Abstract. This paper studied the method for motion tracking of arm using triaxial accelerometer, triaxial gyroscope and electronic compass. The motion model of arm is established. The hardware of tracking system of arm is designed. The track method of arm gesture based on multi-sensors data fusion is analyzed. The compensation algorithm for motion accelerations is researched. The experimental results demonstrate that the motion acceleration compensation algorithm is validity, which can improve the dynamic measure precision of arm gesture angle

Fuhou Xu

Liuyi Ma

Tongda Zhang

Yuxiang Zhang

CiteSeerX

Tracking of Human Arm Based on MEMS Sensors
Yuxiang Zhang1, Liuyi Ma1, Tongda Zhang2, Fuhou Xu1
1203 office, Xi’an Research Inst.of Hi-Tech Hongqing Town,
Xi’an , 710025 P.R.China
2Department of Automation, Tsinghua University,
Beijing, 100084, P.R.China
yuxiangz@tom.com, cuiqin_wu@163.com,
ZT2008@qq.com , bainetsi@foxmail.com
Abstract. This paper studied the method for motion tracking of arm using
triaxial accelerometer, triaxial gyroscope and electronic compass. The motion
model of arm is established. The hardware of tracking system of arm is
designed. The track method of arm gesture based on multi-sensors data fusion
is analyzed. The compensation algorithm for motion accelerations is researched.
The experimental results demonstrate that the motion acceleration
compensation algorithm is validity, which can improve the dynamic measure
precision of arm gesture angle.
Keywords: MEMS, movement track, gesture fusion, lever arm effect.
1   Introduction
The human body movement track technology has been widely used in the areas of
virtual reality and game development. At present, the human body movement track
technology is mainly on the basis of pattern recognition technology or on wearable
equipment technology. The human body movement track technology based on pattern
recognition only need simple equipment and do not affect the personnel movement,
but it has following shortcomings: it is rigorous to the recognition environment and it
has blind angle when not in the open space; distinguishes; The recognition is affected
under circumstance of occlusion; The recognition algorithm is hard to reach high
precision. The wearable equipment used in movement track technology includes
mechanical equipment and electromagnetism equipment. The mechanical devices
adopt the support installation, which will restrict user's activity. The electromagnetism
equipment is easy to be disturbed by the magnetic field, and is not suitable for
complex electromagnetism environment.
With the development of MEMS technology and semiconductor technology, the
mini-accelerator sensors have been used in the human motion track. The movement
track technology based on MEMS sensors has the advantages of frequency bandwidth,
stability small size, low cost, long life and light weight. Many researches have
concerned the technology. Hou W. s., Dai J.m. used triaxial accelerometer to track the
human motion. Because the accelerometer is easy to be disturbed by motion
acceleration and can’t detect the change of horizontal angle, the effect of their method
is not good always. W.w. Feng [2] used both the magnetic sensors and accelerometer
to track the motion of upper limb. Since the magnetic is week and easy to be disturbed
by environment, so the measurement is not accurate. Ryan Aylward [3] applied both
triaxial accelerometer and triaxial gyroscope to measure the attitude of dancers. Liu
X.y., Zhou Z.y.[4] add the triaxial magnetic into micro inertial measurement element
to detect the motion of lower limbs. However, when the limbs have motion
acceleration, their method will produce a relative large error. To obtain high precision
measurement result, the compensation of acceleration is necessary.
This paper studies the arm movement track technology based on the triaxial
accelerometer, triaxial gyroscope and electronic compass, and researches the
compensate algorithm for the accelerate component of arm movement. The arm
movement track system is designed. The experiments show that the movement track
effect is good.
2 The motion model of arm and the movement track principle
The movement of arm can be simplified to the rotation under elbow joint and
shoulder joint. The simplified arm is a linkage mechanism with two joints (figure 1).
Taking the shoulder joint as origin, the reference coordinate system bbb ZYX-bO
and linkage coordinate system p1p1p11 ZYX-pO are established. The references
coordinate system bO  is parallel to the human body, and is constant in the process
of arm movement. The linkage coordinate system 1pO  rotate with the big arm, and
is described with pitch angle 1 , roll angle 1 , course angle 1 . The position of
big arm is as following:










=










−
1
1
1
1
1
p
p
p
b
b
b
z
y
x
T
z
y
x
 . (1)










−
−+
+−−
=
11111
111111111111
111111111111
1
coscossincossin
cossincossinsincoscoscossinsinsincos
sinsincoscossinsincossinsinsincoscos



T  . (2)
Fig. 1. The motion model of arm
where, 1T  is the strapdown matrix between the coordinate system 1pO  and the
coordinate system bO . The position of big arm can be obtained by solving the 1T
real time.
Because the roll angle dose not affect the position change of elbow joint, the roll
angle of main arm can be considered as 0. The position of elbow joint can be
expressed as:










=




















−=










11
11
1
11
11111
11111
11
2
2
2
cossin
coscos
sin
0
0
coscossinsinsin
sincoscossincos
0sincos






ll
z
y
x
op
op
op
 . (3)
where, 1l is the length of big arm.
The linkage coordinate system p2p2p22 ZYX-pO  is established at elbow joint
2pO . the linkage coordinate system 2pO  rotates with the forearm. The forearm can
be described with pitch angle 2 , roll angle 2 , course angle 2 , the position of
forearm can be expressed as:










+










=










+










=










−−
11
11
1
1
2
2
2
1
2
2
2
2
2
2
2
1
2
cossin
coscos
sin



l
z
y
x
T
z
y
x
z
y
x
T
z
y
x
p
p
p
op
op
op
p
p
p
b
b
b
 . (4)
where, is the 2T  is the strapdown matrix between the coordinate system 2pO  and
the coordinate system bO .
3 Hardware of arm movement track system
The arm movement track system consists of big arm gesture detection module,
forearm gesture detection module and the host computer. The hardware frame is
shown in figure 2. The big arm detection module and the forearm detection module
are fixed on the big arm and forearm, respectively. The pitch angle, roll angle and the
course angle data of big arm and forearm can be measured, and then sent to the host
computer by wireless module. According the motion models of arm, the position of
arm can be obtained by the position solver. Hence, the movement track of arm can be
realized.
Fig. 2. The arm movement track system hardware frame
The arm gesture detection modules are consist of triaxial accelerometer, triaxial
gyroscope, triaxial magnetic intensity sonsors, data sample module, microprocessor
and wireless transmit module. The hardware frame is shown in figure 3.
Fig. 3. The arm gesture detection module hardware frame
The triaxial accelerometer ADXL330 is produced by AD corp, which has a
measure rage of ± 3g, with a sensitivity of 300mV/g. The gyroscope
LPR530Al( with a rage of ± 300 o/s) and LY530ALH (with a rage of ± 300 o/s) are
produced by ST corp.. The electronic compass sonsor HMC5843 (with a rage of
± 4gauss) is produced by Honeywell corp..
The data sample module use the ADS8344 (16 bit, 8 channels) which is produced
by TI corp., it used for the A/D translation of the triaxial accelerometer and the
triaxial gyroscope. The microprocessor is STM32F103RBT6, which is used for the
noise reduction, position solver and data fusion. The results from the microprocessor
are sent to the host computer by wireless module RF24L01.
The gesture detection module is shown in figure 4.
Fig. 4. The arm gesture detection module
4 The arm gesture movement track algorithm based on multi-
sensors
4.1 Multi-sensors data fusion based on Kalman filter
The gesture fusion algorithm of arm consists of three parts. Firstly, according the
angle velocity vector measured by the triaxial gyroscope, the gesture angle is solved
by the quaternion rotation vector three samples method which has good compensate
effect to noncommutativity error; secondly, according the observe values of gravity
vector and geomagnetism vector from the triaxial accelerometer, triaxial
geomagnetism sonsors, the gesture angle and the course angle of arm can be obtained;
finally, the arm gesture optimal estimation can be obtained by the data fusion of the
gesture angle and the course angle using Kalman filter. Since the rotational angle is
big and the change of gesture angle is quick, this paper adopts the closed loop
correction indirect method Kalman filter to realize the data fusion of arm gesture [5].
1wtruemtrue nb
 −−=  . (5)
estmest b
 −=  . (6-a)
2
1
wnbb
 −−=

 . (6-b)
where, 1wn
  is the measurement noise of gyroscope, 2wn
 is the drift noise of
gyroscope,  is the drift time.
Take the error angle and the gyroscope drift as status variable
[ ]Tzyx bbbX ∆∆∆∆∆∆=  .The system equation is established as
following:
)()( tWtXX Γ+Α=  . (7)
where,
[ ]








−
−×
=
××
×
3333
33
1
0 I
I
A







−
=Γ
××
××
XI
I
333
3333
0
0
[ ]Tww nntW 21)( =  .
(7-a)
)(tW is white noise with zero-mean-value, and ( ) ( )[ ] QtWtWE T = , [ ]× is the
symmetric matrix of  .
When the object is in non-accelerate status, we can get the error angle m∆ which
is the difference between the observe values from the accelerometer or magenetic
sensors and the calculation value from gyroscope. We can establish the Observation
Equation
KKK VHXZ += . (8)
where, [ ]3333 0 ××= IH , KV  is white noise with zero-mean-value, [ ] RVVE TKK = .
According to Eqs.(7), (8), we can design the Kalman filter to estimate the error
angle of arm gesture. By taking error angle into the arm gesture quaternion, we can
realize the correction of calculation values from gyroscopes.
4.2 Lever arm effect and acceleration compensation of arm gesture detection
module
When the object is in non-accelerate status, the output of accelerometers have no
acceleration components, the accelerometer can be used as inclinometer, the output is
the gesture angle. By using the Kalman algorithm proposed in section 4.1, we can
realize the good estimation of gesture angle and the gyroscopes drift, and then correct
the gesture angle and the gyroscope drift. In our movement track system, the
accelerometer can’t be installed at the joints of arm. Hence, when the arm is moving,
a big deviation is produced due to the normal and tangential acceleration. The
deviation will cause the gesture estimation error increased or even failure, which
known as lever arm effect.
4.2.1 lever arm effect
Lever arm effect will produce if the inertial navigation system is not installed at the
center of rolling motion, which can be described by the following model [6],
io
ix
iy
iz
no
nx
ny
nz
P
OR

PR

pr

Fig. 5. The sketch of installation position
Show as in figure 5, define the static coordinate system iiii ZYX-O  and the
dynamic coordinate system nnnn ZYX-O , and consider nO as the roll center. The
accelerometer of inertial navigation system is installed on the fix point P. p
r

is the
position vector of point P in dynamic coordinate system, and the acceleration f

  of
point P in static coordinate system can be described as:
)( pininpin rrf


××+×=   . (9)
where, pin r
 × is the tangential acceleration, )( pinin r
 ××  is the normal
acceleration. in
  is the angle velocity vector of the dynamic coordinate system
relative to the static coordinate system, in
  is the angle acceleration of the dynamic
coordinate system relative to the static coordinate system.
4.2.2 motion acceleration compensation of big arm detection module
The output of accelerometer in big arm gesture detection module 1a

 can be
expressed as
11111 vgaTfa op
 +++=   . (10)
Where, 1opa
 is the line acceleration of shoulder joint 1pO in reference coordinate
system bO , 1f

 is the acceleration of big arm lever arm, g is the component of
gravity, 1v
 is the measure noise. 1f

 and 11 opaT
 is namely motion acceleration
components, which will affect the observation precision of gesture angle, hence, a
compensation is needed. When the arm is moving, the shoulder joint can consider as
in static, namely, 1opa
 =0, big arm lever arm acceleration can be calculated by Eq(9).
The compensate method of acceleration components of big arm gesture detection
module can be expressed as:
111̂ faa

−=  . (11)
where, 1â

is the observation value of gravity component of big arm gesture detection
module by compensation.
4.2.3 motion acceleration compensation of forearm detection module
The accelerometer output of forearm detection module is affected by gravity
components, forearm lever arm acceleration, shoulder joint acceleration, measure
noise and the line acceleration of elbow joint 2opa

, which can be described as
following
2221222 vgaTaTfa opop
 ++++=   . (12)
According to Eq.(11), the main part of 2opa

is the lever acceleration caused by the
rotation of big arm, which can be calculated as:
2
1
12 opop fTa

−=  . (13)
)( 211212 opopop rrf


××+×=   . (14)
where, 2opr
 is the position vector of elbow joint 2pO  in coordinate system 1pO ,
1
 is the rotational angle velocity vector of big arm. The compensate method of
acceleration components of forearm gesture detection module can be expressed as:
22
1
1222
ˆ ffTTaa OP

 −−= −  . (15)
where, 2â

is the observation value of gravity component of forearm gesture detection
module by compensation.
4.3 Experiments and results
In order to demonstrate the validity of compensation algorithm, we fix the big arm
detection module and forearm detection module upon big arm and forearm,
respectively. The arm is in random motion status. The observation effect of gravity
vector by accelerometer is justified by following equation
gaaa zyx −++=
222  . (16)
If εhas a relative big absolute value, the outputs of accelerometers have relative
big motion components, and the outputs can’t be used for gesture calculation directly.
Figure 6 and figure 7 are the motion acceleration compensation effect of big arm and
forearm, respectively. From figure 6 and figure 7, we can see that the peek value of
ε is decreased from 0.7g to 0.1g by compensation, the motion acceleration
components is filtered effectively. In order to study the influence of motion
acceleration to the arm gesture observation, we compared the calculated gesture angle
using origin acceleration as input and that using compensated acceleration. The
results are shown in figure 6b, 6c and figure 7b, 7c. When the arm gesture changes
slowly, the results are consistent, while the arm gesture change fast, the results that
use origin acceleration as input will produce big error. The big arm gesture error peek
is near 20 degree, and the forearm gesture error peek is near 50 degree.
0 1000 2000 3000 4000 5000 6000 7000
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Time (ms)
 M
ot
io
n 
ac
ce
le
ra
tio
n 
( g
 )
Before acceleration compensation
After acceleration compensation
0 1000 2000 3000 4000 5000 6000 7000
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Time (ms)
 M
ot
io
n 
ac
ce
le
ra
tio
n 
( g
 )
Before acceleration compensation
After acceleration compensation
（6a）  (7a)
0 1000 2000 3000 4000 5000 6000 7000
-200
-150
-100
-50
0
50
100
150
200
Time (ms)
P
itc
h 
(d
eg
re
e)
Before acceleration compensation
After acceleration compensation
0 1000 2000 3000 4000 5000 6000 7000
-80
-60
-40
-20
0
20
40
60
80
Time (ms)
P
itc
h 
(d
eg
re
e)
Before acceleration compensation
After acceleration compensation
(6b) (7b)
0 1000 2000 3000 4000 5000 6000 7000
-100
-80
-60
-40
-20
0
20
40
60
Time (ms)
R
ol
l (
de
gr
ee
)
Before acceleration compensation
After acceleration compensation
0 1000 2000 3000 4000 5000 6000 7000
-150
-100
-50
0
50
100
Time（ ms）
R
ol
l (
de
gr
ee
)
Before acceleration compensation
After acceleration compensation
(6c)  (7c)
Fig. 6. The effect of acceleration Fig. 7. The effect of acceleration
compensation for big arm compensation for forearm
If the gesture angle with big error is introduced into the Kalman filter in section 4.1,
the arm gesture angle estimation will produce big error. Therefore, the measure
precision of arm gesture can be improved by the acceleration compensation method
proposed in this paper.
5 The arm gesture movement track algorithm based on multi-
sensors
According to the motion characteristic of arm, this paper established the motion
model of arm. On the basis of triaxial accelerometer, triaxial gyroscope and triaxial
magnetic field sensors, the arm movement track system hardware is designed. The
arm gesture track method based on multi-sensors data fusion is researched. The
motion acceleration components compensation algorithm is analyzed. The arm
movement track experiments show that: when arm move quickly, the existence of arm
motion acceleration will cause a big measure error of arm gesture; Measure error peek
of big arm is about 20 degrees and that of forearm is about 50 degrees; the proposed
compensation method in this paper can filter the motion acceleration component
effectively, and then improve the arm track precision.
References
1. Hou Wensheng, Dai Jiaman: Detection of human upper limb motion gesture based on
acceleration sensor: Transducer and Microsystem Technologies, 1,106--108 (2009) (in
Chinese)
2. Wenwu Feng: Design and Implamentation of the Motion Attitude Detection system, Master
degree,Chongqing university (2008) (in Chinese)
3. RYAN A,JOSEPH A P: A wireless,compact,multi-user system for interactive dance，
Proceeding of the 2006 international conference on new interfaces for musical expression，
Paris，France， pp. 134-139 (2006)
4. Liu Xiaoyan,Zhou Zhaoying: Design and Test of MEMS Attitude Measurement Unit for
Human Motion Tracking:  Instrument Technique and Sensor, 8, 225-227. (2009) (in
Chinese)
5.Zhang Xiaona: Research on the Key Technologies of Economic Strapdown Attitude Heading
Reference System: Master degree, Xi-Dian University, Xi’an,China, (2008) (in Chinese)
6. Gan Shuai: Research on the Lever Arm Effect of Speed Matching Transfer Alignment,
Master degree, Harbin Engineering University, Harbin, China (2009) (in Chinese)
7. Feng Zhiquan: Research on 3D hand tracking method, Master degree, Shandong University,
China (2006) (in Chinese)


Tracking of Human Arm Based on MEMS Sensors

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Tracking of Human Arm Based on MEMS Sensors

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