## 4 Results and Discussion
### Demonstration of Texture Discrimination
Power Spectral Density (PSD) represents the contact energy. As the module moved horizontally while in contact with the texture sample, the magnitude (energy) of the detected signal from the sensor changed according to regular or irregular bumps on the surface of the sample. As such, this physical quantity is a good representation of the roughness of the surface of the object [14]. The first, second, and third PSDs were obtained by converting time domain signals to the frequency domain through Fast Fourier Transforms (FFT), categorizing signals into the low frequency domain (0-1 Hz, 1 st PSD), medium frequency domain (1-10 Hz, 2 nd PSD), high frequency domain (10-20 Hz, 3 rd  
Figure 7: Mean and standard deviation data derived from 10 repeated measurements of 16 tactile samples for each indicator. (**a**) Hardness & Friction coefficient. (**b**) Roughness. (**c**) Thermal conductivity. PSD), very high frequency domain (20-250 Hz, 4 th PSD), and calculating the area of each frequency domain. The measured PSD values (1 st, 2 nd and 3 rd PSDs) showed differences significant enough to discriminate samples as shown in Figure 7b, but the 4 th PSD value did not exhibit a meaningful difference in our experiments; therefore, we did not use the 4 th PSD value as an indicator. Thermal conductivity (\(\theta\)) is an inherent property of an object and is important in discriminating between textures of objects. The built-in heater was used to maintain the temperature of the module above the ambient temperature (at approximately 30 \({}^{\circ}\)C). As the module maintained contact (static contact) for a certain period of time (15 s in our experiments) with the texture sample, which had achieved equilibrium with the ambient temperature (20-23 \({}^{\circ}\)C), heat began to flow between the module and the sample. The resulting change in temperature of the module could be used to calculate a value representative of the thermal conductivity of the sample. However, since the degree of temperature change may vary depending on the ambient temperature, the measurements were normalized using the difference between the initial temperatures of the module and sample. The temperature of the module was calculated using a linear equation obtained through the linear fitting of the temperature sensing capabilities of the temperature sensor. The equation to estimate the thermal conductivity of the sample can be expressed as follows:  
\[\theta=\frac{T_{\text{c}}-T_{\text{i}}}{T_{\text{i}}-T_{\text{a}}} \tag{10}\]  
where \(T_{\text{c}}\) is the module temperature 15 s after contact with the sample, \(T_{\text{i}}\) is the initial module temperature, and \(T_{\text{a}}\) is the ambient temperature. According to the thermal conductivity values of the 16 samples shown in Figure 7c that were obtained using the aforementioned equation, Samples No. 11 (Styrofoam) and No. 13 (sponge) had high values compared to the other samples. This is due to the insulating effect of these materials as a consequence of their low thermal conductivities. Conversely, Samples No. 6 (copper) and No. 9 (aluminum) had low values due to their high thermal conductivities, which indicates that the temperature decreased rapidly as the finger came into contact with the samples. The texture discrimination experiment was performed with the training database that was constructed using the aforementioned equations. First, an arbitrary sample was measured according to the process flow chart to obtain values (x\({}_{\text{j}}\)) for each indicator (j). Next, we confirmed whether x\({}_{\text{j}}\) was within the range of m\({}_{\text{j}}\pm\sigma_{\text{j}}\) of the 16 samples for each indicator to calculate a weight value (\(w_{\text{j}}\)). The method of calculating \(w_{\text{j}}\) is as follows. If x\({}_{\text{j}}\) is within the range of a specific sample for the corresponding index (m\({}_{\text{j}}-\sigma_{\text{j}}\leq\) x\({}_{\text{j}}\leq\) m\({}_{\text{j}}+\sigma_{\text{j}}\)), \(w_{\text{j}}\) is set as zero.