A Framework for Analysis of Surgeon Arm Posture Variability in Robot-Assisted Surgery

Transcription

1 A Framework for Analysis of Surgeon Arm Posture Variability in Robot-Assisted Surgery Ilana Nisky, Michael H. Hsieh, and Allison M. Okamura Abstract Teleoperated robot-assisted surgery (RAS) provides surgeons with improved dexterity, movement control, and visualization in comparison to standard minimally invasive surgery. However, there exists little quantitative understanding of the motor performance of human operators in RAS. Models of how users control their movements and how this control relates to surgical performance could provide inspiration for new robot or human interface designs, as well as more targeted training methods. Toward this end, we present a framework for the analysis of surgeon arm posture variability based on the uncontrolled manifold (UCM) concept, a method used in the study of human motor control for testing hypotheses about the coupling of control and task variables. We partition users joint angle variability into variability that does and does not result in hand trajectory change. In a preliminary study applying this framework, we explored how expert and novice operators control planar reaching and reversal movements when moving freehand as well as using a teleoperated RAS system. We show that only movements in task-relevant directions are stabilized by the coordination of joint angles, and that this stabilization is stronger for expert movements than novice movements. We also show that stabilization is stronger in freehand than teleoperated movements, especially for the expert. These preliminary findings suggest that the proposed framework can be useful for: (1) assessment of teleoperator design and control that reveals how design parameters affect the ability of the user to exploit the UCM for stabilization of hand movement, and (2) skill assessment in RAS. I. INTRODUCTION Robot-assisted surgery (RAS) has the potential to improve patient outcomes in comparison to standard manual minimally invasive surgery (MIS). RAS offers surgeons many advantages, including: more degrees of freedom (DOF) through wristed instruments that improve dexterity, an intuitive mapping from hand to instrument motion that eliminates the fulcrum effect, motion scaling that improves precision and removes tremor, 3D visualization through a high-definition stereoscopic view, and an ergonomically comfortable setup (Fig. 1). However, many robotic procedures do not show a significant improvement in patient outcomes over manual MIS, and there are a variety of procedures for which robotics seems promising but have not been broadly adopted. We propose that understanding how surgeons control the movement This work is supported by Stanford University, Marie Curie International Outgoing Fellowship, and Weizmann Institute of Science National Postdoctoral Award for Advancing Women in Science. I. Nisky and A. M. Okamura are with the Department of Mechanical Engineering, Stanford University, Stanford, CA, 9435, USA. nisky@stanford.edu and aokamura@stanford.edu M. H. Hsieh is with the Department of Urology, Stanford University, and with the Pediatric Urology Service, Lucile Salter Packard Children s Hospital at Stanford, Stanford, CA, 9435, USA. mhhsieh@stanford.edu Fig. 1. A surgeon seated at the master console of the da Vinci robot-assisted surgery system. Magnetic pose trackers were attached to the shoulder (s), elbow (e), and wrist (w) joints of the arm and to the tip of the master manipulator (t). Inset shows a custom fixture mounted on the da Vinci grasper. The same fixture was detached from the manipulator and used in the freehand experimental condition. of a teleoperated robot can help bridge this gap. Quantitative analysis of the effect of different teleoperators on the coordination of user movement may be used to optimize robot design. In addition, understanding of the difference in movement coordination between skilled surgeons and novice users may be used to improve skill assessment and optimize training protocols. Recently, there has been increasing interest in quantitative analysis of movement and performance in RAS [1]. One prior approach broke down trajectories into gestures and created a language of surgery [2]. Other researchers have used Hidden Markov Models applied to position and force information for modeling surgery and skill evaluation [3, 4]. Our approach is unique in that it aims to model surgeon motion using the framework of human motor control. In a recent study, we analyzed the trajectories of master manipulator tooltips during performance of canonical motor tasks with an RAS system [5]. We found significant differences between teleoperated and freehand cursor control in several aspects of motion, including target acquisition error, movement speed, and acceleration. We also found preliminary evidence for differences between experts and novices. In the current paper, we develop a method to analyze and interpret the trial-to-trial variability of surgeon arm posture during performance of the tasks used in [5].

2 Motor variability is one of the most prominent features of human motion. While there are many standard characteristics in the performance of motor tasks, e.g. point to point reach movements are characterized by nearly straight paths and bell-shaped velocity trajectories [6], no two single movements are truly identical. One important source of this variability is redundancy at the different levels of task execution, starting from the higher level of control (neurons in the brain), through intermediate level of actuation (muscles), and down to the mechanical degrees of freedom (DOF) of the arm. Such redundancy is both a benefit and a burden it allows for flexibility in movement in the face of perturbations and obstacles, but creates an ill-posed control problem to be resolved by the human motor system. From the standpoint of understanding the control of human movements, exploring the coordination of redundant tasks is a way to test hypotheses about the organization of control in the motor system. Moreover, structured variability is related to motor skill level [7], and therefore, our proposed method may lead to the development of novel computational metrics for surgeon skill level assessment. In addition, the study of how robot dynamics affect user movement variability could inspire new surgical robot designs. We apply the uncontrolled manifold (UCM) framework that quantifies how the human motor system resolves the redundancy problem [8, 9, 1]. UCM is used as a tool to test hypotheses about which task variables (e.g. Cartesian coordinates of master manipulator tip or human hand) are stabilized by means of control variables (e.g. arm joint angles) during the performance of redundant tasks. In this approach, the trial-to-trial variability of the hypothesized control variables is partitioned into variability within a manifold that leads to equivalent hand trajectory, namely the UCM, and variability in the orthogonal (to the UCM) manifold that changes hand trajectory. The UCM is related to the self motion manifold in robotics [11]; for linear systems, this is the null space of the matrix that relates control variables to task variables. In this framework, a task variable is defined to be stabilized by a set of control variables when the variability in control space is organized such that configurations that do not change the task variable vary more than configurations that change it [9]. Variability is advantageous if it allows for flexibility, robustness to perturbations, and coping with fatigue, but it can be detrimental if it hampers task performance. The variability that lies within the UCM is of the first kind; therefore, if the system uses the hypothesized control variables to stabilize the task, the variability within the UCM is expected to be high. Such structure is characteristic to the human motor control system, and is consistent with various ideas about how movement is coordinated, such as the minimum intervention principle [12]. We emphasize that the UCM framework is a tool for testing hypotheses about a specific combination of task and control variables for a specific experimental condition, and careful experimental design is necessary to draw meaningful conclusions about the underlying structure of control. The main contribution of the current paper is establishing a framework for analysis of arm posture variability to understand the coordination of teleoperated movements in RAS. We demonstrate application of this method to compare between coordination of arm posture (joint angles) for stabilizing the movement of the hand while moving the tip of the master manipulator in a surgical teleoperation system and while moving freehand. We further explore the difference in coordination between an expert and novices. To that end, we present a preliminary experimental study comparing arm movement coordination in two simple planar movements: reach (movement between rests at two points in a plane) and reversal (out and back movement towards a target without resting at the target itself). These movements were made under two experimental conditions: freehand and teleoperated cursor control. For each of these conditions, we use the UCM to test two control hypotheses: when controlling the motion of a two-dimensional cursor in horizontal plane the motor system stabilizes (I) horizontal hand trajectory and (II) the vertical coordinate of the hand. ecause the movement of the cursor is planar, we expect to find that the system stabilizes (I) but not (II). While both reach and reversal movements are of limited clinical relevance in isolation, they are explored extensively in the study of human motor control, and thus provide a logical starting point for studying movement coordination in RAS. Moreover, these movements are the building blocks for more complicated surgical motions to be studied in future work. A. Experimental Procedures II. METHODS Five volunteers participated in the experiment, approved by the Stanford University Institutional Review oard, after giving informed consent. Three of the participants had no surgical experience, but had some experience in robotic telemanipulation. One of the participants was a surgical fellow, and one was an experienced surgeon with a high volume of RAS cases. ecause the surgical fellow had no direct RAS experience, he was classified as a novice. We instrumented a da Vinci Si teleoperated robotic surgery system (Intuitive Surgical, Inc.) at Lucile Packard Childrens Hospital with 6-DOF magnetic pose trackers (TrakStar, Ascension Technologies) on a lightweight fixture attached to the tip of the master manipulator (shown in Fig. 1 inset, fixture weight with sensors is 5 g), as well as on the surgeons wrist, elbow and shoulder (Fig. 1). Participants were asked to make center-out planar reach and reversal movements towards one of 16 possible targets, without being restricted to move in a plane. Three of the participants performed the movements first freehand, holding a tracked, lightweight grasp fixture (similar to that of the interface of the da Vinci master) not attached to the master manipulator, and second via teleoperation (holding the grasp fixture attached the master manipulator); the other two participants had the reverse order. To provide consistent visual feedback, the user was always shown a cursor that moved based on the tracked grasp fixture (rather than the patient-side robot). The movement of the cursor was mapped one-to-one to the x-y movement

3 A ŷ ˆx α w α e α s β s ẑ β e ŷ β w C Feedback cursor start 6mm 3mm short reversal target Fig. 2. Schematic representation of the experiment: (A) upper view (xy plane projection) and () side view (y-z plane projection) of participant posture during experiment. (C) Participants were presented with planar view of start point, target, and x-y cursor position. of the fixture, regardless of whether it was attached to the master manipulator or moved freehand. The cursor was displayed on a monitor placed on the surgical table, with video of the monitor acquired via the endoscopic camera and displayed on the surgeon s console. In the teleoperated setting, the master manipulator controlled the movement of the (non-visible) patient-side manipulator, ensuring dynamics identical to standard clinical teleoperation. All targets were centered on one of two circles with radius 3 or 6 mm, and were located in one of eight directions on these circles: -135, -9, -45,, 45, 9, or 18 degrees (Fig. 2C). The desired movement type (reach or reversal) was communicated to the participant by the color of the target. The different movement types, distances, and directions were presented in pseudorandom order and were identical for all participants for both sessions. The participants were instructed to be as accurate as possible and to complete a reach within 1 sec and a reversal within 1.5 sec. After the completion of each movement, text appeared on the monitor providing feedback about whether the movement time was good or too slow. A movement was considered complete when the cursor stayed within 5 mm from the target center for.5 sec in reach movements, and when the cursor returned to within 5 mm from start point in reversal movements. Importantly, there were no specific instructions about any other aspect of the path to and from the targets. ecause participants were provided with visual feedback about x-y but not z coordinates of the tip tracker, we expect the x- y task variables to be more stabilized compared to the z task variable. Moreover, because teleoperation requires users to compensate for the dynamics of master manipulator, we expect reduced stabilization in teleoperation when compared with freehand control of the cursor.. Data Analysis 1) Movement segmentation: We sampled marker positions and orientations at 12 Hz, filtered the data offline with a 4th-order low-pass utterworth filter with cutoff at 6 Hz, and calculated velocity by backward differentiation and additional filtering. es longer than 2.5 sec, and reversals longer than 3 sec, were discarded, amounting to less than 5% of discarded movements (and without substantial change in the results with all data included). Movement segmentation was performed based on tip sensor trajectories. ecause we are interested in trial-to-trial variability, we normalized the time between movement onset and end. To identify the onset, we used a method based on a regression of a template consisting of a flat region before onset, and a cubic power of time after onset, described in [13]. Identifying the end of movement was different for each movement kind. For reaches, it was the end of the main movement, without subsequent corrections, and was identified as either the time of first local minimum of speed trajectory, or the time when the speed reduced to less then 5% of its peak value for the particular trial. For reversals, it was the time when the tip returned to within 5 mm from start point. Importantly, we analyzed task performance based on path endpoint the planar (x-y plane) location of the end of movement for the case of reaches, and of the maximal point of position projected on movement direction for the case of reversals (which temporally occurred at about the middle of reversal movement). Then, we time-normalized all trajectories and interpolated them at equal intervals of.1. 2) Calculating joint angles: We placed magnetic pose trackers at the tool tip, and as close as possible to the centers of wrist, elbow, and shoulder joints, each aligned with a specific arm segment direction a geometry that was expected to allow straightforward offline extraction of joints centers and angles (Fig. 1). However, in practice, due to magnetic interference from the da Vinci armrest, we were not able to use the readings of elbow sensor, and therefore, we extrapolated the position of elbow as the center of the shortest line perpendicular to the estimated linear segments of upper and lower arm. These were estimated based on the position and the orientation of the wrist and shoulder sensors that were aligned with forearm and upper arm, respectively. The resulting estimations are biased due to imperfect placement of sensors. However, this is acceptable, because in the current study, we focus on analysis of variability around mean trajectories. ecause the sensitivity of orientation signals to accurate sensor placement is greater than that of position signals, we estimated orientations of the links representing the hand, forearm, and upper arm by subtracting the estimated position vectors of adjacent joint centers in 3D. We estimated the link lengths (L wt, L ew, and L se, respectively) by calculating the median value of the size of these vectors across all the trials of each participant. Arm posture was described in 3D by means of 6 joint angles; for each joint, the orientation was represented using the first two ZYX Euler angles. This is equivalent to measuring the absolute α and β angles with respect to the positive ˆx and ŷ axes in the respective x-y and y-z projections, as depicted in Fig. 2A. We did not measure the X Euler angle representing rotation about the link axis. C. Variability Analysis and UCM In the framework we propose here, we focus on the analysis of variability in the 3-DOF task space that is defined by the Cartesian coordinates of the tool tip sensor x t = ( x t y t z t ) T, and in the 6-DOF control space that is defined by the user s arm joint angles θ = ( α s α e α w β s β e β w ) T, where α s, α e, α w are

4 the horizontal absolute angles of the shoulder, elbow, and wrist joints (Fig. 2A), and β s, β e, β w are the vertical absolute angles of the joints (Fig. 2). We tested two separate control hypotheses: one about the 2-DOF component of horizontal movement (which we hereafter refer to as the x-y hypothesis), and another about the 1-DOF component of vertical movement (which we hereafter refer to as the z hypothesis). We assume that a movement of the arm is well approximated as a sequence of time-varying static postures, and that at each percentage of the trajectory, the same reference postural state is defined by the nervous system [9]. When analyzing variability in general, one can calculate within trial variability with respect to time, or trial-to-trial variability at similar trajectory points. The former provides an estimation of posture reference point variation during movement. The latter measures the stability of a variable around a time-varying reference point in face of various sources of perturbation. This is the variability that is the focus of our paper, and we use the UCM framework to understand its structure. We start by estimating the reference trajectory as the mean trajectory for each combination of movement type i, length j, and direction k, calculated for each sample t, in both task and joint space: x ijk [t] and θ ijk [t]. Now, we can estimate the task space variability for each of the hypotheses as the according to: N ijk V xijk [t] = (x ijkl [t] x ijk [t]) 2 d 1 task N 1 ijk, (1) l=1 where x is a task space vector, d task is the number of task space DOFs, corresponding to the number of elements in x, and N ijk is the number of movements of that kind. For the joint space variability analysis we define the analytical relationship between the hypothesized task and joint variables (i.e., the forward kinematics of the arm). For the x-y hypothesis it is: ( ) ( ) xt Lse cα = s cβ s + L ew cα e cβ e + L wt cα w cβ w, y t L se sα s cβ s + L ew sα e cβ e + L wt sα w cβ w (2) and for the z hypothesis it is: z t = L se sβ s L ew sβ e L wt sβ w, (3) where c and s are short for cosine and sine of, respectively. Eq. 3 highlights that the joint space for the z hypothesis is 3-DOF, and hence, we use a reduced vertical joint angles vector θ = ( β s β e β w ) T for the analysis of the z hypothesis from this point onwards. The UCM of these forward kinematics equations is nonlinear, but for small deviations around the mean trajectories, we can linearize the kinematics using the Jacobian matrix: x[t] x ijk [t] = J( θ ijk [t])(θ[t] θ ijk [t]) (4) where the Jacobian matrices for the x-y and z hypotheses are ( Lsesα J xy(θ[t]) = scβ s L ewsα ecβ e L wtsα wcβ w L secα scβ s L ewcα ecβ e L wtcα wcβ w and ) L secα ssβ s L ewcα esβ e L wtcα wsβ w [t] (5) L sesα ssβ s L ewsα esβ e L wtsα wsβ w J z (θ[t]) = ( L se cβ s L ew cβ e L wt cβ w )[t], (6) respectively. Note that the Jacobian depends on the mean configuration, and is different for each movement type, distance, direction, and sample. The null space of the Jacobian matrix is the linear approximation of the UCM at each of these mean configurations, and its dimension is d UCM = d joints d task. The matrix of the d UCM basis vectors, ɛ, was calculated numerically for each mean configuration using Matlab null() function such that: J( θ ijk [t]) ɛ =. (7) Next, we calculated the projection of the joint space deviations from the mean trajectories onto the null space: and orthogonal to null space: θ UCM [t] = ɛɛ T (θ[t] θ ijk [t]) (8) θ ORT [t] = (θ[t] θ ijk [t]) θ UCM [t]. (9) Finally, the of the deviations projected on the approximated UCM and the orthogonal sub-spaces can be calculated according to: and N ijk V UCMijk [t] = (θ UCMijkl [t]) 2 d 1 UCM N 1 ijk, (1) l=1 N ijk V ORTijk [t] = (θ ORTijkl [t]) 2 d 1 task N 1 ijk, (11) l=1 respectively. The ratio between these two variances is the key metric in this work: [t] = V UCM [t]/v ORT [t]. (12) After calculating the variance ratio for each reference configuration and sample, we use this value to test the hypothesis about the extent of stabilization of the particular task variable in question. If this value is larger than unity, joint space variables are coordinated such that the task variable is stabilized. If the value is equal to or smaller then unity, the coordination in joint space is indifferent to the particular task variable, or even destabilizes it, probably because the motor system is aiming at stabilizing a different task variable. Importantly, with skill acquisition, this ratio can be increased by either increasing V UCM [t], or by reducing V ORT [t]. While the latter will have direct impact on task performance, the former may lead to robustness to unexpected perturbations or improved performance of more complicated tasks involving the same task space variables. Thus, can be used in assessment of skill even in cases when the task itself may be too simple for revealing level of expertise based on task performance.

5 A xt [mm] xt [mm] zt [mm] zt [mm] α [degrees] w α [degrees] w A C Z tele Z free XY tele XY free D Fig. 3. Examples of experimental trajectories of one participant in (A) reach and () reversal movements toward a 6mm target in the direction. Colored traces are individual trial trajectories, and black solid and dashed traces are mean ±1 standard error, respectively, across trials. 1 1 D. Comparison of with Task Performance While detailed task performance analysis is beyond the scope of the current paper, we wish to provide insights into how is related to task performance. Detailed analysis of various movement features has been described elsewhere [5]; here, we used the endpoint error (the distance between the target and the position of tip sensor in x-y plane at the endpoint of movement) as a performance metric. For each participant, teleoperation condition (teleoperated versus freehand), movement type, distance, and direction, we calculated average across time in trial and then averaged across trials, and average endpoint error across trials, yielding 32 data points. We assessed the correlation between endpoint error and using linear regression models. III. RESULTS Fig. 3 shows examples of x, z, and α w trajectories of one participant for all long reach and reversal movements to one target, together with mean trajectories for that target. In the x coordinate, for which visual feedback was provided and was relevant for task performance (left), the within trial variability, namely extent of change in mean trajectory with time, was large. However, the trial-to-trial variability around the mean was small. The z coordinate, which was irrelevant for task performance (middle), stayed nearly constant with time, but varied substantially from trial to trial. The α w trajectory (right) showed intermediate behavior. For clarity of presentation and due to space limitations, we collapsed the analysis across different targets (directions and distances), and focused on the difference between teleoperated and freehand reach and reversal movements. The results of task space variability analysis of novices are presented in Fig. 4A, and of the expert in Fig. 5A. The variance per degree of freedom in x-y coordinates is depicted for teleoperated and freehand movements. Similar analysis for the z coordinate is not presented because it was larger by an order of magnitude (tenfold), and did not vary with. Examining task space variability suggests that teleoperated movements are less variable than freehand both for novices and expert. This result is consistent Fig. 4. Trial-to-trial variability analysis as a function of normalized movement time averaged across different movement directions, distances, and novice participants. A and depict the variability in the x-y plane. C and D depict the ratio between projected on UCM and on the orthogonal manifold for the x-y and z hypotheses. Symbols are means and error bars are ±1 standard error. A C Z tele Z free XY tele XY free D Fig. 5. Trial-to-trial variability analysis as a function of normalized movement time averaged across different movement directions and distances for teleoperated and freehand movements of an expert. Details are similar to Fig. 4. with smaller endpoint error, and is likely related to slower movement caused by the damping effect of the manipulator dynamics reported previously [5]. Not surprisingly, variability is reduced when relevant for task performance: the end of movement for reach and mid-movement for reversal. The results of joints space variability averaged across all novices are shown in Fig. 4CD. Consistent with our prediction, xy is larger than unity, indicating that planar hand motion is stabilized by coordination of joint angles. In general, freehand xy was higher than teleoperated, with the exception of the beginning of reach movements. This difference was most emphasized at the end of reach and middle of reversal movements due to local maxima in the freehand condition. These effects also corresponded to local minima in task space variability. In partial agreement

6 endpoint error [mm] E = R 2 =.5 p < V UCM /V ORT Expert Novice 1 Novice 2 Novice 3 Novice 4 Fig. 6. Endpoint error in reach (circles) and reversal movements (squares) as a function of variability ratio of the x-y hypothesis averaged across time samples. Filled symbols are teleoperated movements, and empty are freehand. lack dashed line depicts a regression model fitted to data. with our prediction, z is unity in the first half of reach movements and in the first and last quarters of reversals, but surprisingly, it is increased almost to the level of xy towards the points in time that were critical for task performance. This effect is stronger in freehand than teleoperated movements. The analysis of the joint space variability of the expert, depicted in Fig. 5CD, reveals that xy of the expert is much higher than that of novices in both teleoperated and freehand conditions. This is consistent with previous findings that relate high variability UCM to skill level. The freehand result is rather surprising, because the expert did not have special expertise in freehand tasks. However, the context of sitting in front of the surgical console may have invoked stabilization mechanisms that are normally utilized when performing RAS. Freehand xy was much higher than teleoperated, and there was a temporal correspondence between lower task space variability and higher xy. As predicted, the values of z did not vary substantially across movement times, and were equal to or below unity. Lower xy in the teleoperated case is consistent with previously reported reduced during reach adaptation to external force field that persisted even at late exposure to the field [1]. It is likely that the dynamics of the master manipulator have a similar effect to applying an external force field, and limit the ability of the user to exploit the redundancy and increase UCM variability. The fact that this effect was very strong in the case of an expert suggests that even though he may have adapted to the RAS system, the adaptation was not complete. This highlights the importance of our proposed framework for analysis of variability: even when task performance is sufficient, the extent of adaptation and expertise is revealed very clearly in the xy metric. The analysis of correlation between endpoint error and, depicted in Fig. 6, suggests that there is significant positive correlation (p<.1), but the trend is very weak, and the R 2 of the regression is extremely small (.5). This finding is not surprising, because our experimental task was simple, and hence, does not necessarily require full exploitation of the UCM for sufficient performance. IV. DISCUSSION We present a framework for analysis of trial-to-trial variability of surgeon arm posture in RAS, and apply it to compare teleoperated and freehand movements of expert and novices in RAS. We utilized the uncontrolled manifold analysis that was developed for the study of human motor control as a means of exploring how redundancy is resolved and exploited by the human motor control system [8, 9, 1]. In this framework, the ratio between UCM and orthogonal to UCM components of surgeon arm joint angles is used for testing hypotheses about the control of task variables, and as an indicator of skilled performance. Using this framework, we found preliminary evidence that during performance of planar movements users stabilize task-relevant directions of their hand movement by the coordination of joint angles, and that this stabilization is stronger in freehand movements than in teleoperation. In addition, the expert showed much larger stabilization than novices, and much stronger difference between freehand and teleoperated movements. It is likely that the differences between teleoperation and freehand are related to the effect of the dynamics of the master manipulator. These preliminary findings suggest that the proposed framework is a promising method for assessment of teleoperator design and control that reveals how design parameters affect the ability of the user to exploit the UCM for stabilization of hand movement. The small sample size of the current study does not allow us to make general statistically significant conclusions from our observations, especially in light of relatively large between-subjects variability. This will be addressed in future work, together with adding more participants with intermediate levels of expertise such as residents or surgical fellows. Such diversity in expertise levels will allow us to test this framework as a tool for RAS surgical skill evaluation. The method of UCM analysis presented in this paper requires knowledge of the analytical relationships between the control and task variables. However, it is also possible to perform this analysis without such knowledge, and estimate the parameters of a linear model that approximates the relationships between control and task variables by means of linear regression [8]. Therefore, this method can be used for the analysis of more complicated tasks where the model is difficult to derive, such as in the case of bimanual suture manipulation or other clinical tasks. The proposed framework includes several assumptions and choices that should be considered. Following the human motor control literature, we assume movement approximation as a sequence of time-varying static reference postures [9]. We also assumed that the deviations from this reference trajectory are small enough for the linearization of the UCM. This assumption was validated by comparing the measured tip sensor positions with the estimated positions according to Eq. 4. We chose to use absolute rather than relative angles to describe joint space configurations because they are extracted from raw data that we collect most directly. We used the Euler representation of joint angles, which

7 suffers from a singularity when the link orientation is exactly vertical. However, this did not appear in our analysis, and normally it is not likely due to the mechanics of the human arm in this posture. The clear difference between the variability ratio of the novices and the expert are consistent with previous studies reporting high variability ratio to be an indicator of skill. Interestingly, because the task was simple enough, we did not observe as large a difference in performance as the difference in variability ratio. However, it is likely that the advantage of such variability structure may be revealed in performance when the task is sufficiently difficult. In future studies, we plan to explore whether teleoperator design that optimizes exploitation of UCM by users will yield a device that allows superior surgical performance and shorter learning curves. We found preliminary evidence for correspondence of local maxima in the variance ratio to points in time that are critical for task performance. Further theoretical development and experimental validation of this framework will be used to study clinically relevant tasks, such as suture handling or knot tying. In such tasks, critical performance points are not necessarily defined a priori, and analysis of posture variability structure using UCM approach may suggest new insights into the coordination of such movements. ACKNOWLEDGMENT The authors thank Taru Roy and Sangram Patil for their help with experimental setup and initial data collection, and Anthony Jarc and Simon DiMaio for valuable discussions about the da Vinci Surgical System. REFERENCES [1] T. J. Tausch, T. M. Kowalewski, L. W. White, P. S. McDonough, T. C. rand and T. S. Lendvay, Content and Construct Validation of a Robotic Surgery Curriculum Using an Electromagnetic Instrument Tracker, The Journal of Urology, vol. 188, no. 3, 212, pp [2] H. Lin, I. Shafran, D. Yuh and G. Hager, Towards automatic skill evaluation: Detection and segmentation of robot-assisted surgical motions, Computer Aided Surgery, vol. 11, no. 5, 26, pp. d [3] J. Rosen, J. D. rown, L. Chang, M. N. Sinanan and. Hannaford, Generalized approach for modeling minimally invasive surgery as a stochastic process using a discrete Markov model, IEEE Transactions on iomedical Engineering, vol. 53, no. 3, 26, pp [4] G. Megali, S. Sinigaglia, O. Tonet and P. Dario, Modelling and Evaluation of Surgical Performance Using Hidden Markov Models, IEEE Transactions on iomedical Engineering, vol. 53, no. 1, 26, pp [5] I. Nisky, S. Patil, M. H. Hsieh and A. M. Okamura, Kinematic Analysis of Motor Performance in Robot-Assisted Surgery: A Preliminary Study, submitted. [6] T. Flash and N. Hogan, The coordination of arm movements: An experimentally confirmed mathematical model, Journal of Neuroscience, vol. 5, no. 7, 1985, pp [7] H. Mller and D. Sternad, Decomposition of Variability in the Execution of Goal-Oriented Tasks: Three Components of Skill Improvement, Journal of Experimental Psychology: Human Perception and Performance, vol. 3, no. 1, 24, pp [8] S. M. S. F. Freitas, J. P. Scholz and M. L. Latash, Analyses of joint variance related to voluntary whole-body movements performed in standing, Journal of Neuroscience Methods, vol. 188, no. 1, 21, pp [9] J. P. Scholz and G. Schoner, The uncontrolled manifold concept: identifying control variables for a functional task, Experimental rain Research, vol. 126, no. 3, 1999, pp [1] J.-F. Yang, J. Scholz and M. Latash, The role of kinematic redundancy in adaptation of reaching, Experimental rain Research, vol. 176, no. 1, 27, pp [11] D. N. Nenchev, Tracking Manipulator Trajectories With Ordinary Singularities: A Null Space-ased Approach, The International Journal of Robotics Research, vol. 14, no. 4, 1995, pp [12] F. J. Valero-Cuevas, M. Venkadesan and E. Todorov, Structured Variability of Muscle Activations Supports the Minimal Intervention Principle of Motor Control, Journal of Neurophysiology, vol. 12, no. 1, 29, pp [13] L. otzer and A. Karniel, A simple and accurate onset detection method for a measured bell-shaped speed profile, Frontiers in Neuroscience, vol. 3, 29. DOI: /neuro