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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.
1186
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
•
•
1187
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)
1188
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
1189
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.
1190
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
1191
( ), , ( , ),
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.
1192
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)
1193
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.
1194
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.
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