Massage Health Benefit

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Massaging Human Feet by a Redundant Manipulator Equipped with Tactile
Sensor
Article · July 2010
DOI: 10.1109/AIM.2010.5695843
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University of Macau
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2. Massaging Human Feet by a Redundant Manipulator Equipped with a
Tactile Sensor
Jingguo Wang and Yangmin Li*, IEEE Senior Member
Abstract— Reflexology is a kind of assisting physical care
through massaging or applying pressure to parts of the feet
where will reflect an image of the human body in order to
improve general health of the human. Based on this principle,
we propose a new application of 7-DOF(degree of freedom)
redundant manipulator to do the massaging work for human
feet with the tactile sensor equipped to the end-effector. To
facilitate the flexible and dexterous manipulation of redundant
manipulator, the hybrid impedance control is adopted and
extended to include the null space motion, not only to generate a
desired motion of the end-effector, but also manage the contact
force between the end-effector and the human feet. In order
to improve the safety and comfortability, the reactive forces
of the tactile sensor cells are monitored and recorded. A real
massaging experiment is carried out on the human feet and the
results demonstrate the effectiveness of the proposed control
system.
Index Terms— Reflexology, foot massage, impedance control,
redundant manipulator
I. INTRODUCTION
In recent years, the development of robots for home
services and human medical care attracts a lot of research
attentions. A massage robot with redundant DOF design
will be a wise choice for such applications required high
dexterous manipulation tasks.
Reflexology, having a very long history in China, is
pressure massage to the feet or hands in order to stimulate
the reflex points and bring about a balance of the eight bodily
systems in order for the body to work together in harmony
and unison and thus creating a feeling of well-being and
optimum health[1]. The human body is completely reflected
in the feet in a three-dimensional form, and a point on the
foot which maps to an area on the body is called a reflex[2]
as shown in Fig.1. The benefits of reflexology will be the
reduction of stress, relaxation, pain reduction, amelioration
of symptoms for health concerns, rejuvenation of tired feet,
improvement in blood flow, etc.
Although there are some kinds of commercial products
available for feet relaxation, they can only do the simple
massaging job due to their limited functions and they cannot
locate accurately on the feet according to the reflexology or
get the feedback of contact forces. In this research, we apply
the redundant manipulator with the tactile sensor equipped
end-effector to do the interaction with human feet, not only
This work was supported by Macao Science and Technology Develop-
ment Fund under Grant no. 016/2008/A1 and the Research Committee of
University of Macau under grant no. UL016/08-Y2/EME/LYM01/FST.
The authors are with Department of Electromechanical Engineering,
Faculty of Science and Technology, University of Macau, Av. Padre Tomás
Pereira, Taipa, Macao S.A.R., P. R. China, ∗Corresponding author: ,
YMLi@umac.mo
for learning and operating of massaging techniques by a
robot, but also for studying on the relationship between the
massaging on a zone of feet and the physiological reaction
in the human body.
Some related works can be found on studying the in-
teractions with human body through massaging, which are
highlighted in the follows. A controlled interaction with the
environment can be sought by imposing a suitable dynamic
behavior or impedance between contact force and manip-
ulator end-effector position[3]-[5]. The work[6] proposes a
novel identification technique of constraint condition that the
environment imposes on the robot’s end-effector, based on
position and force sensing during arbitrary manipulation. A
kind of relaxation system has been developed in[7], which
can change the operation mode and intensity of the massage
seat according to the user current condition and his/her
requirement, and the relationship between massage intensity
and heart rate variability is identified. The work[8] proposes
an intelligent massage control system by using multi-fingered
robot hand with hybrid impedance control, which is able
to create the movement and the force of robot to imitate
the humans massage. A PUMA 562 robot is employed to
perform the massage task through a properly controlled end-
effector following the desired trajectories [9].
tactile sensor sensor controller
redundant manipulator
human foot
feet reflexology
Fig. 1. The system setup of massaging based on reflexology
In this paper, a redundant manipulator with tactile sensor
equipped end-effector is applied to massage the human feet
as shown in Fig. 1. The remaining parts of the paper are
organized as follows: In section 2, the reflex properties are
analyzed. In section 3, the system modeling is given out with
the introduction of tactile sensor and modeling of human
skin. In section 4, the impedance control is extended to con-
trol both the main task and null space motion. Simulations
2010 IEEE/ASME International Conference on
Advanced Intelligent Mechatronics
Montréal, Canada, July 6-9, 2010
978-1-4244-8030-2/10/$26.00 ©2010 IEEE 7

3. and experiments are made and several subjects are discussed
in section 5. The concluding remarks and future works are
obtained in the last section.
II. THE ANALYSIS OF REFLEX PROPERTIES
As the reflexology theory indicates, practitioners believe
that the foot is divided into a number of reflex zones
corresponding to many parts of the body, and the practice
of massaging or applying pressure to parts of the feet will
produce a beneficial effect on corresponding parts of the
body, such as lung, shoulder, pancreas, kidneys and so on.
Pressure applied to the feet generates a signal through the
peripheral nervous system. From there it enters the central
nervous system where it is processed in various parts of the
brain. It is then relayed to the internal organs to allocate the
necessary adjustments in fuel and oxygen. Finally a response
is generated that is sent on to the motoric system. This
message is fed forward to adjust the body’s tone or overall
tension level[1].
The massaging gestures of practitioners always involve the
pressing, kneading, rubbing or tapping. In this paper, the
action of pressing will be performed by a robotic arm with
a series of forces exerted.
Massaging the feet reflexology by the robotic arm, will not
only save the labor to do repeated work, but also guarantee
the steady and standard practice, which will certainly be
helpful to improve the quality of massaging work.
Manipulator
foot
k
K
k
D
m
M
End-effector
Tactile Sensor
skin
m
K
m
D
m
M
Impedance Control
End-effector
PC
Fig. 2. System modeling and human skin model
III. MODELING OF THE SYSTEM AND SKIN
It is very difficult to determine skin properties and to
model its behavior, since human skin is a non-homogeneous,
anisotropic, non-linear viscoelastic material whose properties
also vary with age and individual, which is a very complex
biological structure to study. Therefore in this paper, the
variances of skin properties are not considered and we
consider only different kinds of skin surfaces and different
reflex points in the experiments.
A. System modeling
The massaging action needs both the position control and
the orientation control, therefore a lower-DOF manipulator is
not sufficient. The 7-DOF redundant manipulator is applied
to massage the human feet as the setup of system shown in
Fig. 2. The tactile sensor is installed at the tip of the end-
effector in order to get the pressure of contact points. The
tactile sensor is chosen as the module type of DSA 9210 with
the shell-like shape, having a size of 50mm×25mm, which
provides a spatial resolution of 3.4mm with 70 sensor cells.
The working principle of the tactile sensors depends on an
interface effect between metal electrodes and a conductive
polymer covering the sensing electrodes, and the resistance
between a common electrode and a sensor cell electrode
is a function of the applied load changing with time[10].
The output voltage of a resistive sensor cell in the electrical
circuit can be detected on real-time, and the pressure on it
will be obtained from the transducer characteristics. Then the
forces exerted on the sensor cell can be achieved easily by
transforming the sensor pressure.
B. Three contact types
In general, based on the shape of human feet, three types
of contact can be divided considering different surfaces as
convex, flat and concave surfaces as shown in Fig. 3(a), Fig.
3(c) and Fig. 3(e) respectively. The experiments are made
on three different parts of feet to get the performances of
tactile sensor. The corresponding pressures measured on the
contacted tactile sensor cells are shown in Fig. 3(b), Fig. 3(d)
and Fig. 3(f) respectively.
Comparing among the experiment results, it is easily found
that the reactive forces of the sensor cells are different
although the same force at the end of the end-effector
is exerted. The biggest reactive pressures of the contacted
sensor cells appear in the convex type as shown in Fig. 3(b),
but the concave type has relatively the smallest pressures of
contacted sensor cells in three contact types as shown in Fig.
3(f), since it has more contact areas than others. As expected,
the flat type arrives at a compromise.
C. Derivation of human skin elasticity
Skin can be divided into two separate layers, the epidermis
and dermis, and the studies show that the dermis is primarily
made of collagen, elastin and reticulin fibers, which all
contribute to the mechanical behavior of skin[11], though the
epidermis is stiffer than the dermis. In a soft environment,
the human feet skin is modeled as the mass-spring-damper
system in the control scheme and the contact model between
the end-effector with the tactile sensor equipped and the
human feet skin is built up as shown in Fig. 2, where Mm is
the inertia of the end-effector including the tactile sensor, Kk
and Dk are skin elasticity and damping coefficients while Km
and Dm are stiffness and dumping parameters of impedance
control.
In the simplified model, the reaction force Fe can be
expressed as
Fe = −Dkẋu −Kk(xu −xi) (1)
8

4. Tactile Sensor
Human Skin
(a) Convex Surface
0
10
20
30
−60
−40
−20
0
0
10
20
30
40
50
60
70
80
90
y
x
Pressure(kPa)
0
10
20
30
40
50
60
70
80
(b) Convex Surface Pres-
sure
Tactile Sensor
Human Skin
(c) Flat Surface
0
5
10
15
20
25
−60
−40
−20
0
0
20
40
60
80
100
y
x
Pressure(kPa)
0
10
20
30
40
50
60
70
80
(d) Flat Surface Pressure
Tactile Sensor
Human Skin
(e) Concave Surface
0
5
10
15
20
25
−60
−40
−20
0
0
10
20
30
40
50
y
x
Pressure(kPa)
0
5
10
15
20
25
30
35
40
45
(f) Concave Surface Pres-
sure
Fig. 3. Three contact models of human skin surface
where Fe is the external force in the dynamic model of
the massage motion and it can be obtained easily from the
impedance control discussed in the next section. xi is a initial
position where Fe becomes zero.
IV. IMPEDANCE CONTROL OF REDUNDANT
MANIPULATOR
Impedance control is an unified approach which can deal
with both free and contact motions without any switching
mechanism or selection of controlled subspaces[3][12] and
it is suitable for those tasks where contact forces must
be kept small while accurate regulation of forces is not
required. With generalized impedance control, the position
and force tracking accuracy of manipulator’s end-effector
can be balanced by properly adjusting impedance parame-
ters(stiffness and damping matrices) as a result of unexpected
interactions with the environment. The hybrid impedance
control, an unified approach for motion and force control,
is developed and then extended to redundant manipulator
systems, constructing the end-effector equations of motion
and describing their behavior with respect to joint forces[6].
A. Impedance control
The dynamics equation of a robot manipulator in the joint
space can be written as
M(q)q̈+C(q,q̇)q̇+G(q) = τ −JT
Fe (2)
where M(q) ∈ Rn×n is a symmetric and positive definite joint
inertia matrix, C(q,q̇)q̇ ∈ Rn is the Centripetal and Coriolis
force, G(q) ∈ Rn is the gravity force, τ is the joint torque
generated by the actuator, J is the jacobian matrix and Fe ∈
Rm is the contact force on the tip from the environment.
The desired impedance of the manipulator has the follow-
ing form:
Mdëp +Ddėp +Kdep = αFe (3)
where ep = xd − xu, Md, Dd and Kd ∈ Rm×m
are positive-
definite matrices representing inertia, damping and stiffness
respectively, and α is a force scaling matrix[14].
It can be easily known from the kinematics equation, ẍ =
Jq̈+ ˙
Jq̇, then combining it with (2) and (3) together, so the
required input joint torque can be derived with the pseudo
kinetic energy matrix Λ [JM−1JT ]−1 ∈ Rm×m as follows:
τ = JT
Λ[(ẍd − ˙
Jq̇)+M−1
d (Ddėp +Kdep −αFe)]
+C(q,q̇)q̇ +G(q)+JT
Fe (4)
Here M−1
d = JM−1JT will have some advantages[12], and
the generalized impedance control law can be rewritten as
τ = JT
[Λ(ẍd − ˙
Jq̇)+(Ddėp +Kdep +(In −α)Fe)]
+C(q,q̇)q̇+G(q) (5)
B. Impedance control for massaging manipulator
For a kinematically redundant robot manipulator, if ignor-
ing the null space, many of the redundancy advantages will
be lost. Therefore the null space joint torque will be added to
the impedance control law to control the null space motion.
1) Redundancy Resolution: Considering a n-DOF serial
manipulator operating in a m-dimensional task space (m
n), a nonempty null space N(J) exists and the number
of redundant DOFs is r = n − m. Let N1(q), N2(q), ···,
Nr(q) be a set of smooth and linearly dependant vectors in
the null space of N(J) making up of the matrix N(q) =
N1(q) ··· Nr(q)
, and there will always be the rela-
tionship,
J(q)N(q) = 0 (6)
The general inverse solution can be written as
q̇ = q̇p +q̇h = J†
(q)ẋ+(I −J†
(q)J(q))q̇0 (7)
where J† is the inertia-weighted pseudoinverse, q̇p is the
particular solution and q̇h is the homogeneous solution to
the problem (Jq̇ = 0) in the null space with another form of
q̇h = N(q)ẋN.
Corresponding with two kinds of kinematic solutions, the
kinematics of extended task space can be formulated by the
primary task and secondary task as ẋE =
ẋT ẋT
N
. Since
the vector space xN is not available, the velocity control
of null space motion[16] is the substitute and it has the
following form as: ẋN = (NT MN)−1NT Mq̇ JN(q)q̇.
Then the extended task space kinematics can be expressed
as ẋE =
ẋ
0
= JE(q)q̇, JE =
J
JN
is the extended
Jacobian by augmenting the null space into the bottom of
the Jacobian J. JN stands for the portion of the Jacobian
subjected to the n−m constraint equations f(q) = 0 and the
detailed derivation of JN can be found in [13].
9

5. 2) Extended Impedance Control: As the extended kine-
matics is discussed above in terms of the task space and null
space, the extended impedance control law has the form
τE = τP +τN +C(q,q̇)q̇+G(q) (8)
whereτP and τN are the vectors of task space and null
space joint torques respectively, C represents the coriolis and
centripetal matrix and G denotes the gravity force vector.
The extended impedance control law has the similar form
as the generalized impedance control law (5), and it can be
decomposed into the task space joint torque τP and the null
space torque τN,
τp = JT
[Λ(ẍd − ˙
Jq̇)+(Ddėp +Kdep +(In −α)Fe)] (9)
τN = JT
N {ΛN(ẍNd − ˙
JNq̇)+DNėN} (10)
where ΛN = NT
MN, ėN = ẋNd
− ẋN and DN is the damper
coefficient.
The block diagram of the extended impedance controller is
shown in Fig. 4, where the inner loop is an inverse dynamics
control and the outer loop is an additional control to achieve
the tracking goals.
C. Stability analysis of the system
The derivative of the null space velocity can be written as
VNe = ėN = ẋNd
−JN(q)q̇ (11)
where ẋNd
denotes the desired null space velocity.
Further, differentiating (11), the null space error accelera-
tion is
V̇Ne = ẍNd
−JN(q)q̈− ˙
JN(q)q̇ (12)
Combining (2), (8) and (12) together, by a simplification
of JN(q)M−1JT Λ = 0, the tracking error of null space accel-
eration can be rewritten as
V̇Ne = ẍNd
−JN(q)M−1
τN − ˙
JN(q)q̇ (13)
Substituting the null space control torque (10) into(13),
yields
V̇Ne = −DNėN = −DNVNe (14)
Here a Lyapunov function is defined as
ν =
1
2
VT
NeVNe (15)
6
6
6
6
6
6
6
d
K
)
(q
/
)
(q
J
)
(q
f
)
(q
JT
x
x
q
JN
)
(q
JN
N
D
6 6
G
C
x
q
e
F
W
d
x
x
d
x
x
x
d
x
x
Nd
x
x
x
Nd
x
x
N
x
N
W
p
W q
x
x
x
)
(q
JT
N
)
(q
N
/
x
x
q
J
ARM
D
I
Hu
ma
n
d
D
loop
Inner _
loop
Outer_
Fig. 4. Block diagram of extended impedance control
Then the derivative of the function is
ν̇ = VT
NeV̇Ne = −VT
NeDNVNe (16)
With the existence of null space N(J) and null space
Jacobian matrix J(N) and the diagonal matrix DN with
positive terms, the Lyapunov function ν is positive definite
and its derivative ν̇ is negative definite. Therefore the null
space velocity error converges to zero and the extended
impedance controller stabilizes the null space motion.
D. Optimization of null space motion
In addition to the primary task, the secondary task is
to minimize a desired cost function. Since the null space
has many forms, a proper choice of N(J) will achieve the
avoidance of rank deficient matrix.
The additional task is represented as
Z(q) = N(q)T
Φ(q) (17)
Therefore, the Jacobian matrix of null space can be written
as JN = ∂Zi(q)
∂qi
= ∂N(q)T Φ(q)
∂q . Φ(q) is a scalar objective func-
tion of the joint variables and Φ(q) is the vector function
representing the gradient of Φ. Here the kinematic constraint
function considered is the joint limit avoidance[15].
V. SIMULATIONS AND EXPERIMENTS
A. Simulations
Since reflexology involves the practice of massaging,
squeezing, or pushing on parts of the feet, we try to follow
the physician techniques in the simulations and experiments
and a desired trajectory is designed, which is to simulate
a kind of massaging trajectory on the feet, crossing several
reflex zones and points, such as lung, shoulder, solar plexus,
pancreas, adrenal, kidneys, small intestine and sigmoid colon
as shown in Fig. 5.
Fig. 5. Simulated trajectory
The experiment is set up with the Powercube modular
manipulator and the tactile sensor system(both sensor and
controller) installed on the tip of the end-effector as shown
in Fig. 1. A massaging bed is made mainly to place the feet
and the V-shape configuration will make people feel more
comfortable. The surface of tactile sensor contacts with the
10

6. 0 1 2 3 4 5 6
−100
−80
−60
−40
−20
0
20
40
60
time (s)
rotating
angles
of
seven
joints
q1
q2
q3
q4
q5
q6
q7
Fig. 6. The changes of seven joint variables in the simulation
human skin and the voltage feedbacks of sensor cells can be
monitored by the DSA-Explorer software.
The stiffness matrix is Kd = diag
500 500 500
,
the damping matrices are Dd = diag
50 50 50
and
DN = diag
40
, and the force scaling matrix is α =
diag
0.2 0.2 0.2
. The estimated parameters of human
skin are chosen with the reference of hard skin position[8],
Kk = 1327 and DK = 68. The desired pressing force on the
feet is chosen as Fe = 30N. More information can be found
in our related work[15], such as the initial parameters, the
kinematics modeling of redundant manipulator, the inertial
and Coriolis matrices, the choice of null space and so on.
The simulation results of joints variables are given out in
Fig. 6, which are listed one by one for that there are big
differences among different joints values and it is hard to
view the change if all seven joints variables are arranged in
one figure.
B. Experiments
The real experiment is made to follow the trajectory
similar as a kind of massaging work and the texel-voltages
changes of the contacted sensor cells are recorded through
the MATLAB OPC sever, which are then transformed to the
sensor pressures and contact forces. The force exerted on
each sensor cell will be added together to get the value of
the contact force between the sensor-equipped end-effector
and the human feet. A series of experimental screen shots of
massaging human foot are shown in Fig. 7.
Then the contact force between the end-effector and the
human feet can be obtained as shown in Fig. 8. It can be
easily found that the reactive force has smaller value in the
middle part mainly because of the loose contact in the central
part of human feet with complex shape, which generates
less contact than the beginning and end parts. The reactive
(a) t=0.32s (b) t=1.12s (c) t=1.36s
(d) t=2.00s (e) t=2.16s (f) t=2.36s
(g) t=2.56s (h) t=3.36s (i) t=3.56s
(j) t=4.12s (k) t=4.32s (l) t=4.48s
(m) t=5.12s (n) t=5.46s (o) t=6.00s
Fig. 7. Sequential snapshots of massaging the human foot by the
manipulator
forces obtained in the real experiment is quite different from
that of the simulation, partly because of many unknown and
unexpected factors in the experiments and partly because of
the estimated human skin parameters in the simulation.
C. Discussions
Although there are some ways to determine the human
skin properties[6], it will vary with many factors, like the
locations, the age and different peoples. The skin parameters
chosen lead to the differences between the simulation and
experimental results. So a lot of experiments should be made
on the human feet to determine the feet skin properties with
the aim of better massaging.
Besides, the unavoidable moving of human feet during the
operation will produce some influences on the measurement
of contact force. Also the skin reaction excited by the tactile
sensor will more or less generate some errors.
Another factor should not be neglected is the trajectory,
although it is designed to be close to the shape of human
feet, there’s still the difference between them because the
human feet is hard to model and it has a complex shape.
A challenge of making the sensor-tip follow the surface of
11

7. 0 1 2 3 4 5 6
−40
−35
−30
−25
−20
−15
−10
−5
0
time (s)
Pressing
force
of
feet
skin
in
the
real
experiment
Fig. 8. The reactive force of feet skin in the simulation
the feet will be beneficial to the safety and comfortability of
massaging.
Finally, the forces of all contacted sensor cells are added
together to be seen equivalent to the reaction force at
the contact region, however, since the tactile sensor has a
shell-like shape, the force components generated in other
directions will make it more or less inaccurate in the normal
direction.
VI. CONCLUSIONS AND FUTURE WORKS
A. Conclusions
Based on reflexology, the paper presents a way of mas-
saging human feet by a 7-DOF redundant manipulator with
tactile sensor installed at the end-effector. Since the hu-
man skin is very complicated and difficult to determine its
properties, it is simply modeled as the mass-spring-damper
system. Impedance control is extended to manage both the
task motion and the null space of the redundant manipulator.
Several key subjects are discussed, such as the contact
types, human skin elasticity and so on. Simulations and
real experiments are made respectively to track the desired
massaging trajectory and the results are compared while
several factors influencing the experimental performances are
considered and analyzed carefully.
B. Future Works
In the next step, the force sensor will be combined in
the system and the forces measured can be used to manage
the motion control more easily and accurately. Moreover,
hybrid sensors of tactile sensor and force senor will provide
more methods to implement complex massaging techniques
and guarantee the operating safety and comfortability. Other
control methods or mobile manipulator will also be used
and compared with current one[17][18], while parameters
identifications will be performed to identify accurate system
parameters[19].
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