ZMP Trajectory from Human Body Locomotion Dynamics Evaluated by

Kinect-based Motion Capture System

Igor Danilov, Bulat Gabbasov, Ilya Afanasyev and Evgeni Magid

Intelligent Robotic Systems Laboratory (LIRS), Innopolis University, Universitetskaya 1, Innopolis, 420500, Russia

Keywords:

Motion Capture (MoCap), Zero Moment Point (ZMP), Kinect Sensor, Biomechanical Analysis of Human

Locomotion, Multi-depth Sensor Video Recording.

Abstract:

This article presents the methods of zero moment point (ZMP) trajectory evaluation for human locomotion

by processing biomechanical data recorded with Kinect-based motion capture (MoCap) system. Our MoCap

system consists of four Kinect 2 sensors, using commercial iPi soft markerless tracking and visualization

technology. We apply iPi Mocap Studio software to multi-depth sensor video recordings, acquiring visual and

biomechanical human gait data, including linear and angular coordinates, velocities, accelerations and center

of mass (CoM) position of each joint. Finally, we compute ZMP and ground projection of the CoM (GCOM)

trajectories from human body dynamics in MATLAB by two methods, where human body is treated as (1)

a single mass point, and (2) multiple mass points (with following ZMP calculation via inertia tensor). The

further objective of our research is to reproduce the human-like gait with Russian biped robot AR-601M.

1 INTRODUCTION

The history of humanoid robotics is directly corre-

lated with the active exoskeletons development. Even

though one of the ﬁrst exoskeleton was created al-

most 50 years ago, in 1969, under the leadership of

Yugoslav scientist Miomir Vukobratovic (Vukobra-

tovic and Juricic, 1969), humanoid robotics related

research topics keep attracting signiﬁcant attention

of scientists as humanoid locomotion is still too far

from human walking stability and energy efﬁciency

(Larsen and Stoy, 2011).

Both humans and humanoids are underactuated

systems with no actuation between a foot and support-

ing surface (Dasgupta and Nakamura, 1999). In or-

der to develop energy-efﬁcient locomotion algorithms

for a humanoid, a human gait analysis should be per-

formed (Asano and Luo, 2008). Taking into account

signiﬁcant differences between a human and a hu-

manoid it is not feasible to apply a human gait directly

to a robot (Field et al., 2009). These differences in-

clude distinct amount of Degrees of Freedom (DoFs)

and skeletons, different mass distribution and CoM

position, limited capabilities of humanoids relatively

to humans in terms of joint constraints (position, ve-

locity and acceleration). Thus, there is no direct map-

ping of human relative positions to the robot and kine-

matic mismatch requires kinematic corrections with

calculating the joint angle trajectories. At the same

time to keep locomotion balance an advanced control

should be applied to the robot, overcoming problems

of underactuation and dynamic mismatch (Dasgupta

and Nakamura, 1999; Naksuk et al., 2005).

Nevertheless, a number of research teams re-

ported successful automatic generation of robot walk-

ing from human walking data through different math-

ematical models of locomotion control - analysis of

MoCap data of a human locomotion provided certain

human locomotion outputs, which were further im-

plemented into robotic bipedal locomotion. Sinnet et.

al. (Sinnet et al., 2011) introduced canonical human

walking functions, which were used to form a linear

spring-damper system to estimate human-walking be-

havior. Chalodhorn et al. (Chalodhorn et al., 2007)

described a mapping of a human gait data (obtained

from MoCap data) onto a body skeleton, applying in-

verse kinematics procedure; this was followed by us-

ing principal component analysis (PCA) to reduce di-

mensionality of the joints space, building 3D motion

space representation of kinematic postures.

As far as the terms of static (GCOM) and dy-

namic (ZMP) stabilities (Mrozowski et al., 2007) can

be used to biped and human locomotion balance re-

search, we are going to apply obtained with a Mo-

Cap system human locomotion data for a humanoid

robot balancing. This could be realized by adapt-

162

Danilov, I., Gabbasov, B., Afanasyev, I. and Magid, E.

ZMP Trajectory from Human Body Locomotion Dynamics Evaluated by Kinect-based Motion Capture System.

DOI: 10.5220/0005726001600166

In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 3: VISAPP, pages 162-168

ISBN: 978-989-758-175-5

ing human gait parameters (joint angles and angu-

lar moments, GCOM and ZMP trajectories, etc.) to

the robot ones taking into account relevant constraints

with kinematic and dynamic corrections.

MoCap systems are usually based on

marker/markerless motion capture technologies,

using sensors with different physical principles: opti-

cal, magnetic, inertial, mechanical, and even acoustic

(Field et al., 2009). The most precise technologies

are the most expensive, like mechanical exoskeletons

with direct joint angles tracking (Wong et al., 2015),

inertial sensors (e.g., XSENS system

) with accel-

eration and rotational velocity measurements from

triaxial accelerometers and gyroscopes (Wong et al.,

2015), and optical MoCap based on multi-camera

system (e.g., VICON

), which captures 2D videos

from several cameras and then merges them into 3D

model by triangulation (Field et al., 2009).

In our research we use low cost markerless optical

MoCap system based on four depth sensors Kinect 2

and iPi Soft software. We calculate ZMP and GCoM

trajectories from human body dynamics and estimate

the accumulated errors. Static and dynamic criteria

further will be applied for human data re-projection

onto human-like gait of Russian biped robot AR-

601M, yielding its stable and natural locomotion.

The paper is organized as following. Section 2 de-

scribes our system setup, consisting of Kinect-based

MoCap system, iPi Mocap Studio software and AR-

601M robot. Section 3 considers human body approx-

imation with a single and multiple mass points and

introduces two ZMP evaluation methods. Section 4

presents the results of ZMP and GCoM trajectory cal-

culations based on MoCap measurements with accu-

racy estimation. Finally we conclude and discuss our

future research activities.

2 SYSTEM SETUP

2.1 Kinect-based Motion Capture

For human gait registration we use markerless opti-

cal MoCap system based on four Kinect 2 sensors,

which encapsulate a total area of 23 sq.m with a walk-

ing area of 4.5 m length (Fig. 1, 2). Each Kinect

sensor contains RGB camera and depth sensor. Mo-

Cap system analyzes depth sensor video recordings

XSENS is an inertial 3D motion tracking technology

based on body-mounted MEMS inertial sensors and multi-

sensor data fusion algorithms, www.xsens.com

VICON is a passive optical motion capture technology

based on high resolution multi-camera system and advanced

real-time computer vision algorythms, www.vicon.com

to tracks human motion. Next, in order to reproduce

human locomotion with a human-like bipedal robot,

a human skeleton animation is built and a human 3D

model with linear and angular joint motion parame-

ters is reconstructed. MoCap system acquires human

motion data in three stages: 1) MoCap calibration; 2)

human motion tracking; 3) non-real-time processing

with iPi Soft software and MATLAB. These stages

were executed with iPi Soft which acquired MoCap

data and provided non-real-time processing by merg-

ing depth sensor video data from four Kinect sen-

sors, correcting the data and ﬁltering out the noise.

Each Kinect sensor was connected to an individual

Windows PCs, forming a distributed system with one

master PC, which synchronized three other PCs and

the corresponding depth sensors’ records (Gabbasov

et al., 2015).

Figure 1: Kinect-based MoCap system: The scene view.

Figure 2: MoCap system: The scene conﬁguration.

The detailed information on MoCap calibration,

measurement technique, data acquisition and process-

ing with iPi Soft could be found in (Gabbasov et al.,

2015) and iPi Docs resource

. The MoCap calibration

evaluates ground position and mutual Kinect sensor

localization. During calibration process we had sig-

iPi Docs: User Guide for Multiple Depth Sensors Con-

ﬁguration, http://docs.ipisoft.com/User Guide for Multiple

Depth Sensors Conﬁguration.

ZMP Trajectory from Human Body Locomotion Dynamics Evaluated by Kinect-based Motion Capture System

163

niﬁcant issue with incorrect deﬁnition of a glowing

marker position by iPi Mocap Studio which were pos-

sibly caused by a weak contrast of the glowing marker

relatively to laboratory walls. We have overcome this

problem by performing the calibration in the dark

room. Unfortunately, such approach increased the av-

erage calibration error to 0.045 m (Gabbasov et al.,

2015), and thus decreased MoCap measurement ac-

curacy and also impacted the GCoM and ZMP errors.

In our further calculations of human GCoM and

ZMP trajectories we use the data which were obtained

from iPi Biomech Add-on plugin

, such as CoM co-

ordinates and accelerations. We exported biomechan-

ical characteristics into MATLAB and selected a time

period where a human walked forward, matching X -

axis with forward walking direction and Z-axis with

left-hand direction (on default, Y -axis is in upward di-

rection).

2.2 iPi Soft Package

iPi Soft software

uses 3D depth sensors to track

human joints and produce 3D animations, providing

human pose data with centimeter-level accuracy off-

line (Kim et al., 2015). It consists of free iPi Recorder

and iPi Mocap Studio software. iPi Recorder acquires

depth sensor video data from four Kinect 2 sensors,

and then iPi Mocap Studio processes multiple sen-

sor video records off-line, reconstructing 3D model

of human locomotion applying inverse kinematics ap-

proach. Afterwards we use iPi Biomech Add-on plu-

gin to calculate joint coordinates and angles, linear

and angular velocities, accelerations, and CoM posi-

tions over time.

Finally, we analyze human gait to identify key

features of human locomotion in MATLAB, collect-

ing statistically signiﬁcant data to create an adequate

human gait mathematical model, which could be

adapted to AR-601M robot gait mathematical model.

2.3 AR-601M Robot Description

The AR-601M biped robot

(Fig. 3) is a full-size hu-

manoid with the height of 144 cm and weight of 65

kg, having 43 active DoFs (including 12 DoFs in

robot legs). Nowadays, robot supports slow locomo-

tion with GCoM trajectory laying within support feet

during the its walking (Khusainov et al., 2016).

http://docs.ipisoft.com/iPi Biomech Add-on.

Motion Capture software, supporting markerless tech-

nology from Russian company iPi Soft, http://ipisoft.com

AR-601M robot is being developed by Russian

company Androidnaya Tehnika (Android Technics),

http://en.npo-at.com/products/ar-600

Figure 3: Android Technics AR-601M robot.

3 MOCAP-BASED HUMAN ZMP

CALCULATION

3.1 ZMP from Human Body Dynamics

as a Single Mass Point

The biped/human gait is statically stable when the

GCoM trajectory lays within a foot support area and

the corresponding support polygon (Goswami, 1999),

whereas criterion of dynamical stability is described

with zero moment point (ZMP) term (Vukobratovic

and Borovac, 2004). ZMP of a properly balanced gait

coincides with Center of Pressure (CoP), presenting a

point under the foot where the ground reaction force

fully reduces the effects of forces and moments on the

foot from the whole body (Vukobratovic and Borovac,

2004). ZMP is considered as the dynamical equiv-

alent of the GCoM: a body with the ZMP location

under the foot is stable, otherwise it is not.

To calculate ZMP from body dynamics as a single

mass point we used a rough approximation of biped

locomotion by a so-called cart-table model (Kajita

et al., 2003), which evaluates ZMP as a function of

CoM position and accelerations, anchoring the CoM

height ( ˆy) during locomotion:

(

zmp

(t) = x

com

(t) −

ˆy

¨x

com

(t)

zmp

(t) = z

com

(t) −

ˆy

¨z

com

(t)

(1)

where x

zmp

, z

zmp

are coordinates of ZMP. We applied

equation (1) to the data which were exported into

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

164

MATLAB from iPi Biomech Add-on plugin.

3.2 ZMP from Human Body Dynamics

as Multiple Mass Points

We represent a human body as a model with a 12 mass

points m

set in the middle of the corresponding body

parts (a head, a torso, two shoulders, two forearms,

two thighs, two shins and two feet), and human mass

distribution for the body parts (Table 1) is performed

according to (Haley et al., 1988).

Table 1: Human mass distribution of the body parts (Haley

et al., 1988).

Segment Segment mass

Head 6%

Torso 48%

Shoulder 2.5%

Forearm 2.5%

Thigh 12%

Shin 4.5%

Foot 1.5%

The ZMP equations with multiple mass points via

inertia tensor in the sagittal and frontal planes are cal-

culated as follows (Ha and Choi, 2007):











zmp

(t) =

∑

i=1

( ¨y

+g)x

−

∑

i=1

¨x

∑

i=1

( ¨y

+g)

zmp

(t) =

∑

i=1

( ¨y

+g)z

−

∑

i=1

¨z

∑

i=1

( ¨y

+g)

(2)

where x

zmp

, z

zmp

are coordinates of ZMP and m

is the

point mass of the i-th body part.

3.3 CoM and ZMP Accuracy

Estimation Technique

Kinect-based MoCap brings a stochastic error to the

true measurement characteristics such as coordinates

and accelerations of the i-th body part (Gabbasov

et al., 2015) and therefore MoCap-measured values

should be treated as a non-stationary stochastic pro-

cess. We assume that the total measurement error

consists of several components: Kinect-based MoCap

calibration error (i.e. the error in cross-localization of

four Kinect sensors with regard to each other), the

accuracy of human motion approximation with iPi

Soft, the error in distance estimation between a hu-

man body and sensors, etc. Moreover, measurement

error analysis is a quite difﬁcult task because it is im-

possible to take into account all Kinect sensor conﬁg-

urations and the accuracy of human motion approx-

imation with iPi Soft, which depends on the scene

background, human individual anatomical features,

clothes’ color, etc. Therefore, according to the Cen-

tral Limit Theorem we can assume that the measure-

ment errors are normally distributed and the variance

of the stochastic process is time-independent. Thus,

the probability density of the measured values (coor-

dinates and accelerations of the i-th body part’s CoM)

is deﬁned as:

p(x, t) =

√

2πσ

exp−

(x −µ(t))

2σ

(3)

where x is a measured value, µ(t) is a time-dependent

mathematical expectation (e.g., a true coordinates or

accelerations for a body part’s CoM), σ is a variance

of the measured value.

In our study, the absolute measurement error could

be estimated as a standard deviation from the time-

dependent mean. For example, the measurement error

of x-coordinate of CoM is computed as the unbiased

standard deviation:

∆x

com

∑

i=1

−M(x, t))

(N −1)

(4)

where M(x, t) is mathematical expectation for x-

coordinate of CoM. The mathematical expectation

of CoM for i-th body part changes over time along

x-coordinate during human locomotion (e.g., foot’s

CoM acceleration is shown in Fig. 4, blue curve).

Therefore we smooth the MoCap-measured data (blue

curve in Fig. 4) with moving average to estimate the

mathematical expectation (brown curve in Fig. 4).

Figure 4: Measured foot’s CoM acceleration along the x-

axis (blue curve) and its smoothing (brown curve).

We use the same method to calculate the smoothed

mathematical expectation of CoM acceleration and

coordinates for both human body as a single mass

point (the ﬁrst method, Section 3.1) and all body parts

as multiple mass points (the second method, Sec-

tion 3.2). As far as we provide indirect ZMP measure-

ZMP Trajectory from Human Body Locomotion Dynamics Evaluated by Kinect-based Motion Capture System

165

ments, the Error Theory should be applied to calculate

ZMP measurement error ∆ZMP

with equation:

∆ZMP

(

∑

i=1

∂ZMP

∂x

)

(5)

where

∂ZMP

∂x

is a partial derivative of ZMP function

for one of the variables and dx

is the estimation of

absolute measurement error for this variable.

Therefore, the total ZMP error for the ﬁrst method

is calculated as follows:







∆ZMP

(∆x

com

+ (

ˆy

∆a

xcom

)

∆ZMP

(∆z

com

+ (

ˆy

∆a

zcom

)

(6)

where ˆy is average CoM position along the vertical

Y -axis.

Whereas the total ZMP error for the second

method is calculated as follows:











∆ZMP

∑

i=1

( ¨y

+g)∆x

)

∑

i=1

∆ ¨y

)

∑

i=1

( ¨y

+g)x

−

∑

i=1

¨x

∑

i=1

∆ ¨x

)

∑

i=1

¨x

∆y

)

∑

i=1

( ¨y

+g)x

−

∑

i=1

¨x

∑

i=1

∆y

∑

i=1

( ¨y

+g)

∆ZMP

∑

i=1

( ¨y

+g)∆z

)

∑

i=1

∆ ¨y

)

∑

i=1

( ¨y

+g)z

−

∑

i=1

¨z

∑

i=1

∆ ¨z

)

∑

i=1

¨z

∆y

)

∑

i=1

( ¨y

+g)z

−

∑

i=1

¨z

∑

i=1

∆y

∑

i=1

( ¨y

+g)

(7)

where x

, y

, z

, ¨x

, ¨y

, ¨z

correspond to the coordi-

nates and accelerations of the i-th body part, and

∆x

, ∆y

, ∆z

, ∆ ¨x

, ∆ ¨y

, ∆ ¨z

are absolute error estima-

tions for coordinates and accelerations of the i-th

body part.

4 ZMP TRAJECTORY AND

ACCURACY ANALYSIS

4.1 ZMP and GCoM Trajectories from

Human Body Dynamics

ZMP and GCoM trajectories on the ground plane

were calculated from human body data, where hu-

man body was approximated a single and multiple

mass points methods, according to equations (1) and

(2) correspondingly. Figure 5 represents human ZMP

trajectories obtained by a single mass point method

(red curve) and multiple mass points method (green

curve), whereas blue curve shows the GCoM trajec-

tory and orange ellipses illustrate human footprints.

The ﬁgure shows that both ZMP and GCoM trajec-

tories are located close to the footprints (and conse-

quently to the corresponding support polygons). It

satisﬁes the static (GCoM) and dynamic (ZMP) sta-

bility criteria (Mrozowski et al., 2007) and proves

that the human gait was properly balanced. More-

over, the ZMP trajectory which was calculated apply-

ing multiple mass point method lays slightly closer to

the GCoM trajectory than the calculated with a single

mass point method trajectory. As far as both methods

process the same MoCap data, it means that they have

different accuracy. Only the last segment of ZMP tra-

jectories lays outside the support area (footprint) at

the coordinate of 2 m. It emphasizes the balancing

changes before a human stop at the end of MoCap

walking area.

Figure 5: Human ZMP trajectory from single mass point

(red curve) and multiple mass points methods (green curve),

GCoM trajectory (blue curve) and footprints (orange el-

lipses) on the ground plane. The X-axis and Z-axis are ori-

ented in the human walking and orthogonal to the walking

(lateral) directions respectively.

Figures 6 and 7 show ZMP trajectories vs. time in

sagittal and frontal planes respectively which are cal-

culated from human body locomotion dynamics. The

signiﬁcant deviations of ZMP trajectory in the frontal

plane in the vicinity of the footprint positions arise

from the limitations of MoCap system measurement

accuracy.

Figure 6: Human ZMP trajectory vs. time in sagittal plane

for single mass point (red curve) and multiple mass points

methods (green curve).

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

166

Figure 7: Human ZMP trajectory vs. time in frontal plane

for single mass point (red curve) and multiple mass points

methods (green curve).

4.2 CoM and ZMP Accuracy

Estimation

We estimated the GCoM measurement error as a stan-

dard deviation applying equation (4), which gave us

the typical values:

(

∆x

com

≈ 1cm

∆z

com

≈ 1cm

(8)

For the human body model which is built with a sin-

gle mass point method the total ZMP errors are time-

independent due to the model simplicity (Gabbasov

et al., 2015), and its values are computed according to

equations (6):

(

∆ZMP

≈ 7cm

∆ZMP

≈ 7cm

(9)

For the 12 mass points human body model the to-

tal ZMP errors were calculated according to equa-

tions (7). The calculated values of the total ZMP er-

ror in the walking direction ∆ZMP

varies from 1 mm

to 35 mm (where the value ∆ZMP

= 35 mm corre-

sponds to the MoCap walking area of 2 m length, i.e.

±1 m from the center of MoCap scene in Fig. 2),

whereas ZMP error in lateral direction ∆ZMP

varies

in the range from 1 to 7 mm.

(

∆ZMP

≈ 3.5cm

∆ZMP

≈ 0.7cm

(10)

Moreover, the ZMP error in the walking direction

∆ZMP

strongly depends on the x-coordinate of ZMP

trajectory (i.e., on a human position relatively to the

center of Kinect-based MoCap system), which results

in the minimal total ZMP error at the center of Mo-

Cap walking area and maximal error on the bound-

aries of the MoCap capture zone. The growth of

∆ZMP

is nonlinear from MoCap capture zone center

to its boundaries. While ∆ZMP

was approximately

the same for both ZMP evaluation methods on the

boundaries of the ±1.5 m interval of the MoCap cap-

ture zone (centered in the middle of the 4.5 m walking

zone), for the MoCap capture zone of 4.5 m (which

corresponds to start and stop lines in Fig. 2) the sec-

ond ZMP evaluation method (Section 3.2) gives much

higher total ZMP error ∆ZMP

than the ﬁrst method

(Section 3.1). Therefore, to eliminate the inﬂuence of

acceleration and deceleration within the ﬁrst steps and

thus to minimize the total ZMP error we restricted the

MoCap active capture zone to ±1 m from the center

of the MoCap scene for the second method.

Figures 8 and 9 demonstrate ZMP and GCoM tra-

jectories for the single and multiple mass point meth-

ods of human body correspondingly. The total ZMP

error is shown with the red bars. The comparison of

total ZMP errors for human body models as a sin-

gle and multiple mass points (equations (9) and (10)

correspondingly) demonstrates that the multiple mass

point method is more accurate for the shortened Mo-

Cap capture zone of 2 m length and could be better

applicable to the task of human locomotion analysis

by static (GCoM) and dynamic (ZMP) stability crite-

ria of human gait balance.

Figure 8: ZMP trajectory (red curve) and the total ZMP er-

rors (red bars), calculated with a single mass point method,

and GCoM trajectory (blue curve).

Figure 9: ZMP trajectory (red curve) and the total ZMP

errors (red bars), calculated with a multiple mass points

method, and GCoM trajectory (blue curve).

5 CONCLUSION AND FUTURE

WORK

This paper focused on the analysis of human loco-

motion. The locomotion data was recorded with Mo-

Cap markerless tracking and visualization technol-

ogy, which is based on four Kinect 2 sensors and

non-real-time processing with iPi Soft software and

ZMP Trajectory from Human Body Locomotion Dynamics Evaluated by Kinect-based Motion Capture System

167

MATLAB. Human gait balance was analyzed apply-

ing static (GCOM) and dynamic (ZMP) stabilities.

Human ZMP and GCoM trajectories were calcu-

lated by two methods, which consider human body

as a simpliﬁed approximation with the models of a

single mass point and multiple mass points. Our cal-

culations demonstrated close localization of analyzed

GCoM and ZMP trajectories to the human’s footprints

and the corresponding support polygons. It means

that the human walking had static and dynamic sta-

bility, proving that the human gait was properly bal-

anced. The comparison of total ZMP errors for hu-

man body models as a single and multiple mass points

demonstrated that the later method is signiﬁcantly

more accurate for the limited MoCap walking zone of

2 m length (the maximal ZMP error was 3.5 cm along

the walking direction and 0.7 cm in lateral direction)

than the former one, and thus should be preferred for

human gait estimation. Quite signiﬁcant ZMP trajec-

tory deviations in the vicinity of footprints’ positions

arise from the limitations of MoCap system measure-

ment accuracy.

Finally, we use MoCap system and analyze human

locomotion to identify key features of human walk-

ing, collecting statistically signiﬁcant data to create

an adequate human gait mathematical model, which

could be adapted to Russian AR-601M robot simu-

lation model, yielding its statically and dynamically

stable and more natural locomotion.

ACKNOWLEDGEMENTS

This work was supported by Russian Ministry of

Education and Science, and our industrial partner

Android Technics under Scientiﬁc and Technolog-

ical Research and Development Program of Rus-

sian Federation for 2014-2020 years (research grant

RFMEFI60914X0004). Special thanks to iPi Soft

company for providing temporary access to iPi Soft

Mocap Studio.

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