Feasibility Study of Inertial Sensor-based Joint Moment Estimation

Method During Human Movements

A Test of Multi-link Modeling of the Trunk Segment

Takashi Watanabe

and Jun Kodama

Dept. Biomedical Engineering, Graduate School of Biomedical Engineering, Tohoku University, Sendai, Japan

Dept. Electronic Engineering, Graduate School of Engineering, Tohoku University, Sendai, Japan

Keywords: Joint Moment, Inertial Sensor, Trunk, Rigid Body Link Model.

Abstract: The conventional method of estimating joint moments needs kinematic data measured with a 3D optical

motion measurement system and ground reaction forces measured with force plate. However, the

conventional method is limited generally to laboratory use because of the required measurement systems.

Therefore, we proposed a convenient method to estimate joint moments from measurements only with

inertial sensors for application to clinical evaluation of motor function of paralyzed and elderly subjects. In

this paper, multi-link modeling of the trunk was examined for reliable estimation of joint moments only

from measured data with inertial sensors attached on the body. Body segment parameters (segment length

and mass, center of mass location and moments of inertia) were calculated from anthropometric data.

Experimental test with 3 healthy subjects showed that segmented trunk model estimated joint moments

better than a rigid trunk model for squat and sit-to-stand movements. The estimation results were not

different largely between the 5-link model that modeled the trunk by 3 segments and the 4-link model that

modeled the trunk by 2 segments. However, trunk modeling for 4-link model was suggested to be

appropriate when the upper and the middle trunk segments of the 5-link model were modeled as one

segment.

1 INTRODUCTION

Difficulty in standing up is one of important factors

of preventing independent daily life for elderly or

motor disabled subjects. Joint moments during sit-

to-stand movement can evaluate decrease of muscle

force of lower limbs, from which a cause of the

difficulty in standing up can be estimated. However,

joint moments can not be measured directly with

sensors or measurement equipments, especially

during human movements. Therefore, generally,

joint moments are estimated by indirect means from

data measured with a camera based 3D motion

analysis system and a force plate system. However,

using these systems limits measurement

environment, especially to laboratory, and takes

many costs.

In our previous study, a method of estimating

joint moment only using inertial sensors was

proposed and shown to be feasible in our

preliminary test (Mori and Watanabe, 2011;

Watanabe et al., 2012). Although the proposed

method can remove the limitation of measurement

environment and reduce the cost, estimated joint

moments showed large difference in comparison

with the conventional method using 3D motion

analysis system and force plate. In addition, our

preliminary test suggested that 3-link model of the

body, which modeled the trunk as one segment, can

decrease the difference between inertial sensor based

moment estimation method and the conventional

method in comparison with 4-link model, which

modeled the trunk by 2 segments (Mori and

Watanabe, 2011). However, Zijlstra and Bisseling

reported that segmented trunk model estimated hip

abduction moment using acceleration and angular

velocity signals better than rigid trunk model

(Zijlstra and Bisseling, 2004).

Therefore, this paper aimed at reexamining the

feasibility of joint moment estimation only using

inertial sensors. Especially, in this paper, multi-link

models of the trunk were tested in estimation of joint

moments only from measured data with inertial

sensors attached on the body. Body segment

248

Watanabe, T. and Kodama, J.

Feasibility Study of Inertial Sensor-based Joint Moment Estimation Method During Human Movements - A Test of Multi-link Modeling of the Trunk Segment.

DOI: 10.5220/0005747902480255

In Proceedings of the 9th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2016) - Volume 4: BIOSIGNALS, pages 248-255

ISBN: 978-989-758-170-0

parameters (segment length and mass, center of

mass location and moment of inertia) were

calculated from anthropometric data reported by Ae

et al., (1992) and Kouchi and Mochimaru (2005).

Since there were several definitions of trunk

segmentation, based on the model used by Young et

al., (1983), 5-link model consisted of 3-trunk

segments, 2 types of 4-link model including 2 trunk

segments and 3-link model that uses rigid trunk

model were examined in joint moment estimation

comparing to reference data of joint moment

estimated by the conventional method.

2 ESTIMATION METHOD OF

JOINT MOMENTS

2.1 Rigid Body Link Model

Figure 1(a) shows the rigid body link model for

human body (5-link model), which consists of the

shank (i=1), the thigh (i=2), the lower trunk (i=3),

the middle trunk (i=4) and the upper trunk (i=5). The

foot was fixed on the ground. Definition of

inclination angle of each segment for the 5-link

model is also shown in Figure 1(a). Each segment

was assumed to move in the sagittal plane. The

boundaries between the middle and the lower trunk

segments and between the upper and the middle and

trunk segments were defined at the highest point of

the iliac crest and the lower end of the rib,

respectively. Here, head and upper limbs were

included into the upper trunk segment.

The anthropometric data reported by Ae et al.,

(1992) used the model that segmented the trunk by

the lower end of the rib. For this modeling, the 4-

link model that segmented the trunk by the lower

end of the rib was defined (4-link-A-model). As

another 4-link model, trunk modeling segmented by

the highest point of the iliac crest was also defined

(4-link-B-model). Here, the lower trunk by Ae et al.,

(1992) means the middle-lower trunk of the 5-link

model. Therefore, body segment parameters of the

lower trunk of the 5-link and the 4-link-B models

were calculated from those of the lower trunk

reported by Ae et al., (1992), in which the middle

trunk was approximated by an elliptic cylinder with

the density reported by Clauser et al., (1969). Then,

body segment parameters for the upper-middle trunk

segment were calculated by synthesizing those of the

upper and the middle trunk segments. Size

parameters in calculation of the synthesizing were

obtained from average values in the AIST Human

body size database (Kouchi and Mochimaru, 2005).

(a) Inclinatoin angles

(b) joint reaction force and joint moment of segment i

Figure 1: Definitions of segment inclination angle, joint

reaction force and joint moment. a, b and c shows the

lower end of the rib, the highest point of the iliac crest and

the great trochanter, respectively.

2.2 Estimation of Joint Moment

Center of mass location of each segment was

calculated at first. Each segment length was

calculated from measured height of each subject by

using statistically obtained segment length ratio

(Kouchi and Mochimaru, 2005). The center of

segment mass locations of body segments were

calculated from measured inclination angles of

segments and the calculated segment lengths.

Acceleration of the center of mass and angular

acceleration of inclination angle of each segment

that were required in estimation of joint moments

were calculated by the differential using third order

low pass differentiation algorithm (Usui and Ikegaya,

1978).

Based on Figure 1(b), equations of translational

motion and rotational motion of the center of mass

of each rigid body segment are shown by the

followings:

i=1

i=2

i=3

i=4

i=5

i+1

Feasibility Study of Inertial Sensor-based Joint Moment Estimation Method During Human Movements - A Test of Multi-link Modeling of

the Trunk Segment

249

1



xxGii

FFXm



(1)

gmFFZm

izzGii



1



(2)

iizizi

iixixiiiii

lFrFr

lFrFrMMI



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cos))1((

sin))1((











(3)

Here,

i : segment number

: segment mass

: segment length

: center of mass ratio from the lower end

: moment of inertia

: joint moment

: joint reaction forces



: acceleration of segment center of mass

position





: inclination angle and its angular acceleration

g : gravitational acceleration

Joint reaction forces are calculated from Equations

(1) and (2), and then values of the forces are

substituted in Equation (3). Each joint moment can

be estimated by solving these simultaneous

equations with the assumption that no external force

acts to the upper segment.

3 EXPERIMENTAL METHODS

Figure 2 shows experimental set up. In order to

examine the joint moment estimation method,

human movements were measured with optical 3D

motion measurement system (OPTOTRAK,

Northern Digital), force plate (9286A, Kistler) and

wireless inertial sensors (bluetooth, InvenSense

MPU-9150, ERi). Three healthy subjects (male, 21-

23 y.o.) performed 5 times of 4 movements: 2 types

of squat movement (movement time was 6s and 9s)

and 2 types of sit-to-stand movement (normal and

forward inclination of the trunk imitating elderly

persons).

Figure 2: Experimental setup of measurement of

movement with inertial sensors, 3D motion measurement

system and force plate.

Inertial sensors were attached on the skin with

double-sided adhesive tape near the center of mass

location to the front and the lateral sides of the shank

and the thigh of left lower limb, and the back side at

upper, middle and lower trunk segments as shown in

Figure 3: Multi-link models tested in this paper and sensor attachment positions to the trunk segments. 1, 2 and 3 shows

inertial sensors, and a, b and c shows the lower end of the rib, the highest point of the iliac crest and the great trochanter,

respectively.

: marker

: sensor

force plate

3-link

4-link-B

4-link-A

trun

upper-middle

lower

middle-lower

upper

5-link

upper

middle

lower

BIOSIGNALS 2016 - 9th International Conference on Bio-inspired Systems and Signal Processing

250

Figure 2. Markers for the 3D motion measurement

system were attached on the left side of subject, in

which positions were the acromion, along the long

axis of the trunk at the same height as the lower end

of the rib and the highest point of the iliac crest, the

great trochanter, the lateral femoral condyle, and the

lateral malleolus.

Figure 3 shows sensor attachment to trunk

segments of each link model. Reference moment

data were calculated by the conventional method

from measured data with 3D motion measurement

system and force plate for each link model.

Inclination angles were obtained by calculating

the integral of measured angular velocity with

inertial sensor, in which integrated errors caused by

offset of gyroscope was removed assuming constant

offset value during movement. The measured

inclination angles with inertial sensors and estimated

joint moments were evaluated for movement period

that were detected by angular velocity of the shank

for squat movement and by ground reaction force for

sit-to-stand movement, respectively.

4 RESULTS

4.1 Inclination Angles

Segment inclination angles measured with inertial

sensors were compared to those angles measured

with 3D motion measurement system. Calculation

error of the angle by the integral of angular velocity

was corrected by linear approximation of the integral

error. Figure 4 shows average RMS (root mean

square) errors of angles between inertial sensor and

3D motion measurement system. For inclination

angles of the shank and the thigh segments, sensors

attached to the lateral side showed lower values of

RMS error than those of sensors attached to the front

side. For the angles of trunk segment of the 3-link

model, the sensors 1 and 2 that were attached to the

upper and the middle trunks showed small RMS

errors, although the sensors 2 showed the lowest

errors. For angles of the middle-lower trunk segment

of the 4-link-A model, sensor 3 attached to the lower

trunk showed smaller RMS errors. Sensor 1 attached

to the upper trunk showed smaller RMS errors for

angles of the upper-middle trunk segment of the 4-

link-B model.

Figure 4: RMS values of segment inclination angles measured with inertial sensors and the 3D motion measurement system.

s1, s2 and s3 show sensors attached to the trunk shown in Figures 3 and 4. RMS values were calculated for shank and thigh

segments, and a rigid trunk segment of 3-link model, and upper (U-T), middle (M-T), lower (L-T), upper-middle (UM-T)

and middle-lower (ML-T) trunk segments of 4-link and 5-link models.

shank thigh

front

lateral

RMS error [deg]

(a) lower limb (b) 3-link

ML-T

s3 s2

U-T

s1 s2

UM-T

s3 s2 s1

L-T

s3 s2 s1

U-T

L-T

M-T

Feasibility Study of Inertial Sensor-based Joint Moment Estimation Method During Human Movements - A Test of Multi-link Modeling of

the Trunk Segment

251

Figure 5: Examples of estimated and reference joint

moments during squat movement (5-link model).

From above results, sensors that showed the

lowest RMS errors were used for measurement

inclination angles of segments in joint moment

estimation.

4.2 Joint Moment

Joint moments were estimated by using inclination

angles measured with inertial sensors determined in

the previous section. Figure 5 shows examples of

estimated and reference joint moments during squat

movement with the 5-link model. Estimated

moments were normalized to the weight of subject.

The inertial sensor based joint moment estimation

method was suggested to estimate joints moments

appropriately.

RMS values of differences between reference

Figure 6: RMS values of estimated joint moments only

with inertial sensors.

moment data and the estimated moments were

shown in Figure 6. For squat movement, the RMS

values of the 5-link model were the smallest and the

4-link-B model showed similar RMS values as those

of the 5-link model, which were less than 0.1 Nm/kg

in average. Although the 4-link-A model showed

smaller RMS values than those of the 3-link model,

the average value and variations were larger than

those of the 5-link and 4-link-B models. RMS values

of the estimated moments shown in Figure 6 were

0.098, 0.112 and 0.074 for the hip, knee and ankle

joints, respectively. For sit-to-stand movement,

estimation of ankle and hip joint moments showed

similar results as the squat movement. However,

knee joint moment was estimated well by the 3-link

model.

In order to validate the estimation method,

inclination angles measured with 3D motion

measurement system were substituted for the angles

in Equations (1)-(3) and joint moments were

estimated by the estimation method described in

Section 2.2 without ground reaction forces. The

0246810

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1.0

1.2

0246810

-0.8

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sensor

reference

moment [Nm/kg]moment [Nm/kg]moment [Nm/kg]

(a) hip joint

(b) knee joint

[s]

0.05

0.1

0.15

0.2

0.25

ankle knee hip

RMS value [Nm/kg]

3link 4link-A 4link-B 5link

0.05

0.1

0.15

0.2

0.25

ankle knee hip

RMS value [Nm/kg]

(a) squat

(b) sit-to-stand

BIOSIGNALS 2016 - 9th International Conference on Bio-inspired Systems and Signal Processing

252

Figure 7: RMS values of estimated joint moments using

inclination angles measured with the 3D motion

measurement system and no ground reaction forces.

results were also compared to the reference moment

data as shown in Figure 7. Although 3-link model

showed the largest RMS values for both movements,

most of the values were smaller than those of

estimation with inertial sensor signals. For the squat

movement, similar results were obtained as the

results with inertial sensors. Although the 4-link-A

model showed smallest RMS values for sit-to-stand

movement, the differences from those of the 5-link

and 4-link-B model were not so large.

The results of Figures 6 and 7 suggest that the 4-

link and the 5-link models could estimate joint

moment better than 3-link model. However, RMS

values of the knee joint moment and some variations

of RMS values were larger and than those of the 3-

link model for the sit-to-stand movement with

inertial sensors.

The 4-link and the 5-link models can estimate

joint moments at the joint between trunk segments.

Estimated joint moments of trunk segments were

compared to the results calculated by the

conventional method. RMS values were shown in

Figure 8: RMS values of trunk joints moments estimated

without ground reaction force. 4A, 4B, 5 represents link

model. Waist and abdominal mean joints between the

middle and the lower trunk segments (at the highest point

of the iliac crest) and between the upper and the middle

trunk segments (at the lower end of the rib), respectively.

Figure 8. RMS Values of joint moments of trunk

segments were similar to those of the hip joint

moment estimation, which were less than 0.1 Nm/kg.

These results were almost same between the 4-link

and 5-link models. Segment inclination angles

measured with 3D motion measurement system also

showed similar results with the inertial sensor based

method.

5 DISCUSSIONS

For measurement of inclination angle of lower limb

with inertial sensors, sensors attached to the lateral

side showed smaller RMS errors than those of

sensors attached on the front side as shown in Figure

4(a). In our previous study, inclination angles of

lower limb segments measured with inertial sensors

0.05

0.1

0.15

0.2

0.25

ankle knee hip

0.05

0.1

0.15

0.2

0.25

ankle knee hip

RMS value [Nm/kg]

RMS value[Nm/kg]

(a) squat

(b) sit-to-stand

3link 4link-A 4link-B 5link

0.05

0.1

0.15

0.2

0.25

RMS value [Nm/kg]

0.05

0.1

0.15

0.2

0.25

RMS value [Nm/kg]

waist

54B

abdominal

waist

54B

abdominal

(a) inertial sensors

(b) 3D motion analysis system

Feasibility Study of Inertial Sensor-based Joint Moment Estimation Method During Human Movements - A Test of Multi-link Modeling of

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253

attached to the front side during walking showed

RMS errors less than about 4deg in average in

comparison with the 3D motion measurement

system. The measurements performed in this paper

were during squat and sit-to-stand movements that

involve large hip and knee flexion movements,

which were different from waking. Those large

flexion movements were considered to cause

differences in measurement results between sensors

and markers. That is, deformation of muscles and

sitting on the stool before standing up are considered

to move markers and sensors differently.

As for the trunk inclination angles, 4-link-B

model showed the smallest RMS errors as shown in

Figure 4. Sensor 1 could measure inclination angles

of the upper trunk and the upper-middle trunk with

small RMS values. This suggests that movements of

the upper and the middle trunks are similar even in

the squat and the sit-to-stand movements. Therefore,

4-link-B model that uses the upper-middle trunk

segment is considered to be appropriate. Although

RMS values of the middle trunk of 5-link model was

large, there was a possibility that angle measurement

with the 3D motion measurement system (markers

on the highest point of the iliac crest and the lower

end of the rib) were affected by movements of skin

or subcutaneous fat tissue during trunk bending

movement.

The 5-link and the 4-link-B models showed

similar good RMS values of joint moment

estimation. The 4-link-A model showed increase of

variation of RMS values of hip joint moment for

both movements and ankle joint moment for squat

movement, and the largest RMS values of the knee

joint moment for the sit-to-stand movement in

estimation with inertial sensors. On the other hand,

validation test of the joint moment estimation

method shown in Figure 7 suggested that the 5-link

and 4-link models can estimate joint moments with

similar RMS value. The deterioration of the 4-link-A

model in moment estimation with inertial sensors is

considered to be caused by large difference in

inclination angle of the middle-lower trunk segment.

Variations of RMS values increased for sit-to-

stand movement as seen in Figures 6 and 7. The

variation was considered to be caused by differences

among subjects. Error in modeling subject by rigid

body link model is considered to be caused by using

anthropometric data that were statistic average

values. That is, physical constitution of each subject

was different from average.

RMS values in joint moment estimation with

inertial sensors were less than 0.1 and o.15 for squat

and sit-to-stand movements, respectively. As shown

in Figures 6 and 7, the 5-link and the 4-link-B

models with inertial sensors showed similar RMS

values in joint moment estimation with the 3D

motion measurement system and no ground reaction

forces. These suggest that the method of joint

moment estimation using inertial sensors in this

paper is feasible. However, further studies are

required to make clear if the RMS values are

acceptable or not, increasing the number of subjects.

Joint moment estimation of trunk segments

showed similar RMS values as those of the hip joint

moment. It is considered that this is because

moments of trunk segments were similar values as

those of the hip joint, since the segment masses and

lengths of the middle and the lower trunk segments

were smaller and shorter than those of the upper

trunk segment.

6 CONCLUSIONS

This paper aimed at determination of feasibility of

the method of estimating joint moment only using

inertial sensors. Multi-link model of the trunk was

tested in joint moment estimation after calculations

of body segment parameters based on

anthropometric data. The proposed method could

estimate similar waveform of joint moments as those

of the conventional method. Segmented trunk model

estimated joint moment better than a rigid trunk

model. The estimation results were not different

between the 5-link model that modeled the trunk by

3 segments and the 4-link model that modeled the

trunk by 2 segments. However, trunk modeling for

4-link model was found to be appropriate when the

upper and the middle segments were modeled as one

segment in case of using inertial sensors. The results

of this paper suggested that the inertial sensor based

joint moment estimation is feasible. Further tests are

expected to improve reliability of the inertial sensor

based joint angle estimation method.

ACKNOWLEDGEMENTS

This work was supported in part by the Ministry of

Education, Culture, Sports, Science and Technology

of Japan under a Grant-in-Aid for challenging

Exploratory Research.

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