spatial map of synthesized criteria for the redundancy...

1534-4320 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TNSRE.2014.2382105, IEEE Transactions on Neural Systems and Rehabilitation Engineering

JOURNAL OF IEEE IN TRANSACTIONS ON NEURAL SYSTEMS & REHABILITATION ENGINEERING, VOL. X, NO. X, MONTH YEAR 2

Spatial Map of Synthesized Criteria for the Redundancy Resolutionof Human Arm Movements

Zhi Li, Dejan Milutinovic and Jacob RosenThe kinematic redundancy of the human arm enables the elbow position to rotate about the axis going through the shoulder and

wrist, which results in infinite possible arm postures when the arm reaches to a target in a 3-dimensional workspace. To infer thecontrol strategy the human motor system uses to resolve redundancy in reaching movements, this paper compares five redundancyresolution criteria and evaluates their arm posture prediction performance using data on healthy human motion. Two synthesizedcriteria are developed to provide better real-time arm posture prediction than the five individual criteria. Of these two, the criterionsynthesized using an exponential method predicts the arm posture more accurately than that using a least squares approach, andtherefore is preferable for inferring the contributions of the individual criteria to motor control during reaching movements. As amethodology contribution, this paper proposes a framework to compare and evaluate redundancy resolution criteria for arm motioncontrol. A cluster analysis which associates criterion contributions with regions of the workspace provides a guideline for designinga real-time motion control system applicable to upper-limb exoskeletons for stroke rehabilitation.

Index Terms—arm motion control, kinematic redundancy resolution, upper limb exoskeleton

I. INTRODUCTION

The human arm is kinematically redundant with respectto reaching and grasping tasks in a 3-dimensional (3D)workspace. As a result, an upper limb exoskeleton designedfor stroke rehabilitation requires a motion control strategy thatcan render natural arm postures. For this purpose, this paperstudies reaching movements to infer the motor control strategyused by the healthy human arm, and to apply it to the real-time motion control of the EXO-UL7 upper limb exoskeleton(Fig. 1a).

(a)

Ps

Pe

Pw

Pc

u

v

f

a

(b)

Fig. 1: (a) EXO-UL7, a dual arm exoskeleton with seven DOFs in each arm.This system exhibits kinematic redundancy identical to the human arm. (b)Given a 3D wrist position, the arm plane formed by the positions of theshoulder (Ps), the elbow (Pe) and the wrist (Pw) can move around an axisthat connects the shoulder and the wrist due to kinematic redundancy. Theredundant DOF can be represented by a swivel angle ϕ.

Conventionally, motion control has been viewed as a matterof the structure and function of the central nervous system.Studies from the perspective of neuroanatomy have focusedon relating motor functions to different cortical, sub-cortical,

Zhi Li ([email protected]) is with Intelligent Motion Lab, Departmentof Electrical and Computer Engineering, Duke University, Durham, NC,27708; Dejan Milutinovic ([email protected]) is with the Department ofComputer Engineering, University of California, Santa Cruz, CA 95064,USA; Jacob Rosen ([email protected]) is with Bionics Lab, Departmentof Mechanical and Aerospace Engineering, University of California, LosAngeles, Los Angeles, CA, 90095

Bionics Lab URL: http://bionics.soe.ucsc.edu/

and spinal subsystems [1], [2]. From the perspective of neuro-physiology, Donders’ law has been applied to arm postures inreaching movements, yet it is violated when pointing at a targetwith the elbow flexed [3]. On the other hand, the equilibrium-point (EP) hypothesis specifies physiological variables usedby the central nervous system (CNS) as control variables,to address the redundancy problem (i.e., the behavior of theuncontrolled manifold) in the human motor system at themuscle level [4]. Unlike the neurophysiological perspective,a robotic viewpoint considers the human body, particularlythe musculoskeletal system, as a mechanical system with kine-matic and kinetic properties. The behaviors of this mechanicalsystem are constrained by its physical structures and the lawsof physics. The neural system does not so much to dictatethe movement of this mechanical system as to enhance thecompatibility of the system with the environment so that thetask can be completed according to the requirements andwith satisfactory performance [5], [6]. In this context, theredundancy of the human arm is resolved by control criteriawhich optimize performance variables used in mechanicalengineering. Such criteria have been applied to human motorcontrol processes such as motor planning, control, estimation,prediction and learning [7], [8].

When executing a movement plan on a robot with redundantdegrees of freedom, it is necessary to resolve the ill-posedinverse kinematics and kinetics to determine the mappingfrom the planned trajectory to joint motions, and then tojoint torques. The problem of controlling redundant degreesof freedom (DOFs), i.e., redundancy resolution, has beenconsidered in the control of robot manipulators. Resolutionmethods utilize task dependent constraints [9], [10], or morecommonly, performance criteria. The latter include manipula-bility [11]–[14], energy consumption [3], [15], smoothness ofmovement [16]–[19], task accuracy [20] and control complex-ity [21]. However, there is no general framework that comparesand evaluates these criteria.

Redundancy resolution that synthesizes multiple movementcontrol criteria has addressed the characteristics of movementbehavior to a better extent. For instance, Miyamoto et al.




studied reaching movements in a 2D workspace without end-point boundary conditions. By adding a signal dependent noiseto the movement controls, a linear combination of criteriamaximizing the task achievement and minimizing the energyconsumption resulted in a good match to the experimentally-measured hand trajectories [22]. Biess et al. broke down themotion control task into independent spatial and temporalmotor planning. A control criterion that restricts the armdynamics to geodesic paths is combined with a control thatminimizes the squared jerk along the selected end-effectorpath. The resulting reaching movements in a 3D workspace areclose to those which minimize the change in joint torques andthe peak value of kinematic energy [23]. Kim et al. studied themovements of reaching to a sequence of targets and predictedthe arm postures in real-time by integrating a biological-based kinematic control criterion that maximizes the motionefficiency with a dynamic criterion that minimizes the work injoint space, showing that the kinematic criteria outperforms thedynamic one [24]. A study of the tradeoff between minimizingthe angular joint displacement and averaging limits of theshoulder joint range [25] showed that a 70% − 30% linearcombination of arm posture predicted by these two criterialeads to a satisfactory redundancy resolution.

From the robotic perspective, this paper proposes a generalframework to compare and evaluate motion control strategiesthat predict arm posture in reaching movements. In this frame-work, the arm posture predictions of each candidate criterionare tested against experimental data collected from point-to-point reaching. By combining these candidate criteria accord-ing to their arm posture prediction accuracies, synthesizedcriteria are developed. The candidate criteria that better predictarm posture are assigned larger coefficients in the synthesizedmotion control criteria, and are therefore recognized as theones that dominate the arm motion. For control of an upperlimb exoskeleton in robot-assisted stroke rehabilitation, real-time motion control criteria are preferred, since unlike off-linemotion control criteria (e.g., minimum jerk principle [17]),real-time criteria (e.g. bounded jerk criterion [26]) do notneed to know about future states (e.g., the end position of themovement). Without the constraint of pre-planned movements,the upper limb exoskeleton can deal with unexpected tasks andencourages self-initiated movements on the part of the strokepatients.

In the rest of this paper, Section II describes a human armmodel compatible with the EXO-UL7 upper limb exoskeleton.After introducing the real-time redundancy resolution criteriain Section III, the methods used for criterion contributioninference and the experimental protocol for data collectionare presented in Section IV and Section V, respectively.According to the data analysis results in Section VI, discussionin Section VII infers the contribution of each criterion to thecontrol of arm motion and presents a map that associates thedominant motion control strategy with different task spaceregions.

II. MODELS OF HUMAN ARM

A. Kinematic Model

The kinematic model of human arm has seven DOFs (threeDOFs for the shoulder, three DOFs for the wrist and one DOFfor the elbow motion). The forward kinematics, including theDenavit-Hartenberg (DH) parameters, is described in [27]. Thethree shoulder joint and one elbow joint are actively involvedin reaching movements. As a result, the orientation of the handin the arm model is pre-specified by locking the three DOFsat the wrist joint.

Given the wrist position in 3D workspace, the human armhas one redundant DOF which allows the elbow to movearound an axis that goes through the center of the shoulderand the wrist joints. This redundant DOF can be representedby a swivel angle ϕ (see Fig. 1b). Given a fixed wrist positionin a 3D workspace, the arm plane formed by the positions ofthe shoulder (Ps), the elbow (Pe) and the wrist (Pw) can movearound an axis that connects the shoulder and the wrist dueto the kinematic redundancy. The direction of the elbow pivotaxis (denoted by n) is defined as:

n =Pw − Ps

||Pw − Ps||(1)

A plane orthogonal to n can be determined given the posi-tion of Pe. The point of intersection between the orthogonalplane and the vector

−−−−−→Pw − Ps is Pc.

−−−−−→Pe − Pc is the projection

of the upper arm (−−−−−→Pe − Ps) on the orthogonal plane. u is

the projection of a normalized reference vector a onto theorthogonal plane, which can be calculated as:

u =a− (a · n)n

||a− (a · n)n||(2)

The swivel angle ϕ, representing the arm posture, is definedby the angle between the vector

−−−−−→Pe − Pc and u. If the reference

vector a is [0, 0,−1]T , then the swivel angle ϕ = 0◦ when theelbow is at its lowest possible point [28].

B. Dynamic Model

The dynamic models of the left and right human armsare rendered via the Autolev software package [29]. Themotion equations generated by Kane’s method [30] integratethe estimates of mass, the center of mass and the momentof inertia with the kinematic model of the arm. Given theinitial arm condition, the dynamic model can respond toexternal forces (such as gravity) and provide an analyticalcalculation of the joint space variables (i.e., joint angles,velocities and accelerations), as well as the kinetic energyand potential energy. When customizing the dynamic modelfor each individual subject, the center of mass is estimatedaccording to the distribution of the center of mass (COM)in [31]. On average, the arm contributes 4.8% of the total bodyweight. The mass of arm segments and their inertia matricesare calculated based on the weight of subjects according tothe regression in [32].




III. CRITERIA FOR REDUNDANCY RESOLUTION

The EXO-UL7 exoskeleton is designed to assist self-initiated arm movements in unexpected tasks. Therefore, it re-quires real-time motion control rather than pre-planned motioncontrol, and thus redundancy resolution based on local (insteadof global) optimization. In this section, three kinematic andtwo dynamic motion control criteria are presented, whichhave been successful in resolving the kinematic redundancyof the human arm in reaching movements [3], [14]–[17], [33],[34]. The criteria designed for pre-planned motion control aremodified as in [15] to provide real-time arm posture prediction.

A. Criterion 1: maximizing the motion efficiency

Ps

Pe

Pw

Pm

Pc

Pc

’

n

f

(a)

Ps

Pe

n

Pc

Pw

Pc

’

ve

ve

’

(b)

Fig. 2: (a) Criterion 1 maximizes motion efficiency by maximizing theprojection of the longest principle eigen-vector of the manipulability ellipsoidon the direction from the hand to the virtual target Pm. The correspondingelbow position falls on the plane formed by Ps, Pw and Pm. (b) Criterion2 intends to maintain the arm posture close to the equilibrium arm postureby placing the elbow on the plane formed by the wrist position Pw and thedirection of the equilibrium vector ve.

Criterion 1 provides real-time arm posture prediction bymaximizing the motion efficiency of self-feeding movements.Given the role of the head as a cluster of sensing organs and theimportance of arm manipulation to deliver food to the mouth,the arm postures are determined by the human motor controlsystem for efficiently retracting the hand to the head region.Proposed in [14], Criterion 1 determines the swivel angle bymaximizing the motion efficiency to a virtual target in thehead. A good candidate for the position of the virtual target isthe position of the mouth, which is supported by intra-corticalstimulation experiments [35], [36]. When evoking coordinatedforelimb movements in conscious primates, each stimulationsite produced a stereotyped posture by which the arm movedto the same final position regardless of its posture in the initialstimulation. In the most complex example, a monkey formeda frozen pose with its hand in a grasping position in front ofits open mouth, which implies that during the arm movementtoward an actual target, the virtual target point at the head canbe set so that the potential retraction of the hand to the mouthcan be efficient.

Criterion 1 specifies a unique arm posture for each wristposition Pw in a 3D workspace. As shown in Fig. 2a, whenthe elbow falls on the plane formed by the positions ofthe shoulder Ps, the wrist Pw and the virtual target Pm,the projection of the longest principle eigen-vector of the

manipulability ellipsoid on the direction from the hand to thevirtual target Pm is maximized. In the direction of the longestprinciple axis of the manipulability ellipsoid, the efficiency ofthe velocity-force transmission between the joint space and thetask space is maximized. The end-effector of the manipulatorcan move fastest in this direction given the velocity inputs inthe joint space. If the position of Pm is set to be the position ofmouth, the designated arm postures can be the most efficientones for self-feeding.

B. Criterion 2: maintaining the equilibrium posture

Criterion 2, the rotational axis method proposed in [33],prefers equilibrium postures at which periarticular shouldermuscle actuation is minimized. At such postures, the upperarm is aligned with the equilibrium vector, which pointsout from the center of the shoulder along the axis of thecircumduction cone. Criterion 2 stipulates that the axis ofrotation of the arm plane (i.e., the plane formed by thepositions of the shoulder, elbow, and wrist) should be theequilibrium vector. The wrist position and axis of rotationdetermine the arm plane which fixes the elbow position.

The direction of the equilibrium vector for the upper armhas been experimentally investigated by NASA [37]. In mi-crogravity, the estimated shoulder flexion is about 36◦ and theshoulder abduction is about 50◦. Given the direction of thisaxis, the position of the elbow always falls on the plane formedby the rotational axis ve and the wrist position Pw. As shownin Fig. 2b, v′

e is the vector component of the rotational axisdirection ve perpendicular to n, i.e, the vector rejection of vefrom n. Given that v′

e is parallel with the vector Pe − Pc, theswivel angle is:

ϕ = arctan2(n · (v′e × u), v

′e · u) (3)

C. Criterion 3: minimizing joint angle change

The human motor system prefers motion smoothness. Kine-matic criteria that minimize the jerk in joint space and taskspace were proposed to account for the straight paths and bell-shaped velocity profiles observed in reaching movements [16],[17], [34], while dynamic criteria that minimize the change injoint torque [18], [19] further explained the mild curvaturein the roughly straight task space trajectories. However, theseavailable control strategies for motion smoothness are mostlydesigned for off-line motion control. Therefore, this paperproposes to a real-time motion control strategy based on localoptimization.

Similar to T. Kang’s minimization of the work in jointspace [15], Criterion 3 determines the arm postures in thefollowing way: given the expected positions of the wristPw(k + 1) and the shoulder Ps(k + 1), Criterion 3 exploresthe possible swivel angles for the next time step ϕ

′(k + 1)

and selects the one that minimizes the norm of the change inthe joint angle vector. Experimental data from [15] as wellas data collected in this research show that the swivel anglenever changes more than 0.5◦ per 0.01 sec. Given the currentswivel angle ϕ(k), Criterion 3 searches within the range of




[ϕ(k) − 0.5◦, ϕ(k) + 0.5◦] with a step of δϕ = 0.1◦, and theswivel angle for the next time step ϕ(k + 1) is:

ϕ(k + 1) = argminϕ′(k+1)

|θ(k)− θ′(k + 1)|

= argminϕ′(k+1)

√√√√ 4∑i=1

(θi(k)− θ′i(k + 1))2 (4)

In Eq. (4), θ(k) = [θ1(k), θ2(k), θ3(k), θ4(k)]T is the joint

angle vector for current time step. θ′(k+1) is the joint anglevector for the next time step computed from a possible ϕ

′(k+

1) value. Since this algorithm is generally applicable to localoptimization of various performance indices, in Section III-D itis also used to generate real-time control criteria that minimizekinetic energy.

D. Criterion 4: minimizing the change in kinetic energy

Energy-efficiency is another possible consideration. Sinceactivities of daily living are well adapted to gravity, unless thedynamics of the human body are under additional load, thehuman motor system may be more concerned with the kineticenergy than potential energy. Regarding arm motion control,J.F. Soechting et al. suggested predicting the arm posture inreaching movements by minimizing peak kinetic energy [3].Alternatively, A. Biess et al. minimized kinetic energy bylooking for a geodesic path in the Riemannian configurationspace. The resulting joint space trajectories demand less mus-cular effort since the sum of all configuration-speed-dependenttorques vanishes along this path [23].

The aforementioned methods are for pre-planned motioncontrol. For real-time applications, Criterion 4 determines thearm posture by local minimization of kinetic energy. With thedynamic model, kinetic energy (Ke) for each time step iscomputed given the states of the arm. The algorithm describedin Eq. (5) is similar to that of Criterion 3: given the kineticenergy for the current time step Ke(k), Criterion 4 exploresthe possible swivel angles for the next time step ϕ

′(k + 1)

within the range of [ϕ(k) − 0.5◦, ϕ(k) + 0.5◦] by the stepof δϕ = 0.1◦. The expected kinetic energy demanded at thenext time step Ke

′(k+1) is extracted from the dynamic arm

model. The swivel angle that minimizes the change in kineticenergy will be selected as the swivel angle prediction for thenext time step (ϕ(k + 1)).


|Ke(k)−Ke′(k + 1)| (5)

E. Criterion 5: minimizing the work in joint space

Minimizing the work in joint space is proposed by T. Kangas a real-time dynamic control criterion [15]. The work inthe joint space at each time step depends on (1) the jointtorques and (2) the difference in joint angles, which can beextracted from the dynamic model given the states of the arm.As Eq. (6), Criterion 5 explores in the neighborhood of thecurrent swivel angle ϕ(k) and determines the swivel angleϕ(k + 1) for next time step to be the one that demands theleast work in joint space.


|Wi|tk,tk+1

= argminϕ′(k+1)

4∑i=1

|Wi|tk,tk+1 (6)

In Eq. (6), |Wi|tk,tk+1denotes the work to be done by the

i-th joint.

IV. METHODS OF INFERENCE OF CRITERIONCONTRIBUTIONS

The five arm motion control criteria presented in Section IIIaccount for different performance considerations, includingmotion efficiency, muscle actuation efficiency, motion smooth-ness, and energy consumption. Their prediction performancehas been tested against data collected from different exper-imental setups, but not against a common baseline. As aresult, comparing their performance is difficult, and the relativecontributions of these criteria to arm motion control have notbeen evaluated.

Individual contributions of different criteria inferred fromexperimental data provide an important guideline to coeffi-cient assignment when combining multiple control criteria.However, methods of inferring criterion contributions have notbeen well explored. Kashi et al. inferred criterion contributionsusing brute-force search within a limited number of coefficientcombinations [25]. This inference is neither precise enoughto distinguish the behavior of different subjects, nor efficientenough to compare more control criteria within the same scale.Kim et al. applied least squares regression to infer the criterioncontribution of the two control criteria in comparison. Theinferred criterion contributions for each recorded movementare constant, which reflects behavior differences betweensubjects, but not how criterion contributions change duringmovement. In order to provide real-time inference of criterioncontributions, this paper proposes (1) a modified least squaresmethod and (2) an exponential method, both of which cancompare and evaluate large numbers of criteria efficiently.

A. The Least Squares Method

The least squares method infers criterion contributions dur-ing a period. Considering the five candidate criteria presentedin Section III, given the individual swivel angle prediction ofeach criterion for a time step (denoted by ϕi(k), i = 1, · · · , 5),the prediction of swivel angle for that time step (denoted byϕ(k)) is:

ϕ(k) =5∑1

ci(k)ϕi(k) (7)

ci (i = 1, · · · , 5) is the criterion contribution inferred forthe ith criterion. Using recent swivel angle measurements(twenty continuous time steps in measurement history beforeand including the current time step), the criterion contributionof each criterion for the next time step are computed by:

C(k+ 1)5×1

= A−1 · b (8)




where A is the prediction history from the five criteria (asEq. (9)),

A =

ϕc1(k − 19) · · · ϕc5(k − 19)...

. . ....

ϕc1(k) · · · ϕc5(k)

20×5

(9)

b is the measurement history (as Eq. (10)),

b =

ϕexp(k − 19)...

ϕexp(k)

20×1

(10)

and A−1 is the pseudo-inverse of matrix A using the leastsquares method.

The coefficients that indicate the contributions are furthernormalized as:

c(k + 1)i =C(k + 1)i∑5i=1 C(k + 1)i

(11)

With reference to Eq. (7), these coefficients will used togenerate the k + 1-th swivel angle prediction.

Note that for the least squares method, the more criteria be-ing evaluated the more measurements the least squares methodrequires to render the the estimation for current time step.The precision of the inference can be improved by involvingmore measurements from previous time steps. However, asthe older measurements are involved, the inferred contributionsbecome less sensitive to the temporal variation of the criterioncontributions. As a result of this tradeoff, this paper tentativelyproposes using the last twenty measurements when inferringthe contributions by the least squares method. In experimentaldata, a typical trial in the reaching movement experiments lastsfor 150 to 250 time steps at the sampling rate of 100 Hz.

B. The Exponential method

An alternative method of inferring contribution is the expo-nential method [38]. This method evaluates the contributioncoefficient of a criterion based on the difference between theexperimentally recorded swivel angle ϕexp(k) and the swivelangle predicted by this criterion. At time step k, each of thefive candidate criteria (i = 1, 2, · · · , 5) provides an individualswivel angle prediction, denoted by ϕi(k). The norm of theprediction error for each criterion is computed as:

εi(k) = |ϕexp(k)− ϕi(k)| (12)

Based on the five prediction errors, the standard deviationamong the prediction errors (denoted by σ(k)) can be com-puted.

According to the principle of maximum entropy, the prob-ability of the criterion i can be expressed as:

pi = c · exp(−λε2i ) (13)

(see Section A). Since the maximum entropy principle doesnot result in the probability distribution providing bias towardsany model, the experimental outcomes from all the modelsare assumed possible. Therefore, the standard deviation of the

prediction errors σ is the property shared among the models,which results in the criterion contribution c(k+1)i computedas:

Ci(k + 1) = exp[−ε2i (k)

σ2(k)] (14)

The criterion contributions are then normalized:

c(k + 1)i =Ci(k + 1)∑5i=1 Ci(k + 1)

(15)

which will be used to generate the swivel angle prediction attime step k + 1.

Because it does not rely on as much history, the exponentialmethod is expected to outperform the least squares methodfor real-time contribution inference, particularly when thecontributions of various criteria change during movement.Furthermore, the exponential method has no limit on numberof the criteria it can process in parallel.

C. Criterion Synthesization

The two proposed methods infer criterion contributions inreal-time, which can be used to compare the candidate criteria.These inferred contributions can also be used as coefficientsfor criterion synthesis to improve arm posture predictionaccuracy, because no individual control criterion can fullyaccount for arm postures in reaching movements.

Arm motion control is adapted to various environmentalconstraints and is therefore subject more than one performanceconsideration. Synthesizing multiple control criteria takes thiscomplexity into account. The contribution-inference/criterion-synthesis methods presented here are not limited to the fivecandidate criteria presented in Section III. Instead, these meth-ods are proposed as general frameworks for control criteriacomparison and evaluation. By inferring the contributionsof different control criteria, a limited number of “major”components that are significant to the motor control strategywill be distinguished from the “minor” components that areless prominent considerations in arm motion control. Thesynthesized arm motion control criteria aim to capture theimportant factors that influence the motor control system,rather than generate good arm posture predictions by over-fitting the experimental data with too many variables.

V. EXPERIMENT PROTOCOL

The arm posture predictions of motion control criteria aretested against experimental data collected on point-to-pointreaching movements. In this experiment, ten healthy subjects(six males and four females) are instructed to conduct reachingmovements with their right arms to each of the eight targetsspecified in the spherical workspace (Fig. 3). Each subjectperforms eight reaching movement sessions, one for eachtarget. The reaching movements in each session start from oneof the remaining seven targets. A complete session consistsof five repetitions of seven different movements. The totalnumber of trials for each subject is 8× 7× 5 = 280. Duringthe experiment, the subject sits in a chair with a straight back.The chair is placed such that the subject can point at the




ShoulderCenter ofVirtual Sphere

(a) Top View.

Shouler

Center ofVirtual Sphere

(b) Front View

(c) 3D spherical workspace. (d) Attached markers.

Fig. 3: (a) and (b) show the top and front views of the spherical workspace,respectively. (c) Eight targets are selected among all the available targets(denoted by blue dots in circles). (d) A subject is performing the instructedreaching movements, with markers attached to her right arm and the torso forposition tracking.

targets with comfort and with his/her elbow naturally flexed.The height of the workspace center is adjustable and is alwaysaligned with the right shoulder of the subject. The subject’sright arm is free for reaching movements, but the body ofthe subject is set against the chair back to minimize shoulderdisplacement. During the reaching movements, subjects keepthe pointing fingers in line with the forearm to minimize wristflexion.

Subjects are asked to point with the index finger tip at acomfortable pace. At the beginning of each trial, the subjectis informed of the targets that the trajectory starts with andends at, i.e., the start and end targets. After receiving a “start”command, the subject moves his/her index finger from thestart target to the end target. A motion capture system recordsa single file for each trial at a sampling rate of 100 Hz. Asshown in Fig. 3d, passive reflective markers are attached tothe torso and the right arm of the subject. The recording startsfrom the time when the subject points the index finger to thestart target and ends after the index finger tip becomes steadyat the end target. To minimize the effect of fatigue, subjectstake a rest after completing each session. With the recordeddata of shoulder, elbow and wrist positions, the swivel anglesprofiles are extracted for each trial.

VI. RESULTS

This section presents the results of the arm posture predic-tion performance of the five candidate criteria, as well as theperformance of the synthesized criteria using the least squaresand exponential methods. The comparison shows that the leastsquares method results in prediction performance comparableto the candidate criteria with good prediction performance,

while the exponential method infers the criteria contributionmore accurately and therefore generates much better arm pos-ture predictions. Further data analysis clusters the computedcoefficients to identify characteristic combinations of motioncontrol criteria. The dominant regions of each characteristiccombination are presented in a map that associates the clusterswith wrist positions in task space.

A. Prediction Performance of the Criteria

0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5

prob

µLSQ

σLSQ

(a) Least squares method (LSQ).0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

0.5

prob

µEXP

σEXP

(b) Exponential method (EXPR).

Fig. 5: Swivel angle prediction performance of the synthesized criteria using(a) the least squares method and (b) the exponential method. µ and σ denotethe mean and the standard deviation of the prediction error.

Fig. 4 and Fig. 5 show the means (µ) and standard deviations(σ) of the prediction errors for all the valid trails (2674 out of2800) conducted by ten subjects. Fig. 4 shows the predictionperformance of the five candidate criteria. Fig. 5 shows theprediction quality of the synthesized criteria using the leastsquares method and the exponential method, respectively.Comparison between Fig. 5 and Fig. 4 shows that the pre-dictions of the synthesized criteria using least squares is moreaccurate than Criterion 1 and 2, comparable to Criterion 3 and4, and worse than Criterion 5, while the synthesized criteriausing the exponential method is much more accurate than anycandidate criterion. For the exponential method, 79.32% of thetrials have both µEXP ≤ 5◦ and σEXP ≤ 5◦, and only 3.37%trials have either µEXP ≥ 10◦ or σEXP ≥ 10◦. For the leastsquares method, 15.78% of the trials have both µLSQ ≤ 5◦

and σLSQ ≤ 5◦. 71.20% trials have either µLSQ ≥ 10◦ orσLSQ ≥ 10◦.

The exponential method infers the variance of the criterioncontributions better than the least squares method. As shownin Fig. 6, the contribution coefficients assigned by the ex-ponential method vary more than the those assigned by theleast squares method. In Fig. 6, the swivel angle and thecoefficients were normalized relative to the percentage of thepath length traversed by the hand (instead of time), sincein the reaching experiments each subject moved at his/herown pace. The coefficients corresponding to the candidatecriteria are denoted by ci, where i = 1, 2, 3, 4, 5. “Exp”denotes the measured (experimental) swivel angle profiles,and “Est” denotes the swivel angle predicted (estimated) bythe synthesized criteria. Although both methods for inferringcriteria contribution coefficients result in the predictions thatfollow trends of the measured swivel angle, the predictionerrors of the exponential method are much smaller. This maybe because the exponential method uses the most recent datasample, while the least square method depends on the last




0 10 20 30 40 500

0.1

0.2

0.3

0.4

0.5pr

ob

µEXPR

σEXPR

(a) Criterion 1.0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

0.5

prob

µEXPR

σEXPR

(b) Criterion 2.0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

0.5

prob

µEXPR

σEXPR

(c) Criterion 3.0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

0.5

prob

µEXPR

σEXPR

(d) Criterion 4.0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

0.5

prob

µEXPR

σEXPR

(e) Criterion 5.

Fig. 4: Swivel angle prediction performance for each candidate criterion. µ and σ denote the mean and the standard deviation of the prediction error.

0 0.2 0.4 0.6 0.8 130

35

40

45

50

55

60

65

70

Percentage of path length %

Sw

ivel

ang

le (

deg)

c1

c2

c3

c4

c5

ExpEst

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1


Coe

ffici

ent

c1

c2

c3

c4

c5

(a) Least squares method (LSQ).

0 0.2 0.4 0.6 0.8 130

35

40

45

50

55

60

65

70


Sw

ivel

ang

le (

deg)

c1

c2

c3

c4

c5

ExpEst

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1


Coe

ffici

ent

c1

c2

c3

c4

c5

(b) Exponential method (EXP).

Fig. 6: The swivel angle predictions of candidate criteria, as well as theirinferred contributions. c1 to c5 refer to the candidate criteria. Est refers tothe synthesized criteria. Exp refers to the swivel angle measurements.

20 data samples. Comparison of the coefficient profiles showsthat the criteria with large prediction errors are suppressedefficiently by the exponential method, which result in a biggerspread of coefficient ci values.

B. Characteristic Combinations of Motion Control Criteria

The previous subsection has shown that healthy reachingmovements can be best explained by synthesizing multiplecriteria using the exponential method. The coefficient assignedto each criterion indicates the time-varying contribution ofthat criterion. In the following section, K-means clusteringwill be applied to the contribution coefficients inferred by theexponential method to identify the characteristic combinationsof motion control criteria, which can be further mapped to taskspace the wrist positions.

1) K-means Clustering of Coefficient VectorsFor each step during the movement, the exponential method

has inferred the criterion contribution coefficients, which formscoefficient vectors v = [c1, ...c5]

T . Regardless of the se-quences of consecutive steps, each coefficient vector is consid-ered as an individual data point in the K-means clustering. Inorder to decide the number of clusters, the sum of the squareddistances from each point to the center of its cluster (denotedby sN ) is computed. This sum sN decreases as the number ofclusters increases. Fig. 7 shows the normalized sN with respect

to s1 for N = 1, 2, ...20. At N = 9, the ratio between sN ands1 is reduced to 5%, which is appropriate for clustering. Thepercentages of vector coefficients in each cluster for N = 9 isshown in Fig. 7b. Cluster 1 has about 30% of the coefficientvectors, while the population in every other cluster is less than15%.

0 5 10 15 200

20

40

60

80

100

N of clusters

Sum

of s

quar

ed d

ista

nce

(%)

Nthreshold

= 9

(a) Clustering threshold.

1 2 3 4 5 6 7 8 90

5

10

15

20

25

30

Clusters

Num

ber

of p

oint

s (%

)

(b) Cluster distribution, N = 9.

Fig. 7: The sum of the squared distances to the cluster centroid (sN ) iscomputed for increasing cluster number (N ). When the ratio between sNand s1 is reduced to 5%, the clustering is stabilized, at N = 9.

2) Results of K-means ClusteringShown in Figures 8a to 8i , the K-means clustering of the

coefficient vectors has identified characteristic combinationsof contribution coefficients. With five candidate criteria, athreshold coefficient value of 0.2 is set to distinguish betweenthe dominant and non-dominant criteria. As a result, thecharacteristic combination of coefficients can be encoded afive digit binary string. For instance, the characteristics ofmovements in Cluster 1 (see Fig. 8a) can be encoded as 00111,indicating that Criteria 3, 4, and 5 are the dominant criteria,whereas Criteria 1 and 2 make no significant contribution.

In Fig. 8, the clusters are ordered by point populations.Clusters 1, 2, 3 and 6, which in total have about 70% ofthe point population, are dominated by multiple criteria, whileeach of the remaining five clusters has only one dominant cri-terion. This explains the higher performance of the synthesizedcriteria: most of the data can only be predicted using multiplecriteria. It also explains how individual criteria can have goodprediction performance in some cases: some parts of the dataare best explained by a single criterion.

3) Associating Clusters with Task Space Wrist PositionsThe clusters of coefficient vectors, which indicate the

characteristic combinations of motion control criteria, canbe mapped to wrist position in the task space. As shownin Figures 9a to 9i , the 3D task space is divided into cellswith a 50 × 50mm grid on the plane the subject is facing(i.e., the x-z plane). Every data point (i.e., coefficient vector)




0

0.2

0.4

0.6

0.8

1

1 2 3 4 5Criteria

Coe

ffici

ent

Code: 00111

(a) Cluster 1.

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5Criteria

Coe

ffici

ent

Code: 00101

(b) Cluster 2.

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5Criteria

Coe

ffici

ent

Code: 01100

(c) Cluster 3.

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5Criteria

Coe

ffici

ent

Code: 00100

(d) Cluster 4.

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5Criteria

Coe

ffici

ent

Code: 00010

(e) Cluster 5.

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5Criteria

Coe

ffici

ent

Code: 01001

(f) Cluster 6.

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5Criteria

Coe

ffici

ent

Code: 11000

(g) Cluster 7.

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5Criteria

Coe

ffici

ent

Code: 01000

(h) Cluster 8.

0

0.2

0.4

0.6

0.8

1

1 2 3 4 5Criteria

Coe

ffici

ent

Code: 00001

(i) Cluster 9.

Fig. 8: Characteristic combinations of contribution coefficients are identifiedby K-means clustering. With respect to the threshold coefficient value 0.2, thedominant criteria are distinguished from the non-dominant ones.

falls into a cell according to its associated wrist position. Thefrequency of a cluster in a cell is the ratio between the numberof points from that cluster within that cell and the total numberof points in that cell. Given a specific cluster that represents acharacteristic combination of criteria, arm postures are moreaccurately predicted by that cluster in the regions where it hashigher frequency.

Clusters 1, 2, 3 and 6 correspond to characteristic com-binations with multiple dominant criteria. For instance, thedominant criteria of Cluster 1 minimize the joint angle change,the kinetic energy and the work in joint space. In Fig. 9a,Cluster 1 has high frequency in the lower half of the taskspace, and in the top-right corner. Cluster 2 is like Cluster 1except that it does not minimize kinetic energy. It only has highfrequency in the lower-right of the task space. Both Clusters3 and 6 are dominated by the rotational axis criterion. Cluster3 also minimizes the joint angle change and works best in thetop-left of the task space, while Cluster 6 also minimizes thework in joint space and works best when the wrist is on the

left side of the task space.The remaining clusters correspond to the combinations

dominated by single criteria. As a result, their frequencygraphs indicate the task space regions in which individualcriteria have good arm posture prediction. Cluster 4 minimizesthe change in joint angle and works best for the right side ofthe task space. Cluster 5 minimizes the kinetic energy andworks well in the lower left of the task space. Cluster 7emphasizes Criterion 1 and has high performance predictingarm posture when the hand reaches the leftmost edge of thetask space or moves around the top-right of the task space.Cluster 8 is dominated by only the rotational axis methodand works well for the top half of the task space. Cluster9 minimizes the work in joint space and works best for thetop-right and bottom-left regions.

Fig. 9j is a combination of the individual frequency graphs.In Fig. 9j, each cell in the task space is filled with the colorof the cluster with the highest frequency in that region. Thiscolored map reflects the most frequent combinations of criteriain different regions of the task space.

VII. DISCUSSION

This paper has analyzed recorded data from reaching move-ments and inferred the contributions of various criteria toarm motion control. Five criteria (three kinematic and twodynamic) are investigated, and are compared by their theswivel angle prediction performance. Inference based on syn-thesized criteria using the exponential method predicts thearm postures more accurately than inference using the leastsquares method. Using the exponential method, among 2674valid trials collected from ten healthy subjects, the mean andstandard deviation of the prediction errors during movementwas less than 5◦ for 79% of the trials, and only 3% of trialshad either a mean or standard deviation of the prediction errorof more than 10◦.

Using K-means clustering, the contribution coefficient vec-tors are grouped into nine clusters with distinguishable co-efficient value distributions, which indicate the characteristiccombinations of motion control criteria. The clusters aremapped to wrist positions in the 3D workspace, and theirhigh-frequency regions are presented in a colored map. Basedon the results presented in Section VI, this section willprovide further discussion that highlights the new findingsregarding the strategies of healthy arm motion control. Boththe methodology contribution (i.e., the general framework thatsynthesizes, evaluates and compares motion control criteriathat resolve the kinematic redundancy of human arm) andits application to the real-time control of an upper limbexoskeleton will be addressed.

A. Regional Motion Control Strategies in the Task Space

The data analysis has shown by synthesizing a limitednumber of control criteria that address different aspects ofmotion characteristics, the kinematic redundancy of the humanarm can be resolved to render natural human arm postures inreaching movements. The redundancy resolution according tothe combined control criteria outperforms all of its individual




(a) Cluster 1. (b) Cluster 2.

(c) Cluster 3. (d) Cluster 4.

(e) Cluster 5. (f) Cluster 6.

(g) Cluster 7. (h) Cluster 8.

(i) Cluster 9.−500 −250 0 250 500

−500

−250

0

250

500

(j) Color Map.

Fig. 9: (a) to (i) present the clusters’ frequencies in the task space. (j) comparesthe graphs for the nine clusters and illustrates the most-frequent combinationof motion control criteria for each cell in the task space.

components. The method used to combine the criteria iscritical to getting good estimations of arm posture. The armpostures are not be well-predicted by the least squares method,which assigns the contribution coefficients based on the overallprediction performance within a relatively long history. Thehigher performance of the exponential method, which assignscontribution coefficients only based on the prediction of thelast time step indicates that the contribution of each individualcriterion is time-sensitive. Indeed, the contribution coefficientassigned to each individual criterion varies during the reachingmovement, instead of maintaining a constant value for thewhole movement. In previous research, Kashi et al. integratedtwo kinematic control criteria and suggested constant partial

contributions to combine these two criteria: 70% for thecriterion that minimized angular displacement and 30% forthe criterion that averaged the limits of the shoulder jointrange [25]. Kim et al. combined a criterion that maximizedmotion efficiency (Criteria 1) with one that minimized thework in joint space (Criteria 5) using least squares and claimedthat the contribution of the dynamic criterion is negligiblecompared with the kinematic criterion [14]. Biess et al. sug-gested a global path planning method that defines the temporalproperties of the movement by minimizing the squared jerkalong the selected end-effector path, and the spatial propertiesof the movements by finding the geodesic path in jointspace [23]. According to this method, there exists a singlecontrol criterion that dictates the spatiotemporal propertiesof reaching movements. These results are all challenged byour findings that (1) the contribution coefficients of combinedcriteria should be time-varying instead of constant, and (2) nosingle control criterion can accurately model arm movementsfrom the beginning to the end.

Clustering the contribution coefficient vectors showed thespatial dependence of the criterion contributions in addition toits temporal dependence. A combined map of cluster frequency(Fig. 9j) shows that the lower part of the workspace isdominated by cluster 1 (represented by red). Cluster 1 issignificantly affected by criteria 3, 4 and 5: the kinematiccriterion that minimizes the joint angle change, as well asthe two dynamic criteria that minimize the change in kineticenergy and the work done in joint space. A possible explana-tion for the high frequency of Cluster 1 in this region is thatwhen reaching for targets in the lower part of the workspace,the arm is far away from the center of the stereoscopicvisual range. Without seeing the movements of the wholearm, motion control may be more dependent on proprioceptivefeedback. Low elbow postures in accordance with the directionof gravity do not block the view for reaching movement inthis region, and therefore may be preferred for less energyconsumption. In addition, when reaching to the lower-left partof the workspace, these energy-saving elbow postures may bepreferred since the arm motion range is constrained by thetorso.

In the upper-right part of the workspace, Cluster 3 is themost frequent (represented by yellow in Fig. 9j). Accordingto Fig. 8c, the control strategy of cluster 3 is strongly affectedby two kinematic criteria: maintaining the equilibrium posture(criterion 2) and minimizing the joint angle change (criterion3). With the shoulder position aligned with the center of theworkspace, the upper part of the workspace is about even witheye-level. The equilibrium posture may be preferred since itnaturally brings the hand into the stereoscopic visual range,and results in less work for the periarticular muscles. Note thatthe dynamic model used simulates the human arm as linkedrigid bodies. Without simulating muscular forces, dynamiccriteria are less useful than the equilibrium posture criterion inpredicting motions in this area. The criterion that minimizesthe joint angle change demonstrates a strong impact in Clusters1 to 4. Considering the fraction of the coefficient vectors inthese four clusters (62.56%) and the area of the workspacewhere they have high frequency (see Figures 9a to 9d ), this




criterion that emphasizes smoothness of motion is generallyapplicable to the whole workspace.

B. Methodology Contribution

As a methodology contribution, this paper proposes: (1) ageneral framework for the comparison of real-time motioncontrol criteria and (2) methods for criterion synthesis and con-tribution inference. By synthesizing a highly-accurate motioncontrol criterion out of several candidate criteria, the methodfollowed here is able to infer the contribution of each candidatecriterion to arm motion control, and the temporal and spatialvariation of its contribution. Clustering is used to determinewhich criteria are related, and find characteristic combinationsof criteria that best explain arm motion in different areas ofthe task space. This allows for high-fidelity analysis of thecriterion contributions, and a computationally efficient costfunction which ignores criteria with negligible contributionscould be constructed as a result. This framework could alsobe used to evaluate more candidate criteria besides thosepresented in this paper.

Within the proposed general framework, the least squaresand the exponential methods are investigated. Section VI-Apresents the prediction quality of the synthesized criteria usingthese methods, as well as the prediction quality of eachcandidate criterion. Compared to the least squares method, theproposed exponential method is preferable for criterion synthe-sis and contribution inference: it predicts the arm posture moreaccurately than all of the individual candidate criteria, whilethe least squares method predicts no better than the criterionwith the best individual performance. The main differencebetween the two synthesis methods is that the least squaresmethod considers the last 20 steps of history and tries tofind a set of constant coefficients which maximize predictionaccuracy during that period, whereas the exponential methodonly considers prediction error in the last step and adjuststhe coefficients at each step accordingly. The least squaresmethod would be able to predict arm posture accurately ifthe contribution of each candidate criterion were relativelyconstant, but the more accurate prediction rendered by theexponential method shows that the contributions of candidatecriteria are not constant. As shown in Figures 6 to 9j , thecontribution coefficients vary in time and space.

APPENDIX

The entropy H(k) of the discrete probability distributionpi(k) (i = 1, 2, · · · , N ) at the time step k is:

H(k) =N∑i=1

pi(k) ln pi(k) (16)

The distribution satisfies the constraint

N∑i=1

pi(k) = 1 (17)

Furthermore, based on the observed quantities, the varianceof the distribution should be equal to the experimentallyobserved variance, that is:

N∑i=1

ε2i (k)pi(k) = σ2 (18)

According to the maximum entropy principle [38], the leastinformative prior distribution is defined by the set of valuespi(k) that maximize the entropy (Eq. (16)) under the abovetwo constraints. This maximization problem can be solvedusing Lagrange multipliers λ1 and λ2 as an unconstrainedmaximization problem of the cost function J :

J =N∑i=1

pi(k) ln pi(k)− λ1

(N∑i=1

ε2i (k)pi(k)− σ2

)

− λ2

(N∑i=1

pi(k)− 1

)(19)

The maximum is defined by ∂J/pi(k) = 0 for i = 1, ...Nand ∂J/λj(k) = 0 for j = 1, 2, which yields:

ln pi(k) + 1− λ1ε2i (k)− λ2 = 0 (20)

and the resulted probability pi(k) is computed as:

pi(k) = exp(−1 + λ1ε2i (k) + λ2) = c0 · exp(λ1ε

2i (k)) (21)

According to the constraint on the sum of the probability,the probability pi(k) needs to be normalized as Eq. (22) suchthat the constant c0 can be canceled.

p′i(k) =

exp(λ1ε2i (k))∑Ni=1 exp(λ1ε2i (k))

(22)

Given the prediction error based on the criterion i (i =1, 2, ...N ), λ1 is a common property of p(ε2i |i), which isthe the probability density function of ε2i . These probabilitydensity functions satisfy

∫ ∞

0p(ε2i |i)d(ε2i ) = 1 (23)

such that: (1) p(ε2i |i) is the exponential distribution and (2) itis independent of the criterion and therefore is the same forall i. Since λ1 = −1/σ2

1 , we can set σ21 = σ2 to obtain:

p(ε2i |i) =1

σ2exp

(−

ε2iσ2

)(24)

REFERENCES

[1] E. R. Kandel, J. H. Schwartz, T. M. Jessell, S. A. Siegelbaum, and A. J.Hudspeth, Principles of Neural Science. McGraw-Hill Professional;5th edition, 2012.

[2] D. Purves, G. J. Augustine, D. Fitzpatrick, W. C. Hall, A.-S. LaMantia,and L. E. White, Neuroscience. Sinauer Associates, Inc., 2011, 5thedition.

[3] J. Soechting, C. Buneo, U. Herrmann, and M. Flanders, “Moving effort-lessly in three dimensions: does donders’ law apply to arm movement?”J. Neuroscience, vol. 15, no. 9, pp. 6271–6280, 1995.

[4] M. Latash, “Motor synergies and the equilibrium-point hypothesis,”Motor Control, vol. 14, no. 3, p. 294C322, 2010.

[5] M. H. Raibert and J. K. Hodgins, “Legged robots,” in Biological NeuralNetworks in Invertebrate Neuroethology and Robotics, R. D. Beer,T. McKenna, and R. Ritzmann, Eds. Elsevier Science & TechnologyBooks, 1993, pp. 319–354.

[6] M. Turvey and S. Fonseca, “Nature of motor control: perspectives andissues.” Adv Exp Med Biol., vol. 629, pp. 93–123, 2009.




[7] M. Kawato, “Internal models for motor control and trajectory planning.”Curr Opin Neurobiol., vol. 9, no. 6, pp. 718–727, 1999.

[8] D. Wolpert and Z. Ghahramani, “Computational principles of movementneuroscience.” Nat Neurosci., vol. Suppl., pp. 1212–1217, 2000.

[9] L. Sciavicco, “A dynamic solution to the inverse kinematic problem forredundant manipulators,” in ICRA 1987, vol. 4, Raleigh, NC, USA, Mar.1987, pp. 1081–1087.

[10] ——, “A solution algorithm to the inverse kinematic problem forredundant manipulators,” IEEE Trans. Robot. Automat., vol. 4, no. 4,pp. 403–410, 1988.

[11] H. Asada and J. Granito, “Kinematic and static characterization of wristjoints and their optimal design,” in ICRA 1985, St. Louis, Missouri, Mar.1985, pp. 244–250.

[12] T. Yoshikawa, “Dynamic manipulability of robot manipulators,” in ICRA1985, St. Louis, Missouri, Mar. 1985, pp. 1033–1038.

[13] ——, Foundations of Robotics: Analysis and Control. The MIT Press,1990.

[14] H. Kim, L. Miller, and J. Rosen, “Redundancy resolution of a humanarm for controlling a seven dof wearable robotic system,” in EMBC2011, Boston, USA, Aug. 2011.

[15] T. Kang, J. He, and S. I. H. Tillery, “Determining natural arm configura-tion along a reaching trajectory,” Exp Brain Res, vol. 167, pp. 352–361,2005.

[16] N. Hogan, “An organizing principle for a class of voluntary movements,”J. of Neuroscience, vol. 4, no. 2, pp. 2745–2754, 1984.

[17] T. Flash and N. Hogan, “The coordination of arm movements: anexperimentally confirmed mathematical model,” J. of Neurophysiology,vol. 5, pp. 1688–1703, 1985.

[18] Y. Uno, M. Kawato, and R. Suzuki, “Formation and control of optimaltrajectory in human multijoint arm movement - minimum torque-changemodel,” Biology Cybernetics, vol. 61, pp. 89–101, 1989.

[19] E. Nakano, H. Imamizu, R. Osu, Y. Uno, H. Gomi, T. Yoshioka, andM. Kawato, “Quantitative examinations of internal representations forarm trajectory planning: Minimum commanded torque change model,”The Journal of Neurophysiology, vol. 81, no. 5, pp. 2140–2155, 1999.

[20] C. M. Harris and D. M. Wolpert, “Signal-dependent noise determinesmotor planning,” Nature, vol. 194, pp. 780–784, 1998.

[21] E. Todorov and M. I. Jordan, “Optimal feedback control as a theory ofmotor coordination,” Nature Neuroscience, vol. 5, pp. 1226–1235, 2002.

[22] H. Miyamoto and M. Kawato, “Tops (task optimization in the presenceof signal-dependent noise) model,” Sys. and Comp. in Japan., vol. 35,pp. 48–58, 2004.

[23] A. Biess, D. Liebermann, and T. Flash, “A computational model forredundant human three-dimensional pointing movements: integrationof independent spatial and temporal motor plans simplifies movementdynamics.” J. of Neurosci., vol. 27, pp. 13 045–64, 2007.

[24] H. Kim, Z. Li, D. Milutinovic, and J. Rosen, “Resolving the redundancyof a seven dof wearable robotic system based on kinematic and dynamicconstraint,” in ICRA 2012, St. Paul, Minnesota, USA, 2012.

[25] B. Kashi, I. Avrahami, J. Rosen, and M. Brand, “A bi-criterion modelfor human arm posture prediction.” in 2012 World Congress on MedicalPhysics and Biomedical Engineering, Beijing, China, May 2012, pp.1–4.

[26] A. Frisoli, C. Loconsole, R. Bartalucci, and M. Bergamasco, “A newbounded jerk on-line trajectory planning for mimicking human move-ments in robot-aided neurorehabilitation,” Robotics and AutonomousSystems, vol. 61, no. 4, pp. 404–415, 2012.

[27] Z. Li, H. Kim, D. Milutinovic, and J. Rosen, “Synthesizing redundancyresolution criteria of the human arm posture in reaching movements.”Redundancy in Robot Manipulators and Multi-robot systems, vol. 57,pp. 201–240, 2013.

[28] N. I. Badler and D. Tolani, “Real-time inverse kinematics of the humanarm,” Presence, vol. 5, no. 4, pp. 393–401, 1996.

[29] Unknown, “Motion genesis,” previously Autolev. Accessed: May 13,2014. [Online]. Available: http://www.motiongenesis.com/

[30] T. Kane and D. Levinson, Dynamics: Theory and Applications. NewYork: McGraw-Hill, 1985.

[31] S. L. Roberts and S. K. Falkenberg, Biomechanics: Problem Solving forFunctional Activity. St. Louis: Mosby, United States, 1992.

[32] Aerospace medical research laboratory, “Investigation of inertial prop-erties of human body,” Tech. Rep., Mar 1975.

[33] Z. Li, J. Roldan, D. Milutinovic, and J. Rosen, “The rotational axisapproach for resolving the kinematic redundancy of the human arm inreaching movements.” in EMBC 2013, Osaka, Japan, July 2013, pp.2507–2510.

[34] Y. Wada, Y. Kaneko, E. Nakano, R. Osu, and M. Kawato, “Quantitativeexaminations for multi joint arm trajectory planning using a robust calcu-lation algorithm of the minimum commanded torque change trajectory,”J. of Neural Networks, vol. 14, pp. 381–393, 2001.

[35] R. P. Duma and P. L. Strick, “Motor areas in the frontal lobe of theprimate,” Physiol Behav, vol. 77, pp. 677–682, 2002.

[36] M. Graziano, C. Tylor, and T. Moore, “Complex movements evoked bymicro stimulation of precentral cortex,” Neuron, vol. 34, pp. 841–851,2002.

[37] F. E. Mount, M. Whitmore, and S. L. Stealey, “Evaluation of neutralbody posture on shuttle mission sts-57 (spacehab-1),” Tech. Rep., Feb2003.

[38] E. T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev.,vol. 106, pp. 620–630, 1957.

Zhi Li is a postdoc at the Intelligent Motion Lab,Department of Electrical and Computer Engineering,Duke University. She received her B.Sc. in Mechan-ical Engineering from China Agricultural University(Beijing, China) in 2006, M.A.Sc. in Mechanical En-gineering from University of Victoria (BC, Canada)in 2009, and Ph.D. in Computer Engineering fromUniversity of California, Santa Cruz in 2014. Herresearch interests focus on wearable robotics, sur-gical/rehabilitation robotics, teleoperation, haptics& virtual reality, neuromuscular control and stroke

rehabilitation.

Dejan Milutinovic earned Dipl.-Ing (1995) andMagister’s (1999) degrees in electrical engineeringfrom the University of Belgrade, Serbia and a doc-toral degree in electrical and computer engineering(2004) from Instituto Superior Tecnico, Lisbon, Por-tugal. From 1995 to 2000 he worked as a researchengineer in the Automation and Control Division ofMihajlo Pupin Institute, Belgrade, Serbia. His doc-toral thesis was the first runner-up for the best PhDthesis of European Robotics in 2004 by EURON. Hewon the NRC award of the US Academies in 2008

and Hellman Fellowship in 2012. Dr. Milutinovic is currently an associateprofessor in the Department of Computer Engineering, UC Santa Cruz. Hisresearch interests are in the area of modeling and control of stochasticdynamical systems applied to robotics. He is an associate editor of the ASMEJournal of Dynamic Systems, Measurement, and Control.

Jacob Rosen is a professor of medical roboticsat the Department of Mechanical and AerospaceEngineering, University of California, Los Ange-les (UCLA). His research interests focus on medi-cal robotics, biorobotics, human centered robotics,surgical robotics, wearable robotics, rehabilitationrobotics, neural control, and human-machine inter-face. He received his B.Sc. in Mechanical Engineer-ing, M.Sc. and Ph.D. in Biomedical Engineeringfrom Tel-Aviv University in 1987, 1993 and 1997respectively. From 1987 to 1992 he served as an

officer in the IDF studying human-machine interfaces. From 1993 to 1997 hewas a research associate developing and studying the EMG based poweredExoskeleton at the Biomechanics Laboratory, Department of BiomedicalEngineering, Tel-Aviv University. From 1997 to 2000 he was a postdoc at thedepartments of Electrical Engineering and Surgery, University of Washington.From 2001 to 2008 he was a faculty member at the Department of ElectricalEngineering, University of Washington with an adjunct appointment with theDepartment of Surgery. From 2008 to 2013 he served as a faculty memberat the Department of Computer Engineering, University of California, SantaCruz (UCSC).

spatial map of synthesized criteria for the redundancy...

Documents