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A PVDF film sensor for material identification
Sensors and Actuators, A21-A23 (1990) 886-889
886
A P V D F Film Sensor for Material Identification GUOWEI GAO, Z I C H E N G W A N G and RUI GAO
Beijing Information Technology Institute, Beijing (China)
Al~tract A new sensor for material identification is proposed. This paper describes the mathematical model, design, fabrication and testing of the sensor. The mathematical model can be used to analyze the sensor output and determine the thermal properties of an unknown object. The results of mathematical analysis and testing show the theoretical effectiveness of the proposed sensor. Introduction The ability of robots to perform manipulation tasks is limited by their lack of sensory feedback [1], and many tasks will require multiple sources of sensory information [2]. It seems probable that the main form of feedback will be a combination of visual and tactile sensors providing complementary information to guide a robot's actions. Of these two sensory modes, touch has received the least attention. Most research effort devoted to tactile sensors has been concentrated on devices to measure force, torque and slip [3-5]. However humans derive useful information from the apparent temperature of objects they touch, and this has been suggested as a technique for distinguishing between different materials [2, 3, 6, 7]. A visual observation of a smooth sheet of red metal, a smooth sheet of red wood, and a smooth sheet of red plastic would not uncover any major differences between them. After touching them, however, it becomes clear that they are not the same. The materials will feel different even if their surface textures are identical. It is the difference in their thermal properties that allows us to tell them apart. The human finger's sensing abilities include more than just tactile reception. Clearly, metal feels cooler than wood and plastic. This sensation has nothing to do with the absolute temperature of the material; if they are in the same room they are indeed likely to be at the same temperature. The sensation is in response to the heat conduction properties of metal compared with wood and plastic. The finger is warm, a constant supply of blood acts as a heating source. When contact is 0924-4247/90/$3.50
made with a good thermal conductor such as a metal, heat quickly flows out of the finger. This reduces the temperature of the finger, and hence the metal feels cool. This phenomenon is explained by the second law of thermodynamics. When two materials are placed in contact with each other heat will flow from the warmer one to the cooler one until their temperatures equalize. In this paper we report on a sensor that has been constructed which can measure heat flow from a heat source into an unknown object. Using a mathematical model, the sensor output can be analyzed to determine the thermal properties of the unknown object. This information enables the robot manipulator system to discriminate between objects made of different materials and aids in recognition of unknown objects. Semor Design A schematic diagram of the sensor is shown in Fig. 1. The sensor is composed of three layers. The top layer of thermally conductive rubber forms the sensor's outer covering. The bottom layer is a film active heat source, which produces a surface temperature of about 40 °C, the exact value depending upon the ambient temperature. The inner layer is a PVDF film sensing element, which is mounted at the surface of the sensor, and records the temperature at the junction between the sensor and the material being sensed.
Cover
~ " ~ - - ~ _ _ _ . _ . . ~ Th erm a I iy I ~ conductive covering
[
Film heating electrodes
Fig. 1. Schematic diagram o f the PVDF film thermal sensor.
Mathematical Model [8] We stimulate the transient thermal response of the sensor coming into contact with an object by a one-dimensional model, assuming the width of © Elsevier Sequoia/Printed in The Netbedands
887 h
Sensor
g
T,k,
2a2U PU - T o - a t ~-~x2= 0
Object X Direction
(11)
A solution of eqn. (11) is
U(x,P) f A sh ~--~Px + B c h X / ~ x + T al
u(L,~) =v(L,t) Fig. 2. The one-dimensional model o f sensor and object. The block on the left represents the sensor. The block on the fight represents the material being sensed.
the sensor is much less than its cross section. As shown in Fig. 2, the sensor is considered to be a uniform block of material of length L, thermal conductivity kt. The temperature on the left-hand side is held fixed by a heat source at T. The material being sensed is an infinite rod, uniform conductivity k2. The entire object is initially at temperature To, which is the ambient room temperature; no thermal resistance is assumed to exist at the contact interface. The temperature, U, of the sensor in one dimension, is given by the diffusion equation
(12)
al
By the same method, we can obtain V(P, x)
V(P, x) = C exp(pl/2x/a2) + D exp(p1/2x/a2) + To P (13) Taking the Laplace transform of eqns. (2), (3), (6), (7), (8), we can obtain T U(0, P) -- ~ (14)
(15)
k, aU(L, P) _ i. aV(L, P)
ax
- ,*2
ax
U(L, P) = V(L, P)
(16)
lira V(x, p) =--T°
(17)
X--P OO
P
aU 2a2U a---t--a, ~ x 2 = 0
(1)
We now must find the solutions for A, B, C, D which satisfy boundary conditions (14), (15), (16) and (17). The solutions that work are
U(O, t) = T
(2)
A --
U(x, O) = T k,
(3)
at 2 ----
x ~ [D2 ¢xp(-2P'/Z/aDL]" B - 0
where kt is its conductance, Pt is its density, and Ca is its specific heat. The temperature, V, of a block of material in one dimension, is given by the diffusion equation 2a2V
at
-
(5)
a 2 ~X2 = 0
V(L, t) = U(L, t) k2
a V(L, t) aX
= k,
(7)
r(oo, t) = To
(8)
k2 d2 2 ---(9) p2c2 where k 2 is its conductance, P2 is its density, and c2 is its specific heat. To reduce eqn. (1) from a partial differential equation to an ordinary differential equation, we take its Laplace transform oo
a, 2
(19)
k, a2 ch x / P L exp(p'/2U/a2)A k2al al
C= D =0 where Dt =
(6)
aU(L, t) ax
(18)
nl0
(4)
ptc,
aV
T - To D, e x p ( - P ' / 2 L / a , ) P
(20) (21)
a,k~
(22)
at k2 + a2k,
ark2 - a2kl ark2 + a2k, Therefore, we can obtain D2 ffi
(23)
f--
U(x, P) ffi A s h ~ / P x + T /i
(24)
a,
Taking the inverse Laplace transform of eqn. (24), we can obtain U(x, t)
u= r-½(r-
To)D, ~ D2" n~O
oo
exp( - Pt) ~x2 dt o
which becomes
exp(-Pt) o
dtffiO
× {erfc[.(2n + I)L - x l
]
(10) _ orfor.'
L
+ I)L +
J3
(25)
888 Outp¢t V o l t a g e (V)
Temperature (oC) 1.5 ~=.
28
. . . . . . . . . . . . . . . . Time. (S) •01 • 1 1 10 tOO 10O0 lOO00
0
where erfc is the Gaussian error function, which is defined by
erfc(x) ~ 1-- ~
TJ,me [$) 3.84
Fig. 4. Thermal sensor response to 1, copper; 2, steel; 3, aluminum; 4, PCB metal surface; 5, rubber; 6, polyflon; 7, PCB back surface; 8, paper.
Fig. 3. Behavior o f the thermal sensor's governing equation. T = 4 0 °C, To = 20 °C.
x f exp( -- ~2) d~
. . . . . . . . . . . . . . . •96 1.92 2.08
fairly long, positive recognition can be accomplished more rapidly. The temperature curves are separated from each other by only one second. To successfully identify a material against a library of thermal response curves, the sensor's measurements should be repeatable. A copper block was repeatedly placed on the sensor and response curves were recorded. Figure 5 shows several of these plots. While some variation in sensor output over time is present, in general, each of the trials produces similar results. It should be noted that the material was placed on the sensor in a somewhat haphazard manner. For example, no special setup was used to ensure constant pressure from trial to trial. This should be similar to the sensor's actual operation conditions. Test results of seven materials (copper, aluminum, steel, rubber, polytlon, PCB, paper) from 130 identifications are shown in Table 1. We can identify the material by
(26)
o
A computer program has been written to determine the time evolution of the temperature profile across the sensor and object. Given the parameters T, To, kl, k2, cl, c2, Pt, P2, L and x, beginning with n = 1 and proceeding to n = 50, we can obtain the behavior of eqn. (25) as k2 is varied, as shown in Fig. 3.
Experimental Results and Discussion To measure the sensor's effectiveness in distinguishing among different objects, the following experiment was conducted. A number of objects was placed in contact with the sensor and the temperature over time response was recorded. Figure 4 shows plots of the response of the sensor after contact with the material has been made. The sensor's temperature response to copper, steel, aluminum, rubber, PCB (printed-circuitboard), polyflon and paper is shown to differ significantly enough to distinguish among them. Though the elapsed time shown on the plot is
Copper Steel
1.59 < V < 1.65 1.34 < V < 1.40
Aluminum
(27)
(V)
1.05 < V < 1.09
PCB metal surface Rubber
(V)
(28) (V)
0.95 < V < 0.99
0.78 < V < 0.82
(V)
(29) (V)
(30) (31)
TABLE 1. Test data Material
Ambient temperature
Times
(oc) Copper Steel Aluminum PCB metal surface Rubber Polyflon PCB back surface Paper
20.0 22.5 22.0 22.0 21.0 22.0 22.0 21.0
Average peak voltage
Error (V)
Response time t(s)
(v) 15 20 15 15 15 20 15 15
1.62 1.37 1.07 0.97 0.80 0.72 0.64 0.44
Voltage response
region (v) 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.12
1.13 0.97 1.03 1.02 0.82 0.74 0.82 0.58
1.59-1.65 1.34-1.40 1.05-1.09 0.95 -0.99 0.78-0.82 0.70-0.74 0.62-0.66 0.32-0.56
889
1.6.6~
-.4
thermal conductivity and the thermal sensor will be used as part of a robot sensory system to allow the robot to function autonomously in the unstructured environment found in most factories, offices and homes. In this environment the robot will need to recognize new objects. Information about materials making up an object will aid the recognition process.
(v) t a g e
•96
Time (8)
1.92 2.88
3.84.
Aclmowledgemems
Fig. 5. Thermal sensor repeatability. The curves show the sensor's response to contact with the same block of copper during 10 trials.
Polyflon 0.70 < V < 0.74 PCB back surface Paper
(V)
0.62 < V < 0.66
0.32 < V < 0.56
(V)
The authors would like to thank Professor Xingjiao Li and Professor Fuxue Zhang for their encouragement and support.
(32) (V)
(33) (34)
The correction rates of the testing results of the seven materials (copper, aluminum, steel, rubber, PCB, polyflon, paper) from 130 identifications are 100%. Conclusions
A thermal sensor has been described which is capable of measuring thermal properties of objects grasped by a robot manipulator. The mathematical model which has been developed allows the response of the sensor to be predicted. Using this model, the output can be analyzed to find the
References 1 J. M. Hollerbach, Workshop on the Design and Control of Dexterous Hands, AIM661, Massachusetts Institute of Technology, Artificial Intelligence Laboratory, Cambridge, MA, U.S.A., 1982. 2 L. D. Harmon, Int. J. Robotics Res., 1 (1982) 3-32. 3 W. D. Hillis, Int. J. Robotics Res., 1 (1982) 33-44. 4 S. Hackwood, G. Beni, L. A. Hornak, R. Wolfe and T. J. Nelson, Int. J. Robotics Res., 2 (1983) 46-50. 5 M. Ueda, K. Iwata and H. Shingu, Tactile sensors for an industrial robot to detect slip, Proc. 2nd Int. Symp. Industrial Robots, Dearborn, MI, U.S.A., 1972, Society of Manufacturing Engineers, pp. 63-76. 6 D. M. Siegel, An integrated tactile and thermal sensor, Proc. alEEE Int. Conf. Robotics and Automation, San Francbco, CA, U.S.A., 1986, pp. 1286-1291. 7 R. A. Russel, Int. J. Robotics Res., 4(1985) 35-39.
8 Guowei Gao and Zicheng Wang, A thermal sensor for material identification, Proc. SenJar/Captears 89, Paris, France, 1989.
886
A P V D F Film Sensor for Material Identification GUOWEI GAO, Z I C H E N G W A N G and RUI GAO
Beijing Information Technology Institute, Beijing (China)
Al~tract A new sensor for material identification is proposed. This paper describes the mathematical model, design, fabrication and testing of the sensor. The mathematical model can be used to analyze the sensor output and determine the thermal properties of an unknown object. The results of mathematical analysis and testing show the theoretical effectiveness of the proposed sensor. Introduction The ability of robots to perform manipulation tasks is limited by their lack of sensory feedback [1], and many tasks will require multiple sources of sensory information [2]. It seems probable that the main form of feedback will be a combination of visual and tactile sensors providing complementary information to guide a robot's actions. Of these two sensory modes, touch has received the least attention. Most research effort devoted to tactile sensors has been concentrated on devices to measure force, torque and slip [3-5]. However humans derive useful information from the apparent temperature of objects they touch, and this has been suggested as a technique for distinguishing between different materials [2, 3, 6, 7]. A visual observation of a smooth sheet of red metal, a smooth sheet of red wood, and a smooth sheet of red plastic would not uncover any major differences between them. After touching them, however, it becomes clear that they are not the same. The materials will feel different even if their surface textures are identical. It is the difference in their thermal properties that allows us to tell them apart. The human finger's sensing abilities include more than just tactile reception. Clearly, metal feels cooler than wood and plastic. This sensation has nothing to do with the absolute temperature of the material; if they are in the same room they are indeed likely to be at the same temperature. The sensation is in response to the heat conduction properties of metal compared with wood and plastic. The finger is warm, a constant supply of blood acts as a heating source. When contact is 0924-4247/90/$3.50
made with a good thermal conductor such as a metal, heat quickly flows out of the finger. This reduces the temperature of the finger, and hence the metal feels cool. This phenomenon is explained by the second law of thermodynamics. When two materials are placed in contact with each other heat will flow from the warmer one to the cooler one until their temperatures equalize. In this paper we report on a sensor that has been constructed which can measure heat flow from a heat source into an unknown object. Using a mathematical model, the sensor output can be analyzed to determine the thermal properties of the unknown object. This information enables the robot manipulator system to discriminate between objects made of different materials and aids in recognition of unknown objects. Semor Design A schematic diagram of the sensor is shown in Fig. 1. The sensor is composed of three layers. The top layer of thermally conductive rubber forms the sensor's outer covering. The bottom layer is a film active heat source, which produces a surface temperature of about 40 °C, the exact value depending upon the ambient temperature. The inner layer is a PVDF film sensing element, which is mounted at the surface of the sensor, and records the temperature at the junction between the sensor and the material being sensed.
Cover
~ " ~ - - ~ _ _ _ . _ . . ~ Th erm a I iy I ~ conductive covering
[
Film heating electrodes
Fig. 1. Schematic diagram o f the PVDF film thermal sensor.
Mathematical Model [8] We stimulate the transient thermal response of the sensor coming into contact with an object by a one-dimensional model, assuming the width of © Elsevier Sequoia/Printed in The Netbedands
887 h
Sensor
g
T,k,
2a2U PU - T o - a t ~-~x2= 0
Object X Direction
(11)
A solution of eqn. (11) is
U(x,P) f A sh ~--~Px + B c h X / ~ x + T al
u(L,~) =v(L,t) Fig. 2. The one-dimensional model o f sensor and object. The block on the left represents the sensor. The block on the fight represents the material being sensed.
the sensor is much less than its cross section. As shown in Fig. 2, the sensor is considered to be a uniform block of material of length L, thermal conductivity kt. The temperature on the left-hand side is held fixed by a heat source at T. The material being sensed is an infinite rod, uniform conductivity k2. The entire object is initially at temperature To, which is the ambient room temperature; no thermal resistance is assumed to exist at the contact interface. The temperature, U, of the sensor in one dimension, is given by the diffusion equation
(12)
al
By the same method, we can obtain V(P, x)
V(P, x) = C exp(pl/2x/a2) + D exp(p1/2x/a2) + To P (13) Taking the Laplace transform of eqns. (2), (3), (6), (7), (8), we can obtain T U(0, P) -- ~ (14)
(15)
k, aU(L, P) _ i. aV(L, P)
ax
- ,*2
ax
U(L, P) = V(L, P)
(16)
lira V(x, p) =--T°
(17)
X--P OO
P
aU 2a2U a---t--a, ~ x 2 = 0
(1)
We now must find the solutions for A, B, C, D which satisfy boundary conditions (14), (15), (16) and (17). The solutions that work are
U(O, t) = T
(2)
A --
U(x, O) = T k,
(3)
at 2 ----
x ~ [D2 ¢xp(-2P'/Z/aDL]" B - 0
where kt is its conductance, Pt is its density, and Ca is its specific heat. The temperature, V, of a block of material in one dimension, is given by the diffusion equation 2a2V
at
-
(5)
a 2 ~X2 = 0
V(L, t) = U(L, t) k2
a V(L, t) aX
= k,
(7)
r(oo, t) = To
(8)
k2 d2 2 ---(9) p2c2 where k 2 is its conductance, P2 is its density, and c2 is its specific heat. To reduce eqn. (1) from a partial differential equation to an ordinary differential equation, we take its Laplace transform oo
a, 2
(19)
k, a2 ch x / P L exp(p'/2U/a2)A k2al al
C= D =0 where Dt =
(6)
aU(L, t) ax
(18)
nl0
(4)
ptc,
aV
T - To D, e x p ( - P ' / 2 L / a , ) P
(20) (21)
a,k~
(22)
at k2 + a2k,
ark2 - a2kl ark2 + a2k, Therefore, we can obtain D2 ffi
(23)
f--
U(x, P) ffi A s h ~ / P x + T /i
(24)
a,
Taking the inverse Laplace transform of eqn. (24), we can obtain U(x, t)
u= r-½(r-
To)D, ~ D2" n~O
oo
exp( - Pt) ~x2 dt o
which becomes
exp(-Pt) o
dtffiO
× {erfc[.(2n + I)L - x l
]
(10) _ orfor.'
L
+ I)L +
J3
(25)
888 Outp¢t V o l t a g e (V)
Temperature (oC) 1.5 ~=.
28
. . . . . . . . . . . . . . . . Time. (S) •01 • 1 1 10 tOO 10O0 lOO00
0
where erfc is the Gaussian error function, which is defined by
erfc(x) ~ 1-- ~
TJ,me [$) 3.84
Fig. 4. Thermal sensor response to 1, copper; 2, steel; 3, aluminum; 4, PCB metal surface; 5, rubber; 6, polyflon; 7, PCB back surface; 8, paper.
Fig. 3. Behavior o f the thermal sensor's governing equation. T = 4 0 °C, To = 20 °C.
x f exp( -- ~2) d~
. . . . . . . . . . . . . . . •96 1.92 2.08
fairly long, positive recognition can be accomplished more rapidly. The temperature curves are separated from each other by only one second. To successfully identify a material against a library of thermal response curves, the sensor's measurements should be repeatable. A copper block was repeatedly placed on the sensor and response curves were recorded. Figure 5 shows several of these plots. While some variation in sensor output over time is present, in general, each of the trials produces similar results. It should be noted that the material was placed on the sensor in a somewhat haphazard manner. For example, no special setup was used to ensure constant pressure from trial to trial. This should be similar to the sensor's actual operation conditions. Test results of seven materials (copper, aluminum, steel, rubber, polytlon, PCB, paper) from 130 identifications are shown in Table 1. We can identify the material by
(26)
o
A computer program has been written to determine the time evolution of the temperature profile across the sensor and object. Given the parameters T, To, kl, k2, cl, c2, Pt, P2, L and x, beginning with n = 1 and proceeding to n = 50, we can obtain the behavior of eqn. (25) as k2 is varied, as shown in Fig. 3.
Experimental Results and Discussion To measure the sensor's effectiveness in distinguishing among different objects, the following experiment was conducted. A number of objects was placed in contact with the sensor and the temperature over time response was recorded. Figure 4 shows plots of the response of the sensor after contact with the material has been made. The sensor's temperature response to copper, steel, aluminum, rubber, PCB (printed-circuitboard), polyflon and paper is shown to differ significantly enough to distinguish among them. Though the elapsed time shown on the plot is
Copper Steel
1.59 < V < 1.65 1.34 < V < 1.40
Aluminum
(27)
(V)
1.05 < V < 1.09
PCB metal surface Rubber
(V)
(28) (V)
0.95 < V < 0.99
0.78 < V < 0.82
(V)
(29) (V)
(30) (31)
TABLE 1. Test data Material
Ambient temperature
Times
(oc) Copper Steel Aluminum PCB metal surface Rubber Polyflon PCB back surface Paper
20.0 22.5 22.0 22.0 21.0 22.0 22.0 21.0
Average peak voltage
Error (V)
Response time t(s)
(v) 15 20 15 15 15 20 15 15
1.62 1.37 1.07 0.97 0.80 0.72 0.64 0.44
Voltage response
region (v) 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.12
1.13 0.97 1.03 1.02 0.82 0.74 0.82 0.58
1.59-1.65 1.34-1.40 1.05-1.09 0.95 -0.99 0.78-0.82 0.70-0.74 0.62-0.66 0.32-0.56
889
1.6.6~
-.4
thermal conductivity and the thermal sensor will be used as part of a robot sensory system to allow the robot to function autonomously in the unstructured environment found in most factories, offices and homes. In this environment the robot will need to recognize new objects. Information about materials making up an object will aid the recognition process.
(v) t a g e
•96
Time (8)
1.92 2.88
3.84.
Aclmowledgemems
Fig. 5. Thermal sensor repeatability. The curves show the sensor's response to contact with the same block of copper during 10 trials.
Polyflon 0.70 < V < 0.74 PCB back surface Paper
(V)
0.62 < V < 0.66
0.32 < V < 0.56
(V)
The authors would like to thank Professor Xingjiao Li and Professor Fuxue Zhang for their encouragement and support.
(32) (V)
(33) (34)
The correction rates of the testing results of the seven materials (copper, aluminum, steel, rubber, PCB, polyflon, paper) from 130 identifications are 100%. Conclusions
A thermal sensor has been described which is capable of measuring thermal properties of objects grasped by a robot manipulator. The mathematical model which has been developed allows the response of the sensor to be predicted. Using this model, the output can be analyzed to find the
References 1 J. M. Hollerbach, Workshop on the Design and Control of Dexterous Hands, AIM661, Massachusetts Institute of Technology, Artificial Intelligence Laboratory, Cambridge, MA, U.S.A., 1982. 2 L. D. Harmon, Int. J. Robotics Res., 1 (1982) 3-32. 3 W. D. Hillis, Int. J. Robotics Res., 1 (1982) 33-44. 4 S. Hackwood, G. Beni, L. A. Hornak, R. Wolfe and T. J. Nelson, Int. J. Robotics Res., 2 (1983) 46-50. 5 M. Ueda, K. Iwata and H. Shingu, Tactile sensors for an industrial robot to detect slip, Proc. 2nd Int. Symp. Industrial Robots, Dearborn, MI, U.S.A., 1972, Society of Manufacturing Engineers, pp. 63-76. 6 D. M. Siegel, An integrated tactile and thermal sensor, Proc. alEEE Int. Conf. Robotics and Automation, San Francbco, CA, U.S.A., 1986, pp. 1286-1291. 7 R. A. Russel, Int. J. Robotics Res., 4(1985) 35-39.
8 Guowei Gao and Zicheng Wang, A thermal sensor for material identification, Proc. SenJar/Captears 89, Paris, France, 1989.