## 4 Results and Discussion
### Demonstration of Texture Discrimination  
Since the performance of the robot fingertip module with the built-in multimodal tactile sensor was verified, we attempted to demonstrate whether our module could discriminate textures of objects. We conducted the experiments according to the aforementioned flow chart using the 16 selected tactile samples. First, 10 repeated measurements were conducted for each sample under the training mode and the measurement results were used to calculate the averages (m) and standard deviations (\(\sigma\)) for six specific indicators (h, \(\mu\), 1 st PSD, 2 nd PSD, 3 rd PSD, \(\theta\)) that correspond to the four tactile modalities (hardness, friction coefficient, roughness, and thermal conductivity). The calculated data were used to build a database, which was used to perform the texture discrimination experiment with arbitrary samples. The following paragraphs describe the calculation methods and formulas for the specific indicators of each modality. Hardness (h) is an indicator of the rigidity of a sample and can be estimated using the vertical direction force measurement capabilities of the tactile sensor by moving the module after coming into contact with the sample in the vertical direction in eight steps (n). We calculated hardness by averaging the vertical direction force measurement capability (\(R_{\mathrm{z}}\)) values detected by the sensor for the final four of the total eight steps. This is because there is the potential for the contact area of the module with the sample to increase during the initial four steps, which can slightly alter the angle of the finger module, leading to horizontal forces being applied in tandem with vertical forces. However, such a phenomenon does not take place after the third step. The formula can be expressed as follows:  
\[\text{h}=\frac{1}{4}\times\left(\sum_{\text{n}=5}^{8}\left(R_{\text{z}}\right)_{ \text{n}}-\left(R_{\text{z}}\right)_{\text{n}-1}\right) \tag{8}\]  
Friction coefficient (\(\mu\)) is a proportional constant that refers to the degree of friction between two surfaces in contact and is calculated by dividing the horizontal force by the vertical force. We calculated the horizontal (Y-axis) direction force measurement capability (\(R_{\text{y}}\)) and the vertical direction (Z-axis) force measurement capability (\(R_{\text{z}}\)) of the tactile sensor when the module is rubbed on the sample (dynamic contact). This is because the developed module moves in the Y-axis direction of the cell of the 3-axis sensor. This can be expressed by the following equation:  
\[\mu=\frac{R_{\text{y}}}{R_{\text{z}}} \tag{9}\]  
By plotting the calculated values of the two indicators for the 16 samples on a single graph, the graph could be viewed in quadrants, as shown in Figure 7a. As a result, it was found that the samples could be categorized into groups. In particular, samples located in the first quadrant, which had smooth surfaces, exhibited significant dispersion in terms of friction coefficient due to the rubbing action (dynamic contact), resulting in the stick-slip phenomenon. Conversely, no samples were located in the fourth quadrant, which indicates that none of the samples measured by the developed platform had both high friction coefficient and low hardness. According to the hardness data, Sample No. 11 (Styrofoam) was measured as the hardest material despite the fact that the actual hardness of the material is low, which reflects how humans struggle to determine differences in hardness between Styrofoam and a relatively harder material like Sample No. 10 (acrylic). This is due to the fact that international standards of hardness are measured by indenting a pointed probe to a certain depth on a material. On the other hand, the texture discrimination system developed in this study measures hardness similar to how humans press on materials with their fingers, hence the difficulty in discriminating the samples with the exception of soft materials, as in the case of Sample No. 13 (soft sponge).