## 4 Results and Discussion
### Multimodal Sensing Capabilities of the Tactile Sensor
This can be expressed by the following equations:  
\[R_{\mathrm{x}}=\left(\frac{\Delta R_{\mathrm{W}}}{\left(R_{\mathrm{W}}\right) _{0}}-\frac{\Delta R_{\mathrm{E}}}{\left(R_{\mathrm{E}}\right)_{0}}\right) \times 100(\%) \tag{3}\]  
\[R_{\mathrm{y}}=\left(\frac{\Delta R_{\mathrm{S}}}{\left(R_{\mathrm{S}}\right) _{0}}-\frac{\Delta R_{\mathrm{N}}}{\left(R_{\mathrm{N}}\right)_{0}}\right) \times 100(\%) \tag{4}\]  
To evaluate the 3-axis force measurement capabilities, the outputs of the robot fingertip module were compared with those of a commercial multi-axis load cell (model: SRI-M3701A, Sunrise Instruments, Canton, MI, USA) with Fz, Fx, and Fy capacities of 100 N, 50 N, and 50 N, respectively. A metal tip with a diameter of 3 mm connected to the multi-axis load cell was used to apply horizontal forces to the module. The test started with the preloading of a vertical force of 10 gf, then the metal tip was moved in the (+) Y-axis direction by approximately 20 \(\upmu\)m, 40 \(\upmu\)m, and 60 \(\upmu\)m to apply 20 mN, 40 mN, and 60 mN horizontal forces, respectively, while the sensor signals were observed. As the developed  
Figure 6: Multimodal sensing characteristics of the tactile sensor: (**a**) Output data about hysteresis characteristic and sensing range. (Inset) Sensor resolution data according to 0.5 g step force. (**b**) One-thousand repeated measurement data at maximum sensing normal force (100 gf). (**c**) 3-axis force data related to the shear force vector generated by a 20 \(\upmu\)m step motion in the Y-axis direction. (**d**) Temperature sensor characteristics for the temperature range from room temperature (23 \({}^{\circ}\)C) to human body temperature (35 \({}^{\circ}\)C). sensor comprises of a single cell to measure 3-axis forces, it is necessary to calculate the cross-talk error (S), which indicates whether the sensor is able to independently measure forces in each direction without the reading being affected by the signals of the other force directions [34]. This is calculated by applying the maximum horizontal direction (in our case, Y-axis) force to the module and comparing the changes in the force measurement capabilities in the other directions (X- and Z-axes) to the changes in the horizontal (Y-axis) direction force measurement capabilities before and after the force is applied. This can be expressed by the following equations:  
\[S_{\mathrm{x}}=\left|\frac{\Delta R_{\mathrm{x}}}{\Delta R_{\mathrm{y}}} \right|\times 100(\%) \tag{5}\]  
\[S_{\mathrm{z}}=\left|\frac{\Delta R_{\mathrm{z}}}{\Delta R_{\mathrm{y}}} \right|\times 100(\%) \tag{6}\]  
\[\Delta R_{\mathrm{a}}=\left(R_{\mathrm{a}}\right)_{\mathrm{After\ maximum\ movement}}-\left(R_{\mathrm{a}}\right)_{\mathrm{before\ maximum\ movement}} \tag{7}\]  
where \(\Delta R_{a}\) is the force measurement capability for direction a, and a refers to the X-, Y-, or Z-axes. From the equations, \(S_{\mathrm{x}}\) and \(S_{\mathrm{z}}\) were calculated as 3.57% and 2.14%, respectively. Thus, the developed sensor had sufficient sensitivity to detect horizontal forces as small as 20 mN, and the average cross-talk error was less than 3%. This highlights the 3-axis force sensing capabilities of the sensor. Related sensor characteristics are shown in Figure 6c. To evaluate the temperature sensing capabilities of the sensor, the fingerprinted skin of the robot fingertip module was placed on a hot Plate (MSH-30D, Daihan Scientific, Wonju, Korea) and the temperature of the hot plate was increased by 4 \({}^{\circ}\)C intervals within the range of 23-35 \({}^{\circ}\)C. For accurate temperature measurements, a platinum resistance thermometer with a resolution of 0.01 \({}^{\circ}\)C was attached to the hot plate. The resistance of the temperature sensor was measured 30 min after each temperature increase to ensure the heat from the hot plate had sufficiently transferred to the module to achieve equilibrium.