Motion Capturing with Inertial Measurement Units and Kinect

Tracking of Limb Movement using Optical and Orientation Information

Christoph Kalkbrenner, Steffen Hacker, Maria-Elena Algorri and Ronald Blechschmidt-Trapp

Insitute of Medical Engineering, University of Applied Science Ulm, Albert-Einstein-Allee 55, 89075 Ulm, Germany

Keywords:

Motion Analysis, Inertial Measurement Unit, IMU, Motion Tracking, Kinect, Data Fusion, Kalman Filter.

Abstract:

This paper presents an approach for the tracking of limb movements using orientation information acquired

from Inertial Measurement Units (IMUs) and optical information from a Kinect sensor. A new algorithm

that uses a Kalman ﬁlter to fuse the Kinect and IMU data is presented. By fusing optical and orientation

information we are able to track the movement of limb joints precisely, and almost drift-free. First, the IMU

data is processed using the gradient descent algorithm proposed in (Madgwick et al., 2011) which calculates

the orientation information of the IMU using acceleration and velocity data. Measurements made with IMUs

tend to drift over time, so in a second stage we compensate for the drift using absolute position information

obtained from a Microsoft Kinect sensor. The fusion of sensor data also allows to compensate for faulty or

missing measurements. We have carried out some initial experiments on arm tracking. The ﬁrst results show

that our technique for data fusion has the potential to be used to record common medical exercises for clinical

movement analysis.

1 INTRODUCTION

A considerable amount of literature has been pub-

lished on movement analysis using Inertial Measure-

ment Units (IMUs) (Cloete and Scheffer, 2008; Jung

et al., 2010; Rodriguez-Angeles et al., 2010). An

IMU is a device that measures velocity, orientation,

and gravitational forces, using a combination of ac-

celerometers and gyroscopes, sometimes also magne-

tometers. IMUs can provide tracking data for robotic

controls, gesture recognition and medical applica-

tions, such as joint angle determination or gait analy-

sis. However, a persistent problem of IMU measure-

ments, is that they tend to drift over time. Madg-

wick et al.(Madgwick et al., 2011) presented a ﬁlter to

extract orientation information from IMU data. The

beneﬁt of this ﬁlter is that it reduces the drifting of

the orientation information. The aim of this work is

to fuse relative measurements obtained from an IMU,

with absolute position measurements obtained from

an optical system. We implement the data fusion us-

ing a Kalman ﬁlter, the fused data is then used inside a

control loop and processed for enhanced tracking pre-

cision. The method proposed allows missing or faulty

data from one of the two sources (IMU or Kinect) to

be compensated for allowing for a stable system suit-

able for medical applications.

1.1 Optical Tracking

In recent years, optical based motion analysis

has been increasingly used in medical applications

(Claasen et al., 2011). Common optical systems

record marker positions in order to extract patient mo-

tion information (Liguo et al., 2011). Other types

of optical systems are based on arrays of cameras

that provide 3D sensing. Since camera technology

has become less expensive in the last decade, its use

in medical motion analysis is very popular. Lately,

3D depth sensors have also become inexpensive and

multi-sensor systems like the affordable Microsoft

Kinect (includes an optical camera and a 3D depth

sensor), are an attractive choice for carrying out med-

ical motion detection and analysis. Optical motion

analysis is used in various application ﬁelds such as

joint angle derivation (Bo et al., 2011), evaluation of

patient activity (Cordella et al., 2012), patient posture

analysis (Obdrzalek et al., 2012; Xiao et al., 2012;

Zeng et al., 2012), robotics (El-laithy et al., 2012) and

gesture recognition (Patsadu et al., 2012).

1.2 IMU

Theoretically, speed of movement and distance can

be determined by integration of the acceleration data

120

Kalkbrenner C., Hacker S., Algorri M. and Blechschmidt-Trapp R..

Motion Capturing with Inertial Measurement Units and Kinect - Tracking of Limb Movement using Optical and Orientation Information.

DOI: 10.5220/0004787601200126

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2014), pages 120-126

ISBN: 978-989-758-013-0

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

from an IMU. But since integration operates like a

low pass ﬁlter, drifting errors occur. This effect is

shown in (1).

cos(2π ft)dt =

2π f

sin(2π ft) (1)

As can be seen, the ampliﬁcation term (2π f )

−1

is in-

versely proportional to frequency, so high frequencies

fall off and low frequencies are ampliﬁed. As high

frequency noise present in the IMU measurements is

ﬁltered, the offset in the measurements is ampliﬁed,

which may cause drift.

The Madgwick ﬁlter (Madgwick et al., 2011) was

proposed to calculate the spatial orientation in a com-

putationally efﬁcient, wearable inertial human mo-

tion tracking system used for rehabilitation applica-

tions. The algorithm is applicable to IMUs using tri-

axis gyroscopes and tri-axis accelerometers. It uses

a quaternion representation so that accelerometer and

gyroscopic data can be used in an analytically derived

and optimised gradient descent algorithm to compute

the direction of the gyroscope measurement error as a

quaternion derivative. With that, the orientation of the

IMU relative to the earth frame can be determined.

Because of its low computational load and its abil-

ity to operate at a low sampling rate, the algorithm

greatly reduces the hardware and power necessary for

wearable, inertial movement tracking. In addition to

this, the level of accuracy of the Madgwick ﬁlter ex-

ceeds that of most other approaches to determine the

IMU orientation. IMUs are used because of their ver-

satile capabilities and high precision. Research on

IMUs is found in a wide range of ﬁelds such as joint

angle estimation (Bo et al., 2011), pedestrian track-

ing (Fischer et al., 2012) and general motion analysis

(Liguo et al., 2011; Taffoni et al., 2011; Zhang et al.,

2011).

2 METHOD

The IMU developed by the University of Applied Sci-

ences in Ulm is composed of a tri-axis gyroscope, a

tri-axis accelerometer MPU-6000 (from InvenSense),

a rechargeable battery and a Bluetooth gateway (Glaz,

2011) (Walter, 2012). The IMU delivers seven mea-

surements per sample, three gyroscope values, three

accelerometer values and the temperature. Each value

is coded in two bytes, so the IMU transfers 14 bytes

and two additional Start and Stop bytes to the com-

puter at each sample step. The sampling rate can be

conﬁgured from 60 Hz up to 300 Hz. In the present

study a sampling rate of 100 Hz sufﬁces.

The data delivered by the 3D depth sensor in the

Microsoft Kinect is accessed using the Microsoft

Hand

Wrist

Elbow

Shoulder

Head

Center of

Spine

Hip

Knee

Ankle

Foot

the shoulder

Center of

the hip

Figure 1: Joint positions described within the Skeleton-

model offered by the Microsoft Kinect sensor.

SDK. Data is accessed with a sampling rate of 30

Hz and the SDK is able to track the motion of up to

four persons simultaneously. The SDK provides the

tracking information of each person as 20 absolute

3D position coordinates of the joints shown in the

skeleton model in Fig. 1.

IMU 1

IMU n

Madgwick

Data

Kinect

Joint

Size

orientation

pose

estimated pose

Filter

Madgwick

Filter

Fusion

Extraction

Determination

Figure 2: Flowchart of the data fusion algorithm.

Like most sensors, IMUs and the Kinect sensor

are not immune to measurement artifacts. Besides the

presence of drift, other events (such as rapid move-

ments, occlusions, disturbance in the Bluetooth com-

munication, optical or magnetic noise, etc.) can lead

to faulty or missing measurement data from one of

both sensors. In the present work we try to compen-

sate for drift as well as missing or faulty data using an

algorithm that fuses information from IMUs and the

Kinect. To fuse the data we developed an algorithm

(Fig. 2) that uses an embedded Kalman Filter. We

explain the algorithm next.

We will explain the fusion algorithm using an ex-

ample of tracking a human upper and lower arm (Fig.

3). For this example, the 3D joint positions of the el-

bow P

and the wrist P

are tracked using two IMUs

MotionCapturingwithInertialMeasurementUnitsandKinect-TrackingofLimbMovementusingOpticalandOrientation

Information

121

= P

Figure 3: Derivation of joint positions P

and P

using

two IMUs m1 and m2. The length l1 and l2 as well as the

initial joint positions P

are provided by the Kinect.

m1 and m2. The initial shoulder coordinate P

is taken

from the corresponding position coordinate P

ac-

quired by the Kinect. Using the quaternion represen-

tation that results from processing the IMU data with

the Madgwick ﬁlter, the vector ~o

, which describes

the direction the front side of the IMU is looking at

(commonly known in graphics as lookAt vector, see

Fig. 3), can be determined. Based on the vector ~o

and the known length of the upper arm l

and lower

arm l

the joint positions can be determined. First the

unit orientation vectors of the 2 IMUS ~o

and ~o

are multiplied by the length of the upper and lower

arm.

−→

· l

−→

· l

(2)

With the addition of the resulting vector p

to the

initial shoulder coordinate P

, the position of the el-

bow joint P

can be determined. The calculation of

the wrist joint position P

can then be determined by

adding p

to the now known elbow coordinate P

−−→

−→

−−→

−→

(3)

The 3D coordinates of the elbow and wrist positions

are used for the Kalman ﬁlter. In the next step the

Kinect data is prepared. As mentioned before, the

Kinect measures the absolute 3D coordinates of 20

joint positions of every tracked person. These joint

positions are used inside the Kalman ﬁlter to ad-

just the correspondent joint positions obtained by the

IMUs. The corrected, fused results of the Kalman ﬁl-

ter are fed back to the Madgwick ﬁlter to compensate

for existing orientations errors.

The Kalman ﬁlter is determined using basic

knowledge from (Wendel, 2007), (Koehler, 2005) and

(Jekeli, 2001). The fundamental equations unfold as

follows:

−

n/n1/n2/...









= A ·









+ v (4)

n/n1/n2/...









= H ·









+ w (5)

where (4) describes the system state x

−

n/n1/n2/...

as the

true position in space (x

)

obtained by multi-

plying the parameter matrix A with the coordinates

n/n1/n2/...

= (x

)

calculated in (3) and the cor-

related noise v. The measurement model (5) de-

scribes the vector of true position y

n/n1/n2/...

in space

)

obtained by multiplying the parameter

matrix H with the joint position data of the Kinect

n/n1/n2/...

= (x

)

and the correlated noise w.

A and H are the usual parameter matrices of a Kalman

ﬁlter. For our simple implementation, we used unit

matrices for A and H.

The Kalman-Gain K is described in (6) where P is

the covariance of the IMU and R is the covariance of

the Kinect. For a detailed derivation see (Maybeck,

1982).

K = P · H

(H · P · H

+ R)

−1

(6)

As reference values for the covariances, we used val-

ues taken from the datasheets of the IMUs and the

Kinect. After empirical studies, the basic values were

set to R = 0.015m for the Kinect and to P = 0.005m

for the IMU. The covariance R of the Kinect is dy-

namic and changes depending on the tracking state of

the Kinect and on the identiﬁed outliers in the calcu-

lated positions. The difference between the last cal-

culated position and the next position received by the

Kinect is described by ∆s. For our applications, we

established as maximum ∆s of 0.15m so that, if the

distance between two consecutive measurements ex-

ceeded 0.15m, the covariance matrix R was recalcu-

lated as follows:

R =





0 0

0 R

0 0 R









∆s

0 0

0 ∆s

0 0 ∆s





∗K (7)

where K is empirically set to 15 to obtain best re-

sults. Using the described dynamic covariance ma-

trix R, the system behaves robustly in the presence

of tracking errors produced by the Kinect (Nischwitz

et al., 2007). For each joint n/n1/n2/... both IMU

and Kinect positions are fused in (8) to get the new

position x

. Depending on the Kalman-Gain K the

data gets weighted differently in each step.

= x

−

· K · (y − H ·x

−

) (8)

The resulting positions provided by the Kalman

ﬁlter are then used to create a fused rotation matrix M

for each tracked limb. To create M we need three vec-

tors, v

f ront

, v

and v

side

, which respectively describe

BIODEVICES2014-InternationalConferenceonBiomedicalElectronicsandDevices

122

Quaternions

lookAt Vectors

Kalman

Kinect coordinates

IMU

Kinect

Rotationmatrix

IMU coordinates

Fused coordinates

Rotationmatrix

ﬁlter

, ~o

Quaternions 3D Avatar

Madgwick

Correct

ﬁlter

Madgwick ﬁlter

Figure 4: Flowchart of data types and their interactions between each other.

in what directions the front, up and lateral sides of the

IMUs are looking at. The coordinates resulting from

the Kalman ﬁlter are used to calculate the unit v

f ront

vector,

f ront

−−−→

(9)

The vector v

needed for the fused rotation matrix M

cannot be calculated only from the two joint positions,

but can be extracted from the orientation Quaternions

delivered by the Madgwick Filter. The Quaternion

data from the Madgwick Filter is translated into a ro-

tation matrix (in our case using Microsoft XNA or

OpenGL) from which v

gets extracted. ~v

side

can be

calculated out of the cross product of v

f ront

and v

side

=~v

f ront

×~v

(10)

M =





x, f ront

x,side

x,up

y, f ront

y,side

y,up

z, f ront

z,side

z,up





(11)

The fused rotation matrix M is now used to correct the

orientation results of the Madgwick Filter. To do so

the fused rotation matrix M gets converted back into

a Quaternion (in our case using Microsoft XNA or

OpenGL) and replaces the old orientation information

of the Madgwick-Filter.

An overview of the whole process of converting the

different data types and fusing them together can be

seen in Fig. 4.

3 RESULTS

The ﬁrst step of our evaluation consisted in carrying

out a battery of tests to determine the accuracy of the

proposed system. For these tests, the coordinates of

the right elbow of 10 different test persons were mea-

sured while the test persons were not moving at all.

For each test person a dataset of 1000 measured joint

coordinates of the right elbow was recorded (10s at

a measurement rate of 100Hz). The standard devia-

tion of the resulting joint coordinates of the fusion al-

gorithm compared to the real position was measured.

The evaluation of the measurements provided us with

an average standard deviation of ±1.47cm in the x-

direction, ±1.62cm in the y-direction and ±2.20cm

in the z-direction.

The second step of our evaluation consisted of track-

ing the movement of the arm. For this experiment, a

patient periodically moved his/her tracked arm up and

down as shown in Fig 5. A subset of the Kinect and

IMU measurements of the right elbow position coor-

dinates is shown in Fig 6 and Fig. 7. The Kinect was

Figure 5: Reference exercise of the patient. The gray circle

indicates the tracked elbow position. The black box is the

sensor attached to patients arm.

MotionCapturingwithInertialMeasurementUnitsandKinect-TrackingofLimbMovementusingOpticalandOrientation

Information

123

Figure 6: Tracked x-coordinates by the Kinect while the

patient is moving his/her arm periodically up and down.

Figure 7: Tracked x-coordinates by the IMU while the pa-

tient is moving his/her arm periodically up and down.

Figure 8: Resulting x-coordinates of the fusion algorithm

while the patient is moving his/her arm periodically up and

down.

able to track the elbow without any noticeable drift

while the acquired data from the IMU shows some

drift (0.1mm in 10 s). As shown in Fig. 8 the oc-

curring drift while tracking the elbow movement is

removed in the fused data.

Several problems appear when acquiring move-

ment data with the Kinect sensor. The most com-

mon issue observed occurs whenever body parts of

the tracked person are hidden from the sensor or are

out of the range of sensing. If this happens, the algo-

rithm provided by Microsoft marks appropriate joints

with the state not visible. While in this state, joint po-

sitions cannot be recognized. During such a phase the

fusion algorithm passes on the Kinect data and uses

only IMU coordinates. From our experimental results

we could establish that our IMU presented an average

drift of approximately 0.01mm/s. From this measure-

ment, and depending on the precision required by a

Figure 9: Tracked x-coordinates by the IMU while the pa-

tient is moving his/her arm periodically up and down. The

abrupt movements that cause errors within the Madgwick-

Filter are marked by gray dashed circles.

Figure 10: Resulting x-coordinates of the fusion algorithm

while the patient is moving his/her arm periodically up and

down. The abrupt movements that cause errors within the

Madgwick-Filter are marked by gray dashed circles.

particular application, we can establish an experimen-

tal Kinect time-out window. That is, the maximum

amount of time that we can pass on the Kinect mea-

surements while still holding the IMU measurements

stable. For example, if a precision of 1mm in the mea-

surement of joint coordinates is required, we need to

perform sensor data fusion at least every 100s.

The third step of our evaluation consisted again of

tracking a periodic elbow movement, only this time

the patient would occasionally move the arm fast and

abruptly. Fig. 9 shows the x-coordinates of an IMU

tracked elbow in this scenario. While periodically

moving the arm, the patient introduces intentional er-

rors by moving his/her arm way too fast for the IMU

to track. These moments are marked by gray dashed

circles. After the forced errors the patient continues

his/her periodic movement normally. The fast move-

ments cause the Madgwick ﬁlter to calculate a wrong

orientation of the IMUs placed on the arm of the pa-

tient. Therefore the calculated position coordinates

are incorrect. In Fig. 10 the same experimental results

are shown after fusing the IMU data with the Kinect

data. As can be seen, the orientation error of the IMU

gets corrected within three to four cycles of move-

ment after the error occurred. In a fourth step of our

evaluation protocol, we tried to evaluate if the fusion

algorithm could compensate for artifacts in the Kinect

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124

Figure 11: The black curve shows the resulting x-

coordinates of the fusion algorithm while the vision of the

Kinect is disturbed. The corresponding Kinect coordinates

are shown in the gray curve. While this curve is at zero, the

Kinect is not able to detect the joint and with that, it does

not provide data for the fusion algorithm.

measurements. For this step, the same experiment of

moving the arm periodically up and down was per-

formed. Fig. 11 shows the x-coordinates of the wrist

position obtained from the fusion algorithm in black

and from the Kinect in gray. During this exercise the

view of the Kinect was periodically obstructed on pur-

pose. While the gray curve is on zero, the Kinect

doesn’t see the wrist and is not able to deliver any

data to the fusion algorithm. As can be seen, missing

Kinect data over a short time is compensated for us-

ing only IMU data. An important aspect to maintain

the stability of the Kinect measurements even in the

presence of periodic obstructions is the possibility to

dynamically recalculate the covariance of the Kinect

as shown in (7).

The last step in our evaluation protocol was

a ﬁrst, exploratory measurement done in a single

Parkinson patient. We wanted to qualitatively assess

if the high accuracy of the IMU measurements make

them suitable to track very small movements such as

tremor in Parkinson disease. The proposed system

was in fact able to detect the Parkinson tremor

without drift during a 10 minute experiment.

4 CONCLUSIONS

In this paper we propose a novel algorithm to carry

out sensor data fusion. In particular, we fuse data

obtained from IMUs and the Kinect while tracking

limb movement. Our fusion algorithm uses the Madg-

wick ﬁlter as part of a control loop, a Kalman ﬁlter to

fuse information and quaternion correction to main-

tain stability of the measurements. A battery of initial,

exploratory experiments allowed us to assess that the

fusion of data from the IMUs and the Kinect provide

increased precision and stability for movement track-

ing. We could also assess that data fusion was able to

correct errors in the measurements either by dropping

faulty measurements or by relying only on one sensor

when data from the second one was unavailable.

In (Obdrzalek et al., 2012) the accuracy of the

Kinect sensor was examined. The authors wanted to

determine if the Kinect meets the requirements for

medical posture analysis. During their investigations,

they observed a standard deviation of the joint coordi-

nates measured by the Kinect of ±5.5cm. In our ex-

periments with sensor data fusion we observed a stan-

dard deviation of the joint coordinate measurements

of ±2.20cm, which, while encouraging, is still very

low compared to high end optical tracking systems.

As part of the research carried out in (Jung et al.,

2010) a system of IMUs was used for motion analysis.

The IMUs were used to record and display postures

and movements of the upper body. However, this was

only possible with a limited mobility of the patient

and an additional individual calibration of the IMUs.

By comparison, the introduction of the Kinect sensor

in our experiments allowed for higher ﬂexibility in the

movements without the need to recalibrate the IMUs

for each patient.

To fully evaluate the capabilities of the proposed

system in medical applications, we need to carry out

additional studies on larger groups of patients, differ-

ent locations and different types of movements. Fur-

ther studies are also needed to better outline the lim-

itations of the developed application and improve the

overall system. A quantitative study using controlled

movements in a robotic arm could be used to precisely

quantify the precision of the tracking algorithm pro-

posed. In future work we want to use the system to

track multiple persons, record therapy processes and

support clinical evaluation of diseases such as Parkin-

son.

ACKNOWLEDGEMENTS

The authors would like to thank Karl Dubies and

Michael Stuber for their assistance. This work was

supported by a grant from the Ministry of Science,

Research and the Arts of Baden-Wuerttemberg (Az:

33-7533-7-11.6-10/2).

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