# A Novel Sensorised Insole for Sensing Feet Pressure Distributions

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## Abstract

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## 1. Introduction

## 2. Background

#### 2.1. Mathematical Notation

- Let $\mathbb{R}$ be the set of real numbers.
- Let $\mathit{x}\in {\mathbb{R}}^{n}$ denote an n-dimensional column vector, while x denotes a scalar quantity.
- Let $\left|\right|\mathit{x}\left|\right|$ be the Euclidean norm of the vector $\mathit{x}$.
- Let ${\mathbf{0}}_{m\times n}$ be the zero matrix $\in {\mathbb{R}}^{m\times n}$.
- Let ${\mathit{I}}_{n}$ be the identity matrix $\in {\mathbb{R}}^{n\times n}$.
- Let ${f}_{z}$, ${m}_{x}$ and ${m}_{y}$ denote the vertical ground reaction force and the moments about the horizontal axes, respectively.
- Let ${x}_{i}\in \mathbb{R}$ denote a variable referred to the i-th sensor.

#### 2.2. Tactile Sensors

#### 2.3. A Mathematical Model for Taxels

- -
- ${\u03f5}_{r}$ changes with the pressure because the quantity of air contained between the ground plane and the sensors decreases to zero (we can consider that beyond this point we are saturating the sensors);
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- k changes with the pressure and with time;
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- ${d}_{0}$ is not constant due to the hysteresis in the dielectric mechanical elasticity.

#### 2.4. Recall on Skin Calibration

- The first setup (Figure 3a) consists of inserting the skin inside a Ziploc bag and pumping out air. This decreases the pressure in the bag and creates a uniform pressure distribution over the skin surface. The flow rate is regulated by using valves to ensure a slow and steady pace in order to avoid the dynamic effects of the dielectric material. The pressure reached on the skin is measured with a pressure sensor that sends data to a computer through a CAN network [28].
- The second setup uses an isolation chamber (Figure 3b). Contrary to the vacuum bag experiment explained above, the pressure is now increased in the external environment relative to the skin. The setup consists of an air compressor, the mentioned chamber, a pressure regulator and a micro-controller for pushing air and increasing the pressure inside the chamber [29].

## 3. Contribution

#### 3.1. Insole Prototype

#### 3.2. New Calibration Method

- The vacuum bag method can reach a maximum pressure of 1 Atm, which is not high enough for our application. We need higher pressures during the calibration in order to take data that is consistent with real working conditions. For instance, if we consider a person weighing $80\mathrm{k}\mathrm{g}\mathrm{s}$ standing still on a single foot heel, a vertical force ${f}_{z}$ of about 800 N is applied on a small area of the insole. This force is spread over 4~5 triangles. The area of each triangle is about $A=3.24\times {10}^{-4}$ m${}^{2}$. Thus, recalling (3) and considering four triangles, the pressure on each sensor will be:$$P=\frac{{f}_{z}}{A\ast {n}_{triangles}}\approx 6\mathrm{Atm}.$$
- The calibration setup based on the isolating vessel is not big enough to hold the proposed insole and can only reach a maximum pressure of 3 Atm.

#### 3.3. Model Parameters Identification from the New Calibration Method

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- The quantities ${d}_{0}$ and ${\u03f5}_{r}$ to estimate in the model (9) are not linear with respect to the pressure and to find them we need to solve a non-linear optimisation problem;
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- Hypotheses for deriving the theoretical model are based on ideal behaviours, but the physical insole does not always respect the ideally hypotised case. Thus, a more general model helps to consider factors that we did not take into account in (9).

- -
- Variables to compare, force, moments and pressure have different order. Indeed, force can reach a value of about $1000\mathrm{N}$, moments can reach a value of about $100\mathrm{N}\mathrm{m}$ and pressure assumes values between 0 and ${10}^{6}\mathrm{Pa}$.
- -
- The sample numbers of the two data sets (FT shoes data set and vacuum bag data set) is not the same because they come from different experiments.

## 4. Experiments and Validation

#### 4.1. Experiments for Calibration and Validation

- One data set was collected using the setup described in Section 2.4. The experiments with a vacuum bag (Figure 5a) reached a pressure of 90 kPa and the pressure was uniformly distributed over the insole. The experiment consisted of three cycles of pressure reduction and increase (Figure 6). In Figure 6 we can see that the pressure was negative, which can be explained by the choice of the reference frame W that has the z axis pointing up. Indeed, in order to have compression, the force applied on each taxel has to be negative and as consequence of (3) even the pressure has to be negative. We can even observe that when the pressure increased the measured capacitance decreased. This is because the chips do not stream analog capacitances, as explained in Section 2.3, but the analog capacitances are mapped to a digital value at an 8-bit resolution and the relation (6). The mapping was inverse, that is, values from 255 to 240 indicate that the taxel was not pressed and 0 means that the taxel was measuring the highest analog capacitance that is possible to map with 8 bits.
- Another data set was taken using a pair of sensorised shoes developed at IIT (Figure 5b). Each shoe was equipped with two six-axis FT sensors by the iCub group at Istituto Italiano di Tecnologia (IIT) [35], able to measure the forces and moments. As mentioned in Section 3.2, the data sets had different features in order to excite the activation of the taxels as much as possible in order to obtain different combinations to cover the entire capacitance range of each sensor (Figure 7).

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#### 4.2. Validation

## 5. Conclusions

- A weighted iterative least-square method can be used in order to avoid manually tuning the weights;
- The formulation for describing the relationship between capacitance and pressure for each taxel could also take into account some hysteresis in the stiffness of the skin dielectric and the electric state of the sensor;
- Constraints on the model can be added in the optimisation problem;
- The accuracy and the repeatability of the data collection procedure can be improved.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Main components of the iCub skin. (

**b**) Array of capacitive sensors. Each sensor implements 12 taxels and hosts the capacitive transduction electronics. (

**c**) Deformable dielectric with conductive top layer. (

**d**) Micro-controller tactile board (MTB).

**Figure 3.**(

**a**) Calibration setup based on vacuum bags. (

**b**) Calibration setup based on isolation chamber.

**Figure 4.**(

**a**) Insoles prototype. (

**b**) Inner part of the insole containing the gaps that accommodate the digital converter integrated circuits. (

**c**) Computer-Aided Drafting (CAD) design of the support for the electronics. (

**d**) Micro-controller tactile boards (MTBs) consistency: one for each patch of the insoles.

**Figure 5.**(

**a**) Vacuum bag experiment. The pressure inside the bag was reduced by using a vacuum pump. (

**b**) Sensorised shoes equipped with force/torque (FT) sensors and insoles.

**Figure 6.**Capacitances measured by one triangle (i.e., 10 taxels) and pressures measured by the pressure sensor during the vacuum bag experiment that consisted of three cycles of pressure reduction and increase.

**Figure 7.**Capacitances measured by one triangle (i.e., 10 taxels), vertical force and horizontal moments measured by the sensorised shoes.

**Figure 9.**Vertical force ${f}_{z}$ and horizontal moments ${m}_{x}$ and ${m}_{y}$ tracking. (

**a**) Task T3. (

**b**) Task T4.

**Figure 10.**Zoomed view of the tracking error to highlight the delay between FT sensors and insole estimations.

**Figure 12.**Online visualisation tool for the insoles. On the left-hand side, the comparison between centres of pressure estimated by force/torque (FT) sensors and insole. In the middle, estimation of vertical contact forces ${f}_{z}\left(\mathrm{N}\right)$ and moments ${m}_{x}$, ${m}_{y}$$\left(\mathrm{N}\mathrm{m}\right)$ using the calibrated insole. On the right-hand side, the pressure distribution.

**Table 1.**Root Mean Square Error (RMSE) analysis of vertical ground reaction force ${f}_{z}\left(\mathrm{N}\right)$ and horizontal moments ${m}_{x}$, ${m}_{y}$$\left(\mathrm{N}\mathrm{m}\right)$, respectively, from tasks T1 to T6.

Task | Description | Highest Pressure | RMSE | RMSE | RMSE |
---|---|---|---|---|---|

$\left(\mathbf{k}\mathbf{Pa}\right)$ | ${\mathit{f}}_{\mathit{z}}\left(\mathbf{N}\right)$ | ${\mathit{m}}_{\mathit{x}}\left(\mathbf{N}\mathbf{m}\right)$ | ${\mathit{m}}_{\mathit{y}}\left(\mathbf{N}\mathbf{m}\right)$ | ||

T1 | Still on feet | 220 | 7.5946 | 0.70729 | 2.2892 |

T2 | Still on left foot | 560 | 11.9475 | 1.8784 | 4.5675 |

T3 | Slow movements on feet | 490 | 34.1682 | 1.8559 | 5.2909 |

T4 | Walk 1 | 630 | 93.4157 | 2.1891 | 12.129 |

T5 | Walk 2 | 600 | 84.8782 | 1.9286 | 11.0665 |

T6 | Walk 3 | 360 | 95.1694 | 0.99215 | 7.7857 |

**Table 2.**Tracking accuracy of vertical ground reaction force ${f}_{z}$ and horizontal moments ${m}_{x}$, ${m}_{y}$, respectively, from tasks T1 to T6.

Task | Description | Accuracy (%) | Accuracy (%) | Accuracy (%) |
---|---|---|---|---|

${\mathit{f}}_{\mathit{z}}$ | ${\mathit{m}}_{\mathit{x}}$ | ${\mathit{m}}_{\mathit{y}}$ | ||

T1 | Still on feet | 98.0472 | 70.8789 | 91.1336 |

T2 | Still on left foot | 98.4868 | 73.6694 | 91.4024 |

T3 | Slow movements on feet | 89.3013 | 71.6058 | 83.9142 |

T4 | Walk 1 | 81.8419 | 64.056 | 75.9248 |

T5 | Walk 2 | 83.8964 | 71.886 | 81.69 |

T6 | Walk 3 | 82.5655 | 63.0632 | 70.7365 |

**Table 3.**Root mean square error (RMSE) analysisof centre of pressure $Co{P}_{x}$, $Co{P}_{y}$ (mm), respectively, from tasks T1 to T6.

Task | Description | RMSE | RMSE |
---|---|---|---|

$\mathit{C}\mathit{o}{\mathit{P}}_{\mathit{x}}$ (mm) | $\mathit{C}\mathit{o}{\mathit{P}}_{\mathit{y}}$ (mm) | ||

T1 | Still on feet | 18.6429 | 4.951 |

T2 | Still on left foot | 11.941 | 4.2918 |

T3 | Slow movements on feet | 28.9685 | 6.697 |

T4 | Walk 1 | 19.8642 | 3.8349 |

T5 | Walk 2 | 18.6675 | 3.1547 |

T6 | Walk 3 | 37.5296 | 5.084 |

**Table 4.**Tracking accuracy of centre of pressure $Co{P}_{x}$, $Co{P}_{y}$, respectively, from task T1 to T6.

Task | Description | Accuracy [%] | Accuracy [%] |
---|---|---|---|

$\mathit{C}\mathit{o}{\mathit{P}}_{\mathit{x}}$ | $\mathit{C}\mathit{o}{\mathit{P}}_{\mathit{y}}$ | ||

T1 | Still on feet | 69.5057 | 89.1761 |

T2 | Still on left foot | 84.3097 | 60.71643 |

T3 | Slow movements on feet | 99.9442 | 99.9884 |

T4 | Walk 1 | 99.9805 | 99.9965 |

T5 | Walk 2 | 99.9811 | 99.997 |

T6 | Walk 3 | 99.9484 | 99.9935 |

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## Share and Cite

**MDPI and ACS Style**

Sorrentino, I.; Andrade Chavez, F.J.; Latella, C.; Fiorio, L.; Traversaro, S.; Rapetti, L.; Tirupachuri, Y.; Guedelha, N.; Maggiali, M.; Dussoni, S.;
et al. A Novel Sensorised Insole for Sensing Feet Pressure Distributions. *Sensors* **2020**, *20*, 747.
https://doi.org/10.3390/s20030747

**AMA Style**

Sorrentino I, Andrade Chavez FJ, Latella C, Fiorio L, Traversaro S, Rapetti L, Tirupachuri Y, Guedelha N, Maggiali M, Dussoni S,
et al. A Novel Sensorised Insole for Sensing Feet Pressure Distributions. *Sensors*. 2020; 20(3):747.
https://doi.org/10.3390/s20030747

**Chicago/Turabian Style**

Sorrentino, Ines, Francisco Javier Andrade Chavez, Claudia Latella, Luca Fiorio, Silvio Traversaro, Lorenzo Rapetti, Yeshasvi Tirupachuri, Nuno Guedelha, Marco Maggiali, Simeone Dussoni,
and et al. 2020. "A Novel Sensorised Insole for Sensing Feet Pressure Distributions" *Sensors* 20, no. 3: 747.
https://doi.org/10.3390/s20030747