool tip control performance is ap-plied to all three axes in parallel according to the generatedcontrol signal for each dimension separately. In other variantsof handheld instruments developed in [11] and [28], six-DOFmotion compensation have been developed. The combinationof developed multidimensional modeling approaches with thesix-DOF compensation unit requires further work to be imple-mented in real time. As a part of our continuing research indeveloping handheld surgical instruments, we considered thisexciting combination as our next step to work on.
1654 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 64, NO. 2, FEBRUARY 2017
Although the approach is mainly developed for 3-D tremormodeling, the proposed approach is also suitable for 2-Dmodeling as demonstrated in experiments. The significant im-provement in modeling accuracy with 2-D and 3-D approachesfurther suggest that the information available from otherdimensions can significantly improve the modeling accuracy.The proposed multidimensional modeling can be successfullyapplied to 2-D and 3-D motion control problems [30], [31],bedsides the tremor modeling, with potential applicationsbeing precise 2-D positioning with microscopes, mobility ofrobots, and cell manipulations and digital modeling of humanmotions.
V. CONCLUSION
As a solution to counter the unknown phase delay and per-form simultaneous 3-D modeling of tremulous motion, mul-tidimensional modeling with OS-mdRELM was developed inthis paper. The analysis conducted on tremor data demonstratedthat multidimensional methods provide better tremor estimationcompared to other methods. To evaluate the suitability of mul-tidimensional approach for real-time applications, the approachwas evaluated experimentally in comparison with existing meth-ods. Results show that an average %Accuracy of 79 ± 1.23% isobtained with the OS-mdRELM in comparison to 71 ± 1.89%obtained with the existing method MWLS-SVM (1-D).
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Sivanagaraja Tatinati received the Master’sand Ph.D. degrees in electronics engineeringfrom Kyungpook National University, Daegu,South Korea.
He is currently a Postdoctroal Fellow in theSchool of Computer Science and Engineering,Kyungpook National University, Daegu, SouthKorea. His current research interests includerobotics-assisted medical instruments, adap-tive filtering, and machine learning techniques-based regression with applications in biomedical
engineering.
TATINATI et al.: MULTIDIMENSIONAL MODELING OF PHYSIOLOGICAL TREMOR FOR ACTIVE COMPENSATION IN HANDHELD SURGICAL ROBOTICS 1655
Kianoush Nazarpour (S’05–M’08–SM’14) re-ceived the B.Sc. degree from K. N. Toosi Uni-versity of Technology, Tehran, Iran, in 2003, theM.Sc. degree from Tarbiat Modarres University,Tehran, Iran, in 2005, and the Ph.D. degree fromCardiff University, Cardiff, U.K., in 2008, all inelectrical and electronic engineering.
From 2007 to 2012, he held two PostdoctoralResearcher posts at Birmingham and Newcas-tle Universities. In 2012, he joined Touch Bion-ics, Inc., U.K., as a Senior Algorithm Engineer
working on intelligent control of multifunctional myoelectric prostheses.In 2013, he returned to Newcastle University, where he is currently a Se-nior Lecturer in biomedical engineering. His research interests includeintelligent sensing and biomedical signal processing and their applica-tions in assistive technology.
Dr. Nazarpour received the Best Paper Award at the 3rd InternationalBrain–Computer Interface (BCI) Conference (Graz, Austria, 2006), andthe David Douglas Award (2006), U.K., for his work on joint space–time–frequency analysis of the electroencephalogram signals. He is currentlyan Associate Editor of the Medical Engineering and Physics journal inthe area of biomedical signal processing.
Wei Tech Ang (S’98–M’04) received the B.E.and M.E. degrees in mechanical and produc-tion engineering from Nanyang TechnologicalUniversity, Singapore, in 1997 and 1999, re-spectively, and the Ph.D. degree in roboticsfrom Carnegie Mellon University, Pittsburgh, PA,USA, in 2004.
Since 2004, he has been with the Schoolof Mechanical and Aerospace Engineering,Nanyang Technological University, where he iscurrently an Associate Professor and holds the
appointment of the Head of the Engineering Mechanics Division. His re-search focuses on robotics technology for biomedical applications, whichinclude surgery, rehabilitation, and cell micromanipulation.
Kalyana C. Veluvolu (S’03–M’06–SM’13)received the B.Tech. degree in electrical andelectronic engineering from Acharya NagarjunaUniversity, Guntur, India, in 2002, and the Ph.D.degree in electrical engineering from NanyangTechnological University, Singapore, in 2006.
During 2006–2009, he was a ResearchFellow with the Biorobotics Group, Robotics Re-search Center, Nanyang Technological Univer-sity. Since 2009, he has been with the Schoolof Electronics Engineering, Kyungpook National
University, Daegu, South Korea, where he is currently an Associate Pro-fessor. He is also currently attached to the School of Mechanical andAerospace Engineering, Nanyang Technological University, as a VisitingProfessor for the period 2016–2017. He has been a Principal Investiga-tor or a Coinvestigator on a number of research grants funded by theNational Research Foundation of Korea and other agencies. He has au-thored or coauthored more than 100 journal and conference proceedingsarticles. His current research interests include nonlinear estimation andfiltering, sliding mode-control, brain–computer interface, autonomous ve-hicles, biomedical signal processing, and surgical robotics.
