This study aims to develop a force sensor system with a pressure-sensitive conductive rubber (PSCR), which shows the decrease of electrical resistance when pressure is applied. The biggest obstacle of the sensor is a poor reproducibility in the characteristic between the force and the resistance of the PSCR, which derived from a hysteresis and time variant properties. In this paper, we propose one method for recognizing a magnitude of the force to the PSCR using frequency tables. The validity of the proposed method is confirmed on the basis of experimental results.
Nowadays, force control has been more and more applied to a compliance control for robot arms as well as a feedback control of the humanoid robot hand for grasping fragile objects [
Pressure-sensitive electrically conductive rubber (PSCR) is one of the materials, the characteristics of which depend on the applied pressure. The PSCR consists of a rubber matrix where electrical conductive particles are scattered inside. When the pressure is applied, the particles are connected each other, then the electrical resistance decreases along with the pressure. The change in the resistance is detected as an electric voltage as described later. The PSCR is passive sensor so that it does not need a sophisticated amplifier. Since the PSCR is a soft rubber sheet, the form can be taken freely and it can be used even on a non-flat area. So the PSCR is so attractive for the cost effective force sensing that the application and improvement of the PSCR sensor have been performed recently [
Despite the advantages described above, the PSCR has the fault that it has a hysteresis property in the relationship between pressure and electrical resistance. Another serious problem is a poor reproducibility in measurement value. It really has made an obstacle for practical use. The idea in this article is that applied pressure is roughly recognized from the obtained time-series output data with the help of an experimentally prepared frequency table previously. The efficacy of this method is verified experimentally.
It should be described about the PSCR sensor. In the PSCR electrically conductive particles are randomly embedded in rubber matrix sheet as shown (left) in
There are two types of the PSCR depending on the materials of the conductive particles: metal or carbon. The scheme of the resistance variation is quite different in the two cases. The variation is shown in
In our experiments, the PSCR (produced by PCR Technical) was cut in square of 4.4 cm. Two sheets of Al foil were attached to the both surfaces of the PSCR as the electrodes. This was sandwiched by two Al plates for the purpose that applied pressure should be uniform over the PSCR sensor even when weight was put on it locally.
The electric circuit for the detection is shown in
V o ( t ) = R r ( t ) + R V .
To show the feature of the PSCR sensor briefly, the time responses (100-time repetition) of the output voltage Vo is shown in
We describe here the procedure of the recognition of pressure with a frequency table. At first, some variables are defined here. The origin of time is set to the time when the weight is put on the sensor. The passed time is defined to be ti (I = 1, 2, ∙∙∙, m), where each period is not necessary to be the same. The class of the observed voltage is labelled as j where the voltage is in the region between (j − 1)ΔVo and jΔVo. The weight to be distinguished is defined to be wk (k = 1, 2, ***, n). Frequency tables are prepared from the data obtained so many times with known weights in advance. The frequency table for the time ti is shown in
Then the unknown weight is put on the sensor and the time response of the output voltage is measured. From the obtained time response, the weight can be estimated using the frequency table as follows. The output voltage at ti is in the weight range of ji, then the evaluation function of Jk for the weight wk is defined as
J k : = max ( ω 1 ∗ p ( 1 , j 1 , k ) , ω 2 ∗ p ( 2 , j 2 , k ) , ⋯ , ω m ∗ p ( m , j m , k ) ) .
where ωi is the weight function. With the weight function, it can be opted which time should be emphasized for the evaluation. After the Jk for all k’s are calculated, the estimated weight of wz is obtained as
z : = arg max ( J 1 , J 2 , ⋯ , J n ) .
This method is very helpful for the case that the output voltage includes large experimental errors and that the weight is estimated roughly. The estimation is powerful especially when the measured weight is classified only to small number of discrete groups. However this can also be well applied to the case without large errors definitely.
| Class of Vo[V] | Frequency for each weight | Total | ||
|---|---|---|---|---|
| w 1 | ⋯ | w n | ||
| 0 − Δ V O | p ( i , 1 , 1 ) | ⋯ | p ( i , 1 , n ) | S ( i , 1 ) |
| Δ V O − 2 Δ V O | p ( i , 2 , 1 ) | ⋯ | p ( i , 2 , n ) | S ( i , 2 ) |
| ⋮ | ⋮ | ⋮ | ⋮ | |
| ( j − 1 ) Δ V O − j Δ V O | p ( i , j , 1 ) | p ( i , j , n ) | S ( i , n ) | |
| ⋮ | ⋮ | ⋮ | ⋮ | |
We describe here the conditions of the experiment for the recognition of the weight. We have chosen three kinds of force 4.9, 9.8 and 14.7 N that correspond to 0.5, 1.0 and 1.5 kgw, respectively. In this experiment ti is set to
t i : = 0.1 + 0.05 ∗ ( i − 1 ) , 1 < i < 7 ,
And ΔVo was 0.025 V. the weight function was that ω1 and ω2 were 0.1, ω3 and ω4 were 0.2, ω5 and ω6 were 0.3 and ω7 was 0.4. The sampling period was 0.005 s. For the preparation of the frequency tables, the Vo response was measured 100 times for each weight. The duration of the measurement was 1 s.
The time response of Vo was shown in
Using
This algorithm is shown to be able to evaluate the recognition rate for the discrete weight. This recognition algorithm can give a quantitative performance of the rubber force sensor. It is because the procedure is suitable for the time response output with large errors. This kind of system cannot be treated with any
| Class of Vo [V] | Frequency for each weight | Total | ||
|---|---|---|---|---|
| w 1 | ⋯ | w n | ||
| 0 - 0.025 | 0 | ⋯ | 0 | 0 |
| ⋮ | ⋮ | ⋮ | ⋮ | |
| 0.150 - 0.175 | 16 | 1 | 0 | 17 |
| 0.175 - 0.200 | 20 | 3 | 0 | 23 |
| 0.200 - 0.225 | 4 | 3 | 0 | 7 |
| ⋮ | ⋮ | ⋮ | ⋮ | |
| 0.900 - 0.925 | 0 | 0 | 2 | 2 |
| Magnitude of w(t) | Number of the discrimination | Recognition ratio [%] | ||
|---|---|---|---|---|
| w1 | w2 | w3 | ||
| w1 | 92 | 8 | 0 | 92 |
| w2 | 8 | 84 | 8 | 84 |
| w3 | 0 | 10 | 90 | 90 |
sophisticated control theory anyway. This can be applied to other similar systems including large errors.
The next interesting point is that the recognition rate is studied among conducting rubber sensor under different situations. Further, the parameters such as ti and weight functions are needed to be adapted for the better recognition rate. In order to challenge a complicated system with random portion largely, this kind of primitive approach is inevitable even for further research.
The application of pressure-sensitive conductive rubber to a feedback system to measure the pressure is so cost effective but has a critical problem of its poor reproducibility. In the article, the method for recognition of applied force magnitude is proposed on the basis of frequency table. It was shown that the trial of this method gave the recognition rates above 84%. This method is decently effective for recognition of the data with large errors. We expect further investigations to verify the response when the load is removed as well as the dynamic identification of the load.
This work was partially supported by a Grant-in-Aid for Scientific Research No. 16K01430 from the Ministry of Education Science, Sports, and Culture, for which the authors are grateful.
The authors declare no conflicts of interest regarding the publication of this paper.
Ohmukai, M. and Kami, Y. (2018) Recognition of Force Magnitude Applied to Pressure-Sensitive Conducting Rubber Sensors on the Basis of Frequency Table. Journal of Sensor Technology, 8, 88-95. https://doi.org/10.4236/jst.2018.84007