1185

ADAPTIVE TREADMILL CONTROL BY HUMAN WILL*

HAIWEI DONG, ZHIWEI LUO and AKIRONI NAGANO

Graduate School of System Informatics, Kobe University,

Kobe, 657-8501, Japan

Nowadays treadmill’s control has become more and more popular in many fields, such as

athletic exercise, rehabitation training, computer game, and so on. In the previous

treadmill usage, the subject passively follows the speed of treadmill. However, in many

application cases, the treadmill control strategy by human will is very desirable. Focusing

on this problem, in this paper, by analyzing the formula of center of pressure (COP) and

simulation results, a key index which indicates the intended walking speed was found.

Based on the experiment data, a new model of intended walking speed was established,

and further calibrated by least-squares regression technology. The new treadmill control

strategy proposed in this paper was built with the intended walking speed model. The

treadmill experiment shows that our approach is able to control the treadmill velocity

smoothly, which verifies the validity.

1. Introduction

Nowadays treadmill’s application has become more and more popular in many

fields, such as athletic exercise, rehabitation training, computer game, and so on.

In the previous treadmill applications, the subject passively follows the given

speed of treadmill [1-4]. However, in many application cases, the practical

treadmill control strategy by human will is very desirable. In this paper, a new

treadmill control strategy is proposed by which the subjects control the speed of

treadmill actively. In other words, the treadmill is controlled by the subject’s

intended velocity. Specifically, when a person walks on the treadmill, the force

plate measures the forces in x, y, z directions exerted by the human body. Based

on the sensor data, we estimate the subject’s intended walking speed and adjust

the velocity of the treadmill belts.

In detail, we take a normal skeleton human body as an example to analyze

the walking features. It is found that the ratio of reaction forces y

F and z

F

(notated as ,y zR ) has linear relation with treadmill velocity V , i.e. , ( )

y zR f V= .

Hence, the linear relation f is established by least-squares regression. After

* This work was supported in part by the Japan Society for Promotion of Science under Grant No.

21240019.

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that, the treadmill velocity is controlled by 1

,( )y z

V f R−= . The experiment

shows that our approach is able to drive the treadmill to coordinate with the

intended walking speed of human body smoothly.

This paper is organized as follows. Section II illustrates the system

construction and working mechanism. Section III proposes a velocity control

strategy of the treadmill based on the skeleton model simulation. Section IV

shows that the proposed approach is able to control the treadmill velocity well.

Section VI concludes the whole paper.

2. Problem Formation

When the user walks on the treadmill, the dual force plates (placed under the

treadmill) measure the force and moment signals in x, y, z directions as x

F , yF ,

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

and doing analog-to-digital (A/D) conversion, the digital signals are transferred

to PC. Based on the force signals, walking speed of the user is estimated. Then

the estimated speed is used to drive the three motors which correspond to left

belt control, right belt control and incline control.

The system block diagram is shown in Fig.1. From the viewpoint of control

theory, the control plant is treadmill which is controlled by treadmill inner

controller in the inner loop feedback. When the user walks on the treadmill,

there are noises adding to the control signal. It is noted that our control objective

is to control the treadmill at the user’s will. Hence, we have to establish an outer

loop feedback between the user’s intended velocity intendV and the treadmill

inner controller. In this case, the force plate is chosen to be the observer by

which the reaction forces are measured. Besides of the sensor noise, we want to

establish a relation between intendV and the sensor data, i.e. recognize and identify

the transfer function ( )G s . Here we choose least-squares regression to do so.

Figure 1. System block diagram. The treadmill has an inner controller with many feedback loops to

control the speed of the belts. By a transfer function ( )G s , the desired walking speed of the user can

be obtained from the sensor data.

Sensor Noise

actualV++

++

intendV

•

•

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3. Method

3.1. Force Plate

Each force plate is calibrated individually and the calibration matrix is stored

digitally in the force plate. 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 scale factor for each channel for a gain of unity is given in the

product data sheet supplied with the transducer. The force and moment values

are calculated by multiplying the signal values with corresponding scale factors,

as given

1 1

2 2

3 3

4 4

5 5

6 6

0

0

x

y

z

x

y

z

C SF

C SF

C SF

C SM

C SM

C SM

=

(1)

where, x

F , y

F , z

F and x

M , y

M , z

M are the force and moment component in

the force transducer coordinate system, in N and N.m, respectively. 1S , 2S , 3S ,

4S , 5S and 6S are the output signals corresponding to the channels indicated by

their subscripts, in volts, divided by the respective channel gain. The diagonal

matrix composed of 1C , 2C , 3C , 4C , 5C , 6C is the calibration matrix with

units N/V for the force channels 1 2 3( , , )C C C and moment channels

4 5 6( , , )C C C [5].

Generally, the true origin of the strain gauge force plate is not at the

geometric center of the plate surface due to problems in the manufacturing

process. Furthermore, there is a pad on the force plate. After a series of

calibrations of the true origin, we assume that the true origin 'O is at (0,0, )h .

The moment measured from the plate is equal to the moment caused by F

about the true origin plus z

T as

0

0

x p x p z y

y p y x p z

z z z p y p x z

M x F y F hF

M y F hF x F

M h F T x F y F T

+ = × + = − − − − +

(2)

Eventually,

x y

p

z

M hFy

F

−= (3)

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where, p

y is the coordinate of the application point for the force on the

treadmill belt in y direction; h is the height of pad and z

T is the couple acting

on the force plate.

According to the coordinate definition in Fig.2, p

y has a direct relation

with the walking speed. A critical feature of walking speed is analyzed as

follows. p

y is the sum of two items (3) where /y z

hF F− denotes the main

dynamic process of taking a step and /x z

M F denotes the small tuning of the

CP in the foot contour. Hence, with the increase of /y z

F F∞

, the walking

speed increases, correspondingly. The same applies in reverse.

Figure 2. Coordinate system of the force plate. Four force sensors are placed at the bottom of the

force plate.

3.2. Control Strategy

According to the analysis above, a walking simulation was done by OpenSim

2.0. The skeleton model in the simulation is 72.419 kg weight which is

composed of as many as 12 parts as torso, pelvis, femur-r, tibia-r, talus-r, calcn-

r, toes-r, femur-l, tibia-l, talus-l, calcn-l and toes-l. In order to simulate the real

human model accurately, 28 muscles forces and contact forces are also added. It

is noted that, because upper limbs are not be of crucial importance, the model is

built without upper limbs for simplicity. The motion data of the model is

obtained from OpenSim by following the procedures described below [5-7]. A

subject’s motion is captured and the static data is also collected. The skeleton

model is scaled based on the marker measurements from the static data to match

the anthropometry of the subject. Then inverse dynamics is done to match the

markers on the model with the ones on the subject. Based on the skeleton model

and motion data, the reaction forces of ground are calculated. The simulation

results show that in one dynamic circle, the force z

F is a bell-shape signal, and

x

'x

'z z

y

'y

1F

2F

3F

4FF

zT

plate surface

pad surface

•

•

'P

P

h

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yF is a sine-shape signal (Fig.3 (a)). We can explain the curve shape of

yF and

zF as follows. When the foot gets in touch with the surface of treadmill,

zF

increases very rapidly. At the same time, the foot has to make a break to adjust

its speed to the velocity of the belt by friction. After break process, the foot

applies a force with inverse direction to drive the leg to take a step, i.e. make a

preparation for higher speed of leg in the next moment. It is noted that,

compared with break process, y

F changes its direction at this time. Until now,

the foot is on the treadmill all along. Hence, z

F maintains large (for a normal

person with 70 kg weight, z

F is about 700 N). Finally, the body alternates the

other foot to support body and z

F decreases very rapidly.

0 0.2 0.4 0.6 0.8 1 1.2−200

0

200

400

600

800

Fx,

Fy,

Fz (

N)

0 0.2 0.4 0.6 0.8 1 1.2−0.3

−0.2

−0.1

0

0.1

0.2

Time (s)

Ry,z

Fx

Fy

Fz

(a)

(b)

Figure 3. ,y zR . (a) Interaction forces between feet and ground. yF is a sine-shape curve and zF is a

bell-shape curve. ,y zR is a composite signal of sine-shape signals and zero signals. (b) Acceleration

phase. In the acceleration phase, the origin equilibrium state with low speed transfers to a new

equilibrium state with high speed. The same applies in the explanation of deceleration case.

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Considering the fact that when z

F is large enough, one foot is firmly on the

treadmill. We define an ratio index ,y zR as

,

0

y

z

y z z

FF

R F

others

ξ

≥=

(4)

where ξ is a threshold. In normal cases, it is chosen that max{ } 80%z

Fξ = × .

According to the curve shapes of y

F and z

F , the curve shape of ,y zR is a

composite signal of sine-shape signals and zero signals (Fig.3 (a)).

Without loss of generality, the zero signals are ignored in analysis. ,y zR

becomes a composite signal of connection of various sine-shape signals with

different magnitude. ,y zR has a direct relation with the intended walking speed.

When the user intends to speed up, ,y zR

∞ becomes large, i.e. the magnitude of

peak value and valley value becomes large. After acceleration, ,y zR returns to a

new equilibrium state (Fig.3 (b)). In other words, the envelope curve of ,y zR

determines the intended walking speed. The deceleration case can be explained

in a similar way.

To verify the above hypothesis by experiment, fist of all, define the local

peak value ,y zR

+ and local valley value ,y zR

− of ,y zR as

, ,

0

, ,0

max{ }

min{ }

y z y zt T

y z y zt T

R R

R R

+

≤ ≤

−

≤ ≤

=

= (5)

where T is the period of ,y zR . Then we can get a sequence of measurements

1 , ,1 2 , ,2 , ,( , ), ( , ), , ( , )y z y z n y z n

V R V R V R− − −

⋯ (6)

Assuming that ,y zR

− is predicted as a function of V , one can model this situation

by

, ( , )y z

R f V λ ε− = + (7)

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 zL R f V λ ε−= − − (8)

and we want to minimize it over all choices of parameter vector λ . The solution

that minimizes this loss is called the least-squares solution. To find the

approximation function, we write

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( ), , ( , ),

0y z

L R f V λ ε

λ

−∂=

∂ (9)

It is noted that, the above estimation solution is optima estimation since

( ) ( ),

| ( , ) | ( , ) ( | )

( ) ( ) ( )

y zE R V E f x V f x E V

f x E f x

λ ε λ ε

ε

− = + = +

= + = (10)

4. Experiment

In the experiment, a virtual reality (VR) shopping system was built. Besides of

treadmill control, a VR shopping street was also developed. While the subject is

walking on the treadmill at will, the VR street scene goes on with his (or her)

intended walking speed. As the projector is a stereoscopic projector, by wearing

a pair of 3D glasses, the user can have a more immersive and realistic

experience (Fig.4).

Figure 4. Experiment environment. The subject walks on the treadmill and meanwhile, looks at the

3D scene.

When the velocity of treadmill is set from 1.0 m/s to 1.6 m/s, Fig.5 shows

that y

F is a sine-shape curve and z

F is a bell-shape curve, which verifies the

simulation analysis in Section III, Part B. It is also shown that with the increase

of treadmill velocity, the magnitudes of x

F , y

F and z

F increase.

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Figure 5. Forces xF , yF , zF . With the increase of treadmill velocity (from 1.0 m/s to 1.6 m/s), the

magnitudes of the forces xF , yF , zF increase gradually.

In order to do least squares regression, we have to collect many observation

samples. In the experiment, we measure ,y zR ten times when the velocity varies

from 0.1 m/s to 1.0 m/s. By using the least-squares regression method in Section

III, we get four types of regression models as linear, quadratic, cubic and 4th

degree polynomial. The residual statistics are shown in Table I.

Table 1. Least squares regression results.

Regression Model Results Norm of

Residuals

linear , 0.13 0.011y zR V−

= − − 0.039887

quadratic 2

, 0.067 0.2 0.00072y zR V V− = − − 0.034701

cubic 3 2

, 0.08 0.19 0.25 0.0022y zR V V V− = − + − + 0.034094

4th degree polynomial 4 3 2

, 0.6 1.1 0.56 0.097 0.0021y zR V V V V− = − + − − −

0.031844

It is shown that the residual norms of the four types do not have big

difference. Hence, we choose the simplest linear regression model to use. After

the regression computation (9), the proposed velocity control law becomes very

simple as

( ),

,

( ) 0.011 / 0.13( )

( 1) 0.02 ( ) 0

y z

y z

R k othersV k

V k R k

−

−

− +=

− − =

(11)

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There are many disturbances, e.g. sensor noise, to cause computed velocity not

smooth. To overcome it, we choose a delay-line filter to overcome the problem.

The filter is described by the difference function

4

1

1( ) ( )

4 i

V k V k i=

= −∑ (12)

The smooth velocity curve can be achieved by using above filter several times.

Fig.6 (a) shows a complete dynamic walking process with acceleration motion,

deceleration motion and uniform motion, where the solid line denotes velocity

and dash line denotes y

F , respectively. Fig.6 (b) shows part views of

acceleration motion, deceleration motion and uniform motion from top to

bottom in the time interval [28,34] , [55,65] and [15,24] , respectively.

0 10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

Ve

locity (

m/s

)

Time (s)

0 10 20 30 40 50 60 70−200

−100

0

100

200

Fy (

N)

Velocity

Fy

(a)

28 29 30 31 32 33 340

0.5

1

acce

lert

atio

n

55 60 650

0.2

0.4

Ve

locity (

m/s

)

de

ce

lera

tio

n

15 16 17 18 19 20 21 22 23 240.35

0.4

0.45

0.5

Time (s)

eq

uili

briu

m

(b)

Figure 6. Experiment results. (a) The whole walking dynamic process (about one minute) with

acceleration motion, deceleration motion and uniform motion. (b) Part views of the acceleration

motion, deceleration motion and equilibrium motion are shown from top to bottom.

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5. Conclusion

This paper proposed a new adaptive control strategy for treadmill. Compared

with previous research, the novelty is that the treadmill is controlled by intended

walking speed of the subject. As the control strategy is very practical, it can

even be applied by single-chip. Our future work will make the control strategy

to be able to adjust its parameters based on measurement data automatically.

Acknowledgments

This paper received constructive suggestions from Hisahito Noritake, Yusuke

Taki and Shouichi Katou. The authors also would like to thank Haifeng Dong of

the Arizona State University USA for proofreading.

References

1. M. M. McDermott, P. Ades, J. M. Guralnik, etc, Treadmill Exercise and

Resistance Training in Patients with Peripheral Arterial Disease with and

without Intermittent Claudication: a Randomized Control Trail, J. American

Medical Association, 301, 74 (2009).

2. W. Powell, B. Stevens and M. Simmonds, Treadmill Interface for Virtual

Reality vs. Overground Walking: a Comparison of Gait in Individuals with

and without Pain, Cyberpsychology and Behavior, 12, 645 (2009).

3. W. H. Hu and K. C. Qian, Realizing a Multi-media Treadmill Fusion with

Multiple Characters and Structured Scenes, in Proc. Int. Conf. Cyberworlds,

579 (2008).

4. K. Kott and G. Deleo, Virtual Reality Gaming for Treadmill Training:

Improving Functional Ambulation in Children with Cerebral Palsy,

Cyberpsychology and Behavior, 12, 83 (2009).

5. S L Delp, F C Anderson, A S Arnold et al., OpenSim: Open-source

Software to Create and Analyze Dynamic Simulations of Movement, IEEE

Trans. Bio-medical Engineering, 54, 1940 (2007).

6. D G Thelen, F C Anderson and S L Delp, Generating Dynamic Simulations

of Movement using Computed Muscle Control, J. Biomechanics, 36, 321

(2003).

7. D G Thelen and F C Anderson, Using Computed Muscle Control to

Generate Forward Dynamic Simulations of Human Walking from

Experimental Data, J. Biomechanics, 39, 1107 (2006).

8. Instrumented Treadmill User Manual (Version 3.3), Bertec Corporation.