TA 1-3The 8th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2011)

Nov. 23-26, 2011 in Songdo ConventiA, Incheon, Korea

978-1-4577-0723-0 / 11 / $26.00 2011 IEEE

Real-time Estimation of Human’s Intended Walking Speed for

Treadmill-style Locomotion Interfaces

William Haiwei Dong1, Jianjun Meng

2 and Zhiwei Luo

3

1 Japan Society for the Promotion of Science and Kobe University, Tokyo, 102-8472, Japan

(Tel : +81-78-803-6324; E-mail: haiwei@gold.kobe-u.ac.jp) 2 School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200-240, China

(E-mail: mengjianjunxs008@sjtu.edu.cn) 3 Graduate School of System Informatics, Kobe University, Kobe, 657-8501, Japan

(E-mail: luo@gold.kobe-u.ac.jp)

Abstract - This paper addresses the problem of estimating

human’s intended walking speed. Compared with previous

researches on walking speed estimation, we predict the

walking intention before gait action. In this paper, we find

a composite force index which is significantly correlated

with the intended walking speed. We did two experiments.

One gives a conclusion that intended walking speed has

strong linear correlation with the proposed force index;

The other shows that the coefficients of the linear relation

vary small, guaranteeing the tolerance of individual

variation. Finally, we built a treadmill-style locomotion

interface. Compared with the normal cases of treadmill

control, the tested subject does not have to follow the

speed of treadmill, but can actively changes the speed of

treadmill by his (or her) feet. This locomotion interface not

only shows the validity of the proposed solution, but also

provides a promising human machine interface (HMI) for

entertainment, healthcare and rehabilitation.

Keywords – walking intention, locomotion interface,

treadmill control.

1. Introduction

Walking is one of the most common physical activities

in human’s daily life. Right now, walking does not only

imply the simple meaning of moving around, but also is

considered to be of great importance in etiology,

prevention and treatment of various diseases, such as

obesity, cardiovascular diseases, etc [1-3]. By analyzing

the walking behavior, doctor can evaluate the patient’s

health condition. In addition, for common people, walking

can produce energy balance as walking is a substantial part

of the total daily energy expenditure (EE). In all the above

activities, estimation of walking speed is required.

Actually, the estimation of walking speed is not a new

topic. In the early studies of gait, researchers used high

speed camera to calculate the walking speed [3]. In the last

few decades, as sensors (especially accelerometer and

gyroscope) become available, many researches use

optimal estimation to fuse information of acceleration and

orientation to calculate human’s walking speed. Popular

algorithms include regression method series, like Gaussian

Process-based Regression (GPR) [4], Bayesian Linear

Regression (BLR) [5], Least Squares Regression (LSR)

[6], Support Vector Regression (SVR) [7], and machine

learning series, e.g. neural network [8]. The basic scheme

is based on the periodic pattern of gait which implies

acceleration and deceleration at each step. Such pattern

provides a good target for accelerometer to recognize.

After classifying different phases of gait, data from typical

inertial sensors containing accelerometer and gyroscopes

is fused and the kinematic information is able to be

obtained. Here the optimal estimation algorithm is

essential. In addition, there are also other methods to

obtain walking speed. For example, Alberto et al. from

Philips Research Laboratories assess human ambulatory

speed by measuring near-body air flow [9]. Noma et al.

used video tracking system that tracks bright markers on

the front of shoes to measure walking speed [10].

In fact, the previous researches measure walking

behavior after action. However, it is better to estimate the

walking speed before the walking motion which we call it

intended walking speed estimation. The fact is that

human’s intention is hard to estimate. Although the brain

computer interface (BCI) is a promising method [11], until

now there are still many limitations, such as the

information bandwidth is narrow, the estimation accuracy

is not high enough, etc. Another feasible solution is to use

motion capture techniques to import the joint motion data

into the skeleton model. By solving inverse dynamics and

forward dynamics, the intended walking speed can be

predicted [12, 13]. However, such kind of solution is

complicated and time-consuming.

In this paper, we consider the intended walking speed

estimation based on the natural fact of how human’s

intention physically exerts the surrounding environment.

Our aim is making the proposed approach easy to use, to

be able to apply on a single-chip. The two considerations

constitute the stand point of this paper.

The overall idea of this paper is illustrated as follows.

As we all know, under the condition of low speed, macro

object in the world obeys Newton’s Laws of Motion, i.e.,

the motion comes from force. Taking walking for example,

there exists interaction force between foot and ground, i.e.

friction force. Here, the interaction force is the original

power to drive the walking motion which occurs before the

gait action. In this paper, we find a critical force index

which is significantly correlated with the intended walking

2011 8th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI)

speed. The experiments not only verify the linearity

mentioned but also show the coefficients of the solution

shows small variation, which guarantees tolerance of

individual variation.

As an application of intended walking speed estimation

method, we designed a treadmill-style locomotion

interface (LI) where LI is defined as traveling through a

virtual reality (VR) environment by subject’s

self-propulsion [14, 15]. Under the aid of locomotion

interface, subject can freely drive a VR environment to

move on by his or her will. Below we give the previous

researches of treadmill-style locomotion interface with

great impact. The early work was done by Noma et al. who

built a treadmill locomotion interface system ATLAS [16]

where stance duration and body position are applied in PI

control for driving the treadmill. In [17], Darken and

Carmein developed the first omni-directional treadmill to

facilitate turning. In [18], Iwata and Yoshida built another

two dimensional treadmill which employs twelve small

treadmills to form a large-belt. In [19, 20], Hollerbach et al.

designed two generations of treadmill-style locomotion

interfaces named Sarcos Treadport which imitates slope

by pushing or pulling a tether located at the back of the

subject. In this paper, we build a new treadmill-style

locomotion interface driven by human’s will. Compared

with the previous treadmill control strategies, the subject

can freely changes the speed of treadmill by his or her will.

The locomotion interface not only shows the validity of

the proposed method of intended walking speed estimation,

but also provides a promising human-machine-interface

(HMI) for entertainment, healthcare and rehabilitation.

2. Problem Formation and Settings

2.1 Coordinate System Setting First of all, let us define a standard coordinate system

for the problem. From the viewpoint of the walker, the

positive y-direction points forwards; x-direction points left

when looking in the y-direction; z-direction is defined

downwards by the right hand rule. The origin of the

coordinate system is centered at the inner corner of the

outer back roller support block of the corresponding (right

or left) half (Fig. 1).

Fig. 1. Coordinate system setting.

2.2 Apparatus We use two separate force plates to analyze the states of

human locomotion for both feet. Different from the

previous researches, we put the two force plates under the

treadmill. Specifically, the treadmill used in our research

is Bertec Treadmill TM07-B including a control unit, two

belts, three motors to adjust belt speed and inclination

degree. Each half of Bertec dual belt treadmill

incorporates an independent force measurement of six

load components: three orthogonal components of the

resultant force and three components of the resultant

moment in the same orthogonal coordinate system. All the

forces acting between the foot and the ground can be

summed to yield a single ground reaction force F and a

torque vector zT . The point of application of the ground

reaction force on the plate is the center of pressure (CP).

All the small reaction forces (1F , 2F ,

3F and 4F )

collectively exert on the surface of the plate at the CP. The

point of force application and the couple acting can be

calculated from the measured force and moment

components on each half of the treadmill (Fig. 1).

In detail, the two force plates are calibrated before hand

and the calibration matrix is obtained from the testing. The

voltage output of each channel is in a scaled form of the

load with the units of N and N ⋅ m for the forces and moments, respectively. The force and moment values are

calculated by multiplying the signal values with

corresponding scale factors.

We designed a user interface by LABVIEW (a graphic

programming software package) to send control signals to

Bertec treadmill control unit and read measurements from

force plates (Fig. 2). Specifically, the communication is

based on TCP/IP protocol where the sender’s IP address is

127.0.0.1 and the port is defined as 4000.

Fig. 2. Operation interface based on LABVIEW.

3. Walking Intention Estimation

3.1 Experiment 1: Regression Studies

The purpose of this section is to prove that human

intended walking speed linearly correlates with an

interaction force index which is defined as ,y zR−

0,

min

0

y

zt T

y z z

FF

R F

others

ξ− ≤ ≤

≥

=

(1)

where ξ is a threshold which is normally chosen as

max{ } 80%zFξ = × . T is the cycle period of one step.

We get a discrete input and output sequence

1 , ,1 2 , ,2 , ,( , ), ( , ), , ( , )y z y z n y z nV R V R V R− − −� (2)

Assumed that ,y zR

− is predicted as a function of V then

one can model this situation by

, ( , )y zR f V λ ε− = + (3)

where λ is parameter vector. The random variable ε is independent of V and on average it is equal to zero, i.e.

( ) 0E ε = . We want to find f that fits the measurement

data best and we define the loss function to measure the

quality of the fit as

, 2

( , )y z

L R f V λ ε−= − − (4)

and we minimize it over all choices of parameter vector λ

min L (5)

The solution of the above optimization problem is

( ), , ( , ),

0y zL R f V λ ε

λ

−∂=

∂ (6)

We set the treadmill speed from 0.0 m/s to 1.3 m/s with

0.1 m/s increment and search for proper model in Eq. (3).

By using Eq. (6), we obtained four types of regression

models including linear, quadratic, cubic and 4th degree

polynomial (Fig. 3).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Velocity (m/s)

Ry,z

y = - 0.13*x - 0.011

y = 0.067*x2 - 0.2*x - 0.00072

y = - 0.082*x3 + 0.19*x2 - 0.25*x + 0.0022

y = - 0.6*x4 + 1.1*x3 - 0.56*x2 - 0.097*x - 0.0021

Ryz+

Ryx-

linear

quadratic

cubic

4th degree

Fig. 3. Curve fitting of four regression models.

We find that the residual errors of the four models do

not have big difference. Hence, we choose the linear

model. Hence, intended walking speed linearly correlates

with ,y zR−

, , 0 1 intend,i , 1,2, ,y z i iR V i nλ λ ε− = + + = � (7)

where 1ε ,

2ε , � , nε are independent variables (white

noise). n is the number of observation samples. Then the

linear model parameters can be calculated as

0 , intend 1

1

ˆ ˆ

ˆ

y z

xy xx

R V

L L

λ λ

λ

− = −

=

(8)

where

intend intend,i

1

1 n

i

V Vn =

= ∑

, , ,

1

1 n

y z y z i

i

R Rn

− −

=

= ∑

( )( )intend,i intend , , ,

1

n

xy y z i y z

i

L V V R R− −

=

= − −∑

( )2

intend,i intend

1

n

xx

i

L V V=

= −∑

3.2 Experiment 2: Statistical Analysis

Next, we have to prove the linear relation is suitable for

all the human beings. Six subjects, including three male

and three female, were studied (mean ± s.d.): age: 24.17±0.75 y; body mass: 58.50±17.85 kg; body height: 168.67±11.71 cm; body mass index (BMI): 20.22±3.41 kg/m2. All the subjects gave written informed consents.

We used analysis variance methods to test the model’s

linearity for all the subjects (Table 1). The coefficient of

determination R2 is the squared value of the correlation

coefficient. It shows that more than 90% of the variation is

explained by the linear model. The regression displays

information about the variation accounted for by the linear

model. The residual denotes the difference between the

observed and model-predicted values of the dependent

variable. The regression is more than ten times larger than

the residuals, which also implies the validity of model.

The significance value of the F statistic is less than 0.05,

which means that the variation explained by the linear

model is not due to chance. All the significance values of

the t statistic is less than 0.05. Thus, the remaining

predictors are adequate in the model. Hence, the linear

model (Eq. (7)) is suitable for all individuals.

Table 1 Analysis of variance (ANOVA).

Coefficients Relevance Subject

No. 1λ 0λ R2

1 .198 .023 .951

2 .189 .006 .933

3 .183 .014 .944

4 .165 .035 .905

5 .198 .000 .967

6 .148 .015 .946

F Test t Test Subject No. F Sig. t Sig.

1 215.416 .000 -14.677 .000

2 152.858 .000 -12.364 .000

3 187.050 .000 -13.677 .000

4 104.727 .000 -10.234 .000

5 323.460 .000 -17.985 .000

6 193.564 .000 -13.913 .000

It is noted that an excellent property is that the slope of

the liner model 1λ varies in a small range. Hence, the

average slope can be approximately used for different

individuals in practical applications.

3.3 Physical Meaning of Linearity In the following part, we discuss the physical meaning

of the linearity relation. In one dynamic cycle of walking,

zF is a bell-shape signal, and yF is a sine-shape signal

(Fig. 4 (a)).

(a)

(b)

velocity

,y zR

velocity

,y zR

(c)

Fig. 4. (a) Interaction force between foot and ground in

one walking cycle. (b) The curve shape of yzR . (c) The

origin equilibrium state of low speed transfers to a new

equilibrium state of high speed.

The explanation of the curve shape is illustrated as

follows. When the foot gets in touch with the ground, zF

increases rapidly. At the same time, the foot makes a break

to adjust its speed to the velocity of ground by friction.

After break process, the foot applies a force in the inverse

direction to drive the leg to take a step, i.e., makes a

preparation for higher speed of leg in the next moment. It

is noted that, compared with break process, yF changes its

direction at this time. Until now, the foot is firmly on the

ground. Hence, zF maintains large. Finally, the body

alternates the other foot to support body and zF decreases

rapidly. According to the curve shapes of yF and zF , the

curve shape of /y zF F is a composite signal of sine-shape

signals and zero signals (Fig. 4 (b)). Without loss of

generality, the zero signals are ignored in analysis. As

,y zR− is actually the extreme value of /y zF F , the extreme

value of /y zF F in every walking circle has a statistically

linear relation with the intended walking speed. Joining all

the extreme points with a line shapes an envelope of

/y zF F . Thus, the physical meaning of linearity is that the

envelope curve has a linear relation with the intended

walking speed (Fig. 4 (c)).

4. Locomotion Interface Application

As an application of the intended walking speed

estimation, we designed a locomotion interface – an

adaptive treadmill control system. The designed system

can follow the human’s intended walking speed.

4.1 System Overview

Specifically, when one subject walks on the treadmill,

the force plate measures the forces in x, y, z directions

exerted by the subject. Based on the sensor data, the

subject’s intended walking speed is estimated and the

velocity of the treadmill belts is adjusted correspondingly.

Meanwhile, the 3D projector goes on with the walking

action (Fig. 5). Compared with previous treadmill-style

locomotion systems, there are two characteristic properties

of the system. First, we use the human’s intended walking

speed to drive the treadmill. Second, our system not only

gives natural feeling of walking, but also gives natural

sensation of vision and hearing. The 3D display based on

virtual reality and the ambient sounds of the environment

make the subject have an immersed sensation. In addition,

the layout of shops is based on a real market located in

Hokkaido Japan, which makes the whole system be much

more realistic.

Fig. 5. Experiment environment.

Ths system bolck diagram is shown in Fig. 6. The dual

force plates (placed under the treadmill) measure the force

and moment signals in x, y, z direction as xF , yF , zF ,

xM , yM , zM and output them as analog signals. After

amplifying them and doing analog-to-digital conversion

by LABVIEW data acquisition card, the digital signals are

transferred to centural processing PC. Based on the force

signals, intended walking speed is estimated to drive the

motors corresponding to the left belt and right belt. In this

system, the control plant is Bertec treadmill which is

controlled by treadmill inner controller in the inner loop

feedback. When the user walks on the treadmill, there is a

noise adding to the control signal. To drive the treadmill

by the subject’s intended walking speed, an outer loop

feedback between the intended walking speed and

treadmill inner controller was built. In this case, the force

plate is chosen as an observer measuring the interaction

force between foot and treadmill.

4.2 Control Performance

We asked subjects to test the adaptive treadmill control

system. The subjects walk on the treadmill and control the

speed of treadmill by feet for two minutes. The whole

process includes three kinds of walking behaviors,

including acceleration phase, deceleration phase, and

constant speed phase (Fig. 7).

accelertation

phase

Velocity (m/s)

deceleration

phase

Time (s)

constant speed

phase

Fig. 7. Treadmill control result.

It is a part view of three walking processes. The subject

controls the treadmill to accelerate from standing still to

0.5 m/s in the time interval [28, 34] s; decelerate from 0.4

m/s to stopping in the time interval [55, 65] s; maintain the

speed of 0.43 m/s in the time interval [15, 24] s.

5. Conclusion

This paper analyzed the relation between human

intended walking speed and foot-ground interaction force

by two experiments. Based on it, an effective method for

walking intention estimation is provided. The designed

treadmill-style locomotion interface verified the

experimental conclusion and estimation method. The

experimental method used in this paper is a valuable

example in human-robot interaction research.

Acknowledgement This work was partially supported by Japan Society for

the Promotion of Science. The authors would like to thank

Tatuo Oshiumi, Hisahito Noritake, Yusuke Taki and

Shouichi Katou for their advice and support in the

experiment.

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