Rapidly Locating and Accurately Tracking the Center of Mass UsingStatically Equivalent Serial Chains

§Ali Almandeel1, David H. Myszka1, Alejandro Gonzalez2, Philippe Fraisse2, Andrew P. Murray1

Abstract— This paper presents a center of mass (CoM) esti-mation technique that uses the statically equivalent serial chain(SESC). A SESC is a representation of any multilink branchedchain whose end-effector locates the CoM. Locating the CoM isuseful for modeling humans and humanoid robots. The methodstarts with an experimental phase involving a force plate and amotion capture system (MoCap) to construct a model to predictthe CoM location. Subsequent motion of the subject updatesthe CoM model based on the MoCap node positions withoutneed of a force plate, overcoming disadvantages of some otherCoM estimation methods. The results show that the SESCmethodology allows rapid and accurate real time estimationof the CoM. This paper includes the CoM estimation for ahuman from low-end and high-end MoCap and force platesensors. The CoM in the plane of the force plate is shown tohave an average error of less than 5 mm. A discussion of theaccuracy of the vertical component of the CoM is also presented.Additionally, the presence of a static body in the workspace (awalker or chair, for example) to create stability in test subjectsis presented.

I. INTRODUCTION

In humanoid systems, estimating the center of mass (CoM)provides an important aid in the control of static balanceand posture stance [1]. For human beings, the stabilityof human motion during standing and walking is highlyinfluenced by the position of the individual’s CoM and centerof pressure (CoP). The CoM for humans is an indicatorof stability and is an important parameter in the posturalcontrol system that relies on the information received fromthe visual, vestibular, and somatosensory systems to maintainbalance [2]. Winter [3] showed that the average CoP is equalto the average CoM projection when standing as still aspossible. Furthermore, computing the CoM can prove criticalin assessing rehabilitation success [4], in pathology detection[5], in describing gaits [6], in stroke rehabilitation [7] andin elite sports training [8]. Estimating the CoM position isa complex issue, for example, the process may involve theestimation of limb weight and composition or involve thetreatment of motion data by optimization-based integrationapproaches [9]–[11].

Human body segment parameters can be obtained fromanthropometric tables [12], but are limited to subjects sim-ilar to the sample population. Therefore, their accuracy is

§Address all correspondence to this author.1Ali Almandeel, Andrew P. Murray and David H. Myszka are with the

Design of Innovative Machines Laboratory, Department of Mechanical &Aerospace Engineering, University of Dayton, Dayton, OH 45469, USA(almandeela1, amurray1, dmyszka1)@udayton.edu

2Philippe Fraisse and Alejandro Gonzalez are with the LIRMM, Univer-site Montpellier 2, 161 rue Ada, 34095 Montpellier, France (fraisse,gonzalezde)@lirmm.fr

questioned when estimating the individual’s CoM due to thedifferences in subject age, race, and physical fitness level [9],[11]. Venture et al. [13] proposed an identification methodcapable of providing specific subject mass and inertial pa-rameters of each body segment that requires a high-endmotion capture system (MoCap) and force platform due tothe need for accurate measurement of segment acceleration.

The literature contains several methods for predicting theCoM position of an articulated system of bodies while thesystem is moving. One of the most common is to estimatethe horizontal location of the CoM by recording the CoP,using data generated via a force platform, and then using thisinformation in Newton’s equations [14], [15]. Schepers et al.[10] combined the CoP trajectory with the double integratedCoM acceleration to estimate the CoM continuously whilewalking. Betker et al. developed two methods to estimatethe CoM using a hybird genetic algorithm sum of sinesmodel [16] and using a feedforward backpropagation neuralnetwork model [17]. Although these two methods produceacceptable CoM estimation error, they remain sensitive tothe complexity of the motion (i.e. covering the full range ofpossible values of the CoM or balance patterns).

The use of the statically equivalent serial chain (SESC)approach [18]–[20] for estimating the CoM of articulatedrigid body systems can overcome the difficulties of theprevious methods. Unlike the previous approaches whichseek an estimation of CoM location based on continuousdata recording from force plates, the SESC method consistsof two phases, the identification phase and the implemen-tation phase. The identification phase starts with an initialexperiment to construct a model to predict the CoM location,while the implementation phase updates this model basedon current joint angles in the system. SESC is based on amanipulation of the equation for determining the CoM [21],[22].

A substantial advantage of CoM estimation using theSESC technique is that it does not depend on the knowledgeof the system’s static parameters including the total height,the masses of individual bodies or links, or the relative CoMlocation of individual bodies or links. Furthermore, experi-mental determination of a SESC does not require knowledgeof any lengths in the system. The SESC’s experimentalconstruction only depends on the total mass, and the system’skinematic architecture which includes the joint types andthe order in which they are connected. The generated SESChas the same number of degrees of freedom as the originalsystem and its joint movements correspond to those of theoriginal system.

2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids) November 3 - 5, 2015, Seoul, Korea

978-1-4799-6885-5/15/$31.00 ©2015 IEEE 570

This paper introduces a Node-Based SESC modelingtechnique for estimating the CoM of articulated rigid bodysystems to be consistent with the data generated by MoCap.Additionally, the Node-Based method has been extended toinclude a static body in the modeling process. The introduc-tion of a static body such as a wheelchair or walker willimprove balance and stability for many subjects.

The remainder of this paper is arranged as follows. TheNode-Based SESC method and its extension to include astatic body will be presented in Section II. The equipmentand experimental protocol will be introduced in Section III.The experimental results from the low-end (Kinect/WBB)and the high-end (VICON/AMTI-OR6) sensors will be dis-cussed in Section IV. Section V concludes the paper.

II. NODE-BASED SESC MODELING

The CoM of an articulated system of rigid bodies canbe expressed as the end effector of a virtual serial chain.Such a chain is termed the statically equivalent serial chain(SESC). The Node-Based SESC method is now formulated,a methodology based on node positions defining a skeletalframe.

A. Node-Based SESC Method

This theory eliminates the need for calculating the jointangles by utilizing MoCap position data directly and sim-plifying the process. The theory is presented here via theanalysis of a system composed of 13 links connected byspherical joints. Consistent with [11], [23], the CoM positionfor each of the links is assumed to lie along the line definedby the nodes at successive joints as shown in Fig. 1. The

Z

Y

X

Z

YX

MoCap camera

Force plate

Fig. 1: The skeleton model of a human subject composedof 13 links including the static body to provide the neededbalance/stability for subjects or while preforming unconven-tional body postures.

position of the CoM (~C), of the nth posture, for the system

of 13 bodies depicted in Fig. 1 is

Mt~Cn =m1(~Pn +λ1~τ1n

)+m2

(~Pn +~τ1n +λ2~τ2n

)+m3

(~Pn +~τ1n +~τ2n +λ3~τ3n

)+m4

(~Pn +λ4~τ4n

)+m5

(~Pn +~τ4n +λ5~τ5n

)+m6

(~Pn +~τ4n +~τ5n +λ6~τ6n

)+m7

(~Pn +λ7~τ7n

)+m8

(~Pn +~τ7n +λ8~τ8n

)+m9

(~Pn +~τ7n +~τ8n +λ9~τ9n

)+m10

(~Pn +~τ7n +~τ8n +~τ9n +λ10~τ10n

)+m11

(~Pn +~τ7n +λ11~τ11n

)+m12

(~Pn +~τ7n +~τ11n +λ12~τ12n

)+m13

(~Pn +~τ7n +~τ11n +~τ12n +λ13~τ13n

)+mo~Po, (1)

where mi is the mass of body i of the subject, λi is a scalar,~Pn ∈ R3 is the position vector of the reference system joint(node) in the MoCap reference frame, mo is the mass of thestatic body, ~Po ∈R3 is the position vector of the static body,and ~τin ∈ R3 is a vector between the nodes defining body i.Grouping terms in (1),~Cn =Ms~Pn +~τ1ns∗1 +~τ2ns∗2 +~τ3ns∗3 +~τ4ns∗4 +~τ5ns∗5 +~τ6ns∗6

+~τ7ns∗7 +~τ8ns∗8 +~τ9ns∗9 +~τ10ns∗10 +~τ11ns∗11 +~τ12ns∗12

+~τ13ns∗13 +Mo~Po, (2)

where, s∗1 through s∗13 are termed the SESC parameters:

s∗1 =m1λ1 +m2 +m3

Mt, s∗2 =

m2λ2 +m3

Mt, s∗3 =

m3λ3

Mt,

s∗4 =m4λ4 +m5 +m6

Mt, s∗5 =

m5λ5 +m6

Mt, s∗6 =

m6λ6

Mt,

s∗7 =m7λ7 +m8 +m9 +m10 +m11 +m12 +m13

Mt,

s∗8 =m8λ8 +m9 +m10

Mt, s∗9 =

m9λ9 +m10

Mt,

s∗10 =m10λ10

Mt, s∗11 =

m11λ11 +m12 +m13

Mt,

s∗12 =m12λ12 +m13

Mt, s∗13 =

m13λ13

Mt, (3)

and

Mt =13

∑i=1

mi +mo = ms +mo, Mo =mo

Mt

Ms =ms

Mt. (4)

The SESC parameters contain the kinematic and static pa-rameters of the original system. The goal of this section isto derive the method for determining the s∗i in (3) from thedata generated by the force plate and MoCap sensors. Notethat ~Pn may be an arbitrarily selected node and that (1)-(3)may be readily reformulated relative to the selected node.Rearranging (2),

~Cn = Ms~Pn +[~τ1n ~τ2n . . . ~τ13n

]

s∗1s∗2...

s∗13

+Mo~Po

= Ms~Pn +Tn~S∗+Mo~Po, (5)

571

where ~S∗ ∈ R13 contains the SESC parameters and Tn ∈R3×13 contains the relative node locations ~τ1n through ~τ13n .The values of the ~τin correspond to the links (rigid bodies)and their lengths at positions n and n+1 are equal neglectingexperimental error (i.e. |~τ1n |= |~τ1n+1 |). Noting that the forceplate and MoCap have separate frames of reference, asillustrated in Fig. 1,

~Cn = A~cln +~d (6)

where, A ∈ SO(3) is the relative orientation of the twoframes, ~cln ∈R3 is the position of the CoM in the force platereference frame, and ~d ∈R3 is a displacement. Equating (5)-(6) and solving for ~cln ,

~cln = AT(Ms~Pn +Tn~S∗+Mo~Po− ~d). (7)

However,~cln cannot be obtained from the force plate, since itis only capable of providing the horizontal (x-y) coordinatesof the CoM under static conditions. Accordingly, in the caseof static postures we can obtain the projection of ~cln ontothe force plate plane as[

1 0 00 1 0

]~cln = I~cln =~cwn =

{cwx

cwy

}, (8)

where I projects a point ∈R3 onto the x-y plane. Substituting(8) into (7) yields

~cwn = IAT(Ms~Pn +Tn~S∗+Mo~Po− ~d), (9)

noting that A = IAT ∈ R2×3 where

AAT =

[1 00 1

]. (10)

B. Numerical Approximation of A and the SESC Parameters

Using (9) with two experimental postures from the MoCapand force plate,

~cwn = A(Ms~Pn +Tn~S∗+Mo~Po− ~d),

~cwn+1 = A(Ms~Pn+1 +Tn+1~S∗+Mo~Po− ~d). (11)

Subtracting the two instances in (11) yields

∆~c = A(Ms∆~P+∆T~S∗

)=

{δcxδcy

}, (12)

noting that the term corresponding to the static body is elim-inated as a result of the subtraction process. Equation (12)for the kth experimental posture divides as

δcxk =[x1 y1 z1

](Ms∆~Pk +∆Tk~S∗

),

δcyk =[x2 y2 z2

](Ms∆~Pk +∆Tk~S∗

). (13)

Expanding (13) for δcxk ,

δcxk =x1Msδ pxk + y1Msδ pyk + z1Msδ pzk +δτ[1,1]k s∗1x1

+δτ[2,1]k s∗1y1 +δτ[3,1]k s∗1z1 +δτ[1,2]k s∗2x1

+δτ[2,2]k s∗2y1 +δτ[3,2]k s∗2z1

+ · · ·+δτ[3,13]k s∗13z1. (14)

Rearranging (14) and acquiring enough instances yields

δcx1δcx2

...δcxk

=

Msδ px1 . . . Msδ pz1 δτ[1,1]1 . . . δτ[3,13]1Msδ px2 . . . Msδ pz2 δτ[1,1]2 . . . δτ[3,13]2

......

... · · ·. . .

...Msδ pxk . . . Msδ pzk δτ[1,1]k . . . δτ[3,13]k

x1y1z1

s∗1x1s∗1y1s∗1z1

...s∗13z1

.

(15)

Noting that the process is identical in δcyk , (15) is repre-sented as

∆~cx = D~ε1, ∆~cy = D~ε2, (16)

where ∆~cx and ∆~cy ∈ Rk×1, D ∈ Rk×42, ~ε1 and ~ε2 ∈ R42×1.Via the pseudo-inverse,

~ε1 = D+∆~cx, ~ε2 = D+

∆~cy. (17)

Extract from the vector ~ε1 in (17) the values for x1, y1 andz1, and from the vector ~ε2 the values for x2, y2 and z2. Intheory, these values form unit vectors. Hence, the values arenormalized to produce the expected vectors of A as

~X =

{x1 y1 z1

}T∥∥{x1 y1 z1}∥∥ , ~Y =

{x2 y2 z2

}T∥∥{x2 y2 z2}∥∥ ,

A =

[~XT

~Y T

]. (18)

From ~Z = ~X ×~Y , the three vectors combine to form anapproximation of A as

A =[~X ~Y ~Z

]. (19)

To find the SESC parameters, solve for ~S∗ from (12) byappending many instances as

∆~c1− AMs∆~P1...

∆~ck− AMs∆~Pk

=

A∆T1...

A∆Tk

~S∗ =~κ = B~S∗, (20)

where, ~κ ∈ R2k×1, B ∈ R2k×13, and

~S∗ = B+~κ. (21)

The ~S∗ contains the kinematic and static parameters of theentire system including the static body. The ~S that describesonly the subject can be determined as

~S =Mt

ms~S∗. (22)

Note that ~S contains the links properties of the SESC chainfor the subject. The CoM of the subject for a given instantcan be obtained from (5) by setting mo = 0, which yields

~Csn = ~Pn +[~τ1n ~τ2n . . . ~τ13n

]

s1s2...

s13

= ~Pn +Tn~S.

(23)

572

Note that ~Csn may be readily obtained without the need of aforce plate. Also observe that the addition of the static bodyto the modeling process is handled without the need for anyadditional equipment. The introduction of a static body suchas a wheelchair or walker will improve the balance of manysubjects and will allow for more diverse postures.

III. EQUIPMENT AND EXPERIMENTALPROTOCOL

The equipment used for data acquisition in the experi-mental portion of this work includes the Kinect/WBB andVICON/AMTI-OR6 sensors. The Kinect/WBB are used toverify the presented methodology due to their portability,cost accessibility and simplicity. The VICON/AMTI-OR6 areused for cross validation. This section will cover the relevantdetails of the two systems.

A. Equipment

Kinect was introduced as a product for allowing con-sumers to interact with videogames by directly tracking bodypostures. The Kinect sensor consists of an RGB camera, anIR projector, and an IR camera. Kinect allows real time 3Dmotion tracking using a skeletal model capable of tracking20 skeletal nodes. The Kinect sensor works best when thesubject is directly facing it [24]. Stepan et al. [24] showedthat in controlled body posture, the variation in bone lengthswere about 20 mm for the frontal plane.

The Nintendo WBB is equipped with sensors (straingauges) at each of its four corners. By utilizing the forcesmeasured at these locations the CoP position and the verticalcomponent of the ground reaction force (GRF) may beapproximated. Harrison et al. [25] found that the repeatabilityof a single measurement within a WBB was about 1.5 mm.

The VICON system (Oxford Metric Group) is one of thecommon MoCap systems that relies on markers for detectionas shown in Fig. 2. MoCap systems are used to reconstructtwo or three dimensional movement data either by using asingle camera or multiple cameras.

The AMTI-OR6 (Advanced Mechanical Technology, Inc.)is a piezoelectric force plate that uses piezoelectric crystalssuch as quartz.

B. Experimental Protocol

Microsoft Visual Studio tools where used to develop aMicrosoft Windows Foundation (WPF) application capableof processing both the data coming from the WBB andthe Kinect sensors simultaneously. During the SESC modelidentification phase the Kinect sensor was placed on a flatstable surface and in such a way as to capture the frontalplane of the subject.

Observing the Kinect/WBB (or the VICON/AMTI-OR6)data simultaneously, both need to be nearly static to attainan accurate estimate for the CoM projection. To identify if aposture is stable, the CoP position and the subject’s nodes aremonitored for 1 second, corresponding to 30 frames. Thenfor the 30 frames the standard deviation for each of the x, y,and z elements of the nodes along with the x and y elements

of the CoP are calculated. The posture is considered static ifall of the nodes and CoP locations pass the standard deviationscreening for the 1 second window. The standard deviationfor the nodes must be ≤ 10 mm, while for the CoP must be≤ 3 mm. The subject is notified once a posture is deemedstatic, the average values are added to the data set and theprocess starts over. In contrast, if the screening test fails,the algorithm removes the oldest frame and acquires a newone. Then the algorithm evaluates the standard deviationsand tests them against the threshold. This process continuesuntil a suitable number of postures is acquired.

For the VICON/AMTI-OR6 case the CoP position andthe subject’s nodes were monitored for 6 seconds during theidentification phase. The acquired poses were not processedfor being near static. At the time of data collection thedata were searched in an offline process similar to the onedescribed for Kinect/WBB case. This process generates therequired number of poses.

Fig. 2: The VICON/AMTI-OR6 setup during the experimen-tal phase shows the static body (red object not currently onthe force plates used to assist in producing various numberof postures while being fixed in one location on top of theforce plate surface) and the 35 passive markers placementfollowing the Plug-in-Gait (PiG) template to define the bodysegments.

IV. EXPERIMENTAL RESULTSThe presented method was validated by conducting two

experiments. The first experiment relies on the Kinect/WBBsensors. The second experiment relies on the VICON/AMTI-OR6 sensors and includes an extra body in the workspace.

A. Method Validation using Kinect/WBB

In an experiment, a total of 106 static postures wererecorded in approximately 15 minutes. From this data, a totalof 96 postures were used to identify the SESC parametersfor the articulated chain described in Fig. 1. As a result,the position of the CoM of the original branched chain ismodeled by the end-effector location of a virtual spatial serialchain of appropriate size. The serial chain is depicted by the

573

green dashed lines in Fig. 3 where the end-effector terminatesat the CoM.

−0.2

0

0.2

0.4

−0.2

0

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

1

1.2

Fig. 3: The SESC model of a human subject where the SESCdepicted by the green dashed lines terminates at the CoM.

In order to verify the accuracy of the method, an additionalten postures are tested from the remaining data by evaluatingthe CoM. This is done by comparing the predicted CoM andthe measured CoM from the force plate as depicted in Tab. I.The CoM in the plane of the force plate is seen to have anaverage error (average of the absolute value) of about 4 mmand a root mean square error (RMSE) of about 5.2 mm.

TABLE I: The CoM positions predicted by the Node-BasedSESC method for the ten postures using the data from theKinect/WBB sensors. The table includes the deviations ofthe predicted CoM from the measured CoM.

Predicted CoM (mm) Measured CoM (mm) Error (mm)

Postures x y x y ∆x ∆y

1 14.4 2388.0 1.53 2377.0 12.8 8.742 18.0 2388.0 13.8 2377.0 4.17 6.053 10.4 2388.0 3.86 2388.0 6.52 2.984 -1.47 2411.0 -2.45 2422.0 0.978 -6.375 6.2 2411.0 3.41 2411.0 2.8 -0.4566 8.19 2400.0 3.3 2400.0 4.89 -0.6397 0.461 2400.0 -2.65 2400.0 3.11 -2.718 7.81 2388.0 7.26 2399.0 0.544 -2.529 -1.36 2399.0 -1.38 2399.0 0.0246 2.510 1.63 2455.0 3.5 2455.0 -1.87 4.93

B. Method Validation using VICON/AMTI-OR6 Including anExtra Static Body in the Workspace

In an experiment, a total of 93 postures were recorded inapproximately 2 hours. A total of 22 postures were recordedwithout the aid of the extra static body. Including the staticbody, a total of 71 postures were recorded and used toidentify the SESC parameters for the articulated chain. As aresult the position of the CoM of the original branched chainis modeled by the end-effector location of a virtual spatialserial chain of appropriate size.

In order to verify the accuracy of the method, an additional22 postures from the remaining data were used to evaluatethe CoM. The difference between the predicted CoM and the

measured CoM from the force plate is in Tab. II. The CoMin the plane of the force plate is shown to have an averageerror (average of the absolute value) of about 4.5 mm and aroot mean square error (RMSE) of about 5.2 mm.

TABLE II: The CoM positions predicted by the Node-Based SESC method for the 22 postures using the data fromVicon/AMTI-OR6 sensors. The table includes the deviationsof the predicted CoM from the measured CoM.

Predicted CoM (mm) Measured CoM (mm) Error (mm)

Postures x y x y ∆x ∆y

1 1.359 21.27 0.2705 21.93 1.089 -0.65912 -21.91 274.3 -28.4 274.7 6.495 -0.38643 -23.32 269.3 -27.14 269.9 3.823 -0.58614 -22.41 272.5 -23.49 271.6 1.081 0.8915 -21.33 274.1 -21.44 274.0 0.1115 0.085316 -18.52 275.0 -24.61 280.1 6.092 -5.1537 -20.59 274.1 -26.15 279.0 5.563 -4.8558 -25.75 273.3 -30.31 277.1 4.562 -3.8349 -28.64 271.2 -32.26 272.1 3.617 -0.929810 -44.38 372.3 -36.26 368.2 -8.124 4.03711 24.86 68.01 26.17 70.2 -1.306 -2.19712 -18.34 173.0 -13.59 169.7 -4.751 3.25913 -9.291 222.4 -5.344 224.3 -3.947 -1.94814 -38.51 191.6 -42.33 188.3 3.817 3.37415 -72.08 116.5 -68.74 115.2 -3.343 1.31816 -17.99 211.6 -14.38 211.9 -3.613 -0.2717 41.05 258.0 33.7 259.3 7.344 -1.33718 -21.67 181.8 -13.96 181.8 -7.714 0.056319 15.52 171.0 9.161 173.9 6.36 -2.87820 -16.86 293.1 -14.57 291.9 -2.289 1.13121 -5.703 238.0 -1.759 236.4 -3.944 1.54222 6.418 288.0 -4.539 286.2 10.96 1.788

C. Accuracy of the Vertical Component of the CoM

Force plates are not capable of measuring the verticalcomponent of the CoM. The WBB and the AMTI-OR6 areonly capable of providing the horizontal coordinates of theCoM under static conditions. Therefore, they do not validatethe vertical component of the CoM.

The validation can be partially performed by examiningpostures with mere horizontal components as depicted inFig. 4. Preforming horizontal postures is a challenging taskdue to the limitations of the MoCap systems (the Kinectand the VICON). When recording the horizontal postures thebody limbs get close to each other making it problematic forthe MoCap to recognize and capture the joint positions. TheKinect will lose tracking of the nodes and fail to constructthe motion. Similarly the VICON will lose the detection ofthe markers as they get obstructed by other limbs.

In the experiment mentioned in the previous subsection,two such postures (17 and 18) were obtained. The CoM inthe plane of the force plate is shown to have an error of 7.3mm in the x direction and –1.3 mm in the y direction forposture 17. The error for posture 18 is –7.7 mm in the xdirection and less than 0.1 mm in the y direction as depictedin Tab. II.

V. CONCLUSIONS

This work introduced the development of the Node-Based SESC modeling technique for estimating the CoMof humanoid robots and human beings. This technique isa modification to the original statically equivalent serialchain modeling by relying on nodes/joints positions ratherthan joint angles and relative reference frames. Accordingly,this eliminates the need for calculating the joint angles byutilizing Kinect’s (or any MoCap system’s) position data

574

−0.2

0

0.2

−0.2

0

0.2

0.4

0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

(a)

−0.2

0

0.2

0.4

0

0.2

0.4

0

0.2

0.4

0.6

0.8

1

1.2

(b)

Fig. 4: The two postures with mere horizontal componentsused to validate the vertical component of the CoM, (a)posture number 17 and (b) posture number 18 , as depictedin Tab. II.

directly and reduces the processing time. The significanceof this technique is that it does not require the knowledgeof the mapping between the MoCap system and the forceplate reference frames. Another significance of the Node-Based SESC method is the ability of the method to utilizethe affordable Kinect/WBB as well as the laboratory gradeVICON/AMTI-OR6 sensors.

This paper also introduced an extension to the Node-BasedSESC modeling technique to include an extra static bodyto the modeling process. The introduction of an extra staticbody such as a wheelchair or walker will improve the sta-bility of elderly people or when preforming unconventionalbody postures. As a result, this will impact and minimize thetime required for capturing static postures.

This work includes CoM estimation for a human fromthe Kinect/WBB and from the VICON/AMTI-OR6 sensors.Based on the work presented in this paper, the CoM in theplane of the force plate is shown to have an average error ofless than 5mm.

REFERENCES

[1] L. Sentis, “Synthesis and control of whole-body behaviors in hu-manoid systems,” Ph.D. dissertation, Stanford University, 2007.

[2] M. G. Gaerlan, “The role of visual, vestibular, and somatosensorysystems in postural balance,” Ph.D. dissertation, UNIVERSITY OFNEVADA, LAS VEGAS, 2010.

[3] D. A. Winter, “Human balance and posture control during standingand walking,” Gait & posture, vol. 3, no. 4, pp. 193–214, 1995.

[4] J. J. Buchanan and F. B. Horak, “Emergence of postural pat-terns as a function of vision and translation frequency,” Journal ofNeurophysiology, vol. 81, no. 5, pp. 2325–2339, 1999.

[5] K. F. Zabjek, C. Coillard, C.-H. Rivard, and F. Prince, “Estimationof the centre of mass for the study of postural control in idiopathicscoliosis patients: a comparison of two techniques,” European SpineJournal, vol. 17, no. 3, pp. 355–360, 2008.

[6] S. E. Halliday, D. A. Winter, J. S. Frank, A. E. Patla, and F. Prince,“The initiation of gait in young, elderly, and parkinson’s diseasesubjects,” Gait & posture, vol. 8, no. 1, pp. 8–14, 1998.

[7] M. Agmon, C. K. Perry, E. Phelan, G. Demiris, and H. Q. Nguyen, “Apilot study of wii fit exergames to improve balance in older adults,”Journal of Geriatric Physical Therapy, vol. 34, no. 4, pp. 161–167,2011.

[8] A. Baca and P. Kornfeind, “Rapid feedback systems for elite sportstraining,” Pervasive Computing, IEEE, vol. 5, no. 4, pp. 70–76, 2006.

[9] M. A. Jaffrey, “Estimating centre of mass trajectory and subject-specific body segment parameters using optimisation approaches,”Ph.D. dissertation, Victoria University, 2008.

[10] H. M. Schepers, E. H. van Asseldonk, J. H. Buurke, and P. H.Veltink, “Ambulatory estimation of center of mass displacement duringwalking,” Biomedical Engineering, IEEE Transactions on, vol. 56,no. 4, pp. 1189–1195, 2009.

[11] P. De Leva, “Adjustments to zatsiorsky-seluyanov’s segment inertiaparameters,” Journal of biomechanics, vol. 29, no. 9, pp. 1223–1230,1996.

[12] D. A. Winter, Biomechanics and motor control of human movement.John Wiley & Sons, 2009.

[13] G. Venture, K. Ayusawa, and Y. Nakamura, “Real-time identificationand visualization of human segment parameters,” in Engineeringin Medicine and Biology Society, 2009. EMBC 2009. AnnualInternational Conference of the IEEE. IEEE, 2009, pp. 3983–3986.

[14] T. Shimba, “An estimation of center of gravity from force platformdata,” Journal of Biomechanics, vol. 17, no. 1, pp. 53–60, 1984.

[15] D. L. King and V. M. Zatsiorsky, “Extracting gravity line displacementfrom stabilographic recordings,” Gait & Posture, vol. 6, no. 1, pp. 27–38, 1997.

[16] A. Betker, Z. Moussavi, and T. Szturm, “Center of mass functionapproximation,” in Engineering in Medicine and Biology Society,2004. IEMBS’04. 26th Annual International Conference of the IEEE,vol. 1. IEEE, 2004, pp. 687–690.

[17] A. Betker, T. Szturm, and Z. Moussavi, “Application of feedforwardbackpropagation neural network to center of mass estimation foruse in a clinical environment,” in Engineering in Medicine andBiology Society, 2003. Proceedings of the 25th Annual InternationalConference of the IEEE, vol. 3. IEEE, 2003, pp. 2714–2717.

[18] S. Cotton, A. Murray, and P. Fraisse, “Estimation of the center ofmass using statically equivalent serial chain modeling,” in ASME2009 International Design Engineering Technical Conferences andComputers and Information in Engineering Conference. AmericanSociety of Mechanical Engineers, 2009, pp. 961–967.

[19] ——, “Statically equivalent serial chains for modeling the center ofmass of humanoid robots,” in Humanoid Robots, 2008. Humanoids2008. 8th IEEE-RAS International Conference on. IEEE, 2008, pp.138–144.

[20] S. Cotton, A. P. Murray, and P. Fraisse, “Estimation of the centerof mass: from humanoid robots to human beings,” Mechatronics,IEEE/ASME Transactions on, vol. 14, no. 6, pp. 707–712, 2009.

[21] B. Espiau, R. Boulic, et al., “On the computation and control of themass center of articulated chains,” 1998.

[22] O. Fischer, “Uber die reduzierten systeme und die hauptpunkte derglieder eines gelenkmechanismus und ihre bedeutung for die technis-che mechanik,” Z. f. math. Phys, vol. 47, pp. 429–466, 1902.

[23] R. Drillis, R. Contini, and M. Bluestein, “Body segment parameters,”Artificial limbs, vol. 8, no. 1, pp. 44–66, 1964.

[24] S. Obdrzalek, G. Kurillo, F. Ofli, R. Bajcsy, E. Seto, H. Jimison, andM. Pavel, “Accuracy and robustness of kinect pose estimation in thecontext of coaching of elderly population,” in Engineering in Medicineand Biology Society (EMBC), 2012 Annual International Conferenceof the IEEE. IEEE, 2012, pp. 1188–1193.

[25] H. L. Bartlett, L. H. Ting, and J. T. Bingham, “Accuracy of force andcenter of pressure measures of the wii balance board,” Gait & posture,vol. 39, no. 1, pp. 224–228, 2014.

575