El papel y las acciones que han emprendido las autoridades ante esta

The objective of this calibration process is to determine the constants in the mathemat- ical model of the piezoresistive and capacitive sensors described by Eqs. (3.8) and (3.13) respectively. This is an important step since the mathematical model is used for both deter- mining individual element forces to create the tactile pressure map and for determining the total force based on the average reading.

Calibration Apparatus: To be able to properly calibrate the sensors and evaluate the

characteristics of individual sensing elements, a specialized calibration device was devel- oped (Fig. 3.11). This device is essentially a small 3D Cartesian positioning system that can move a high-precision unidirectional Futek LSM-300 load cell in any direction with an accuracy of 2.5µm. The load cell has a replaceable probe attached to it that has a 2 ×

2 mm tip contact area, the same size as an individual sensing element. The device can apply a desired downward force with an accuracy of 0.05 N anywhere within the 60 × 30 mm workspace, and measure the actual applied force with an accuracy of 0.01 N.

Piezoresistive Tactile Sensor Calibration: The first step in calibrating the piezoresistive

tactile sensor is to characterize the piezoresistive material by determining the constantsC1,

C2andρ0. To accomplish this, the probe on the calibration device was replaced with a 5× 5 mm contact area probe. The device was then used to apply predetermined pressures on a piece of the piezoresistive material and the resistance across it was measured and recorded.

3.7 Evaluation 80 (a) (b) (c) (d) (e) (f) (g) (h)

Figure 3.9: PCB fusing and component side assembly steps in the manufacture of the proto- type tactile sensors: (a) the bare PCBs as obtained from the PCB manufacturer, (b) the stencil used to apply solder paste onto the PCBs, (c) a PCB with the sol- der paste applied ready for fusing, (d) mould used to align the two PCBs before fusing, (e) the fusing process on a hot plate with the PCBs between two steel bars to ensure proper fusing, (f) the fused PCB with the components soldered, (g) the PCBs placed in the Teflon encapsulation mould, (h) the mould filled with epoxy to encapsulate the electronic components.

This process was repeated for ten samples, and the collected data points are presented in Fig. 3.12. The least-squares best–fit quadratic curve has an excellent fit with anR2 value of 0.98. The calibration was performed up to 750 kPa even though the desired maximum

3.7 Evaluation 81

(a) (b) (c) (d) (e)

Figure 3.10: Sensing side assembly steps in the manufacture of the prototype tactile sen- sors: (a) the sensing side as seen after the encapsulation process, (b) the com- ponents side as seen after the epoxy is sanded down to the correct height, (c) the sensing side with the layers placed on top, (d) the sensing side after apply- ing the protective covering, (e) the components side of the finished sensors.

pressure is 150 kPa just to obtain the characteristics of the material over the entire pressure range that it can measure. The data collected from the ten samples fall within±8% error margins indicating good repeatability.

Based on this calibration curve, the constants C1, C2 and ρ0 are 9e-5, 0.125 and 55 respectively. Also, based on the calibration curve, the resistance of a single sensing element varies in the range of 0.5 kΩ to 2.7 kΩ. The series resistor Rs was chosen to be 1 kΩ to

obtain good voltage sensitivity since it lies within this range. It was observed that the value ofRs used in the model had to be adjusted slightly for every element to achieve good data

fit due to imperfections on the PCB surface and in the piezoresistive material. Based on the measured response of several individual sensing elements, the best data fit was obtained on average whenRs was taken to be 1.07 kΩin the model. Using this data, the constantsK1,

K2andK3were determined to be 2.78 N, -2.06 N2and 3.80 N2, respectively, to be used in the model for generating the tactile pressure map from the element readings. For the min– max total force calibration performed as a part of the bulk calibration process described earlier, Rs is kept as a free variable that is determined based on the calibration values to

3.7 Evaluation 82 Tactile Sensor Probe Load Cell Stepper Motors

Figure 3.11: Calibration device used for characterizing and evaluating individual sensing elements of the sensors.

obtain the best fit for relating the total contact force to the average sensor reading.

Capacitive Tactile Sensor Calibration: The model developed for the capacitive sen-

sor assumes that the dielectric material has a linear stress–strain response. The chosen dielectric material is a silicone elastomer, and it has an approximately linear stress–strain relationship for only under about 20% strain [5]. Since its Young’s modulus is 1.2 MPa, the response is almost linear for stresses up to 240 kPa, which is 60% higher than the max- imum pressure of 150 kPa that the sensor has been designed for. The only unknown to be determined via calibration is the parasitic capacitanceCp. This value was found to vary

slightly for different sensing elements due to different lengths of PCB traces, and imper- fections on the PCB surface and in the dielectric material. Based on the measured response

3.7 Evaluation 83 ρ = 9E-05P² - 0.125P + 55 R² = 0.98 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 0 125 250 375 500 625 750 Resist iv it y, ρ ( Ω .m ) Pressure, P (kPa)

Figure 3.12: Characterization curve of the piezoresistive material.

of several individual sensing elements, the average value ofCpthat results in the best data

fit was found to be 2.7 pF. Using this data, the sensor calibration constantsJ1and J2were determined to be 4.80 N and 17.8 N·pF, respectively, to be used in the model for generating the tactile pressure map from the element readings. For the min–max total force calibration performed as a part of the bulk calibration process described earlier,Cp is kept as a free

variable that is determined based on the calibration values to obtain the best fit for relating the total contact force to the average sensor reading.