**3. Dynamic Weight-Bearing Calculation**

Canes can be used to reduce pain in one lower extremity by allowing users to support some weight on them. Load on cane depends on the person's own weight, but also on their condition. To design a cane sensor, it is necessary to grant that its range is wide enough to capture this weight

variations. As commented, low-cost sensors have lower ranges and accuracies. However, in this section we propose a method to increase their range by combining two cheap sensors into a single sensing module.

Cane users can be categorized into contralateral and ipsilateral. Users who support weight on the cane and on the closest foot to the cane at the same time are ipsilateral. The others are contralateral. Ipsilateral users reportedly load up to 7% of their body weight on the cane. Contralateral users are more frequent and more critical, as they load up to 9% [28]. These percentages may increase when users have some physical issues. Our solution relies on cheap FSR 402 force sensors to measure loads. FSR 402 sensors have a limited range up to only 10 kg. Therefore, contralateral users could weigh as much as 111 kg, whose 9% is 10 kg, before sensors saturate. Unfortunately, this limit could be significantly more restricting for users with physical issues.

To increase the measurement range while keeping sensors affordable, we have placed two (Due to the limit in the inner cane diameter (maximum of 22 mm), only two force sensors can be placed) FSR 402 sensors at different depths on a circular 3D printed plastic piece. First, weight is distributed all over the surface of the piece (Figure 3a), so each sensor only receives part of the load, effectively increasing the global piece range. Additionally, the tip rubber applies different pressure on each sensor (Figure 3b), i.e., lower loads will not affect the deepest sensor. Unfortunately, factors like the nature of materials, non-linearity in sensors, and other physical variables, make unfordable to analytically calculate the sensor area output function. However, it is possible to estimate it. To obtain an estimated function of the sensors' outputs, we have calibrated the system through extensive testing using depths ranging from 0 mm to 5 mm.

**Figure 3.** Pressure distribution is done at two different levels: (**a**) First the rubber tip pressure distribution among the force sensors and the sensor area; (**b**) Second, pressure distribution on the sensors depends on the depth.

Calibration consisted of automatically applying different static weights on the fully vertical cane when one FSR 402 was connected to the sensor electronic board (Figure 2) and the other was bypassed. The readings were performed using one Analog Digital Converter (ADC), range 0–1023, from the BLE nano v2 board. First, we tested different sensor depths to select the most appropriate one, i.e., depths that provide the best reading range. Figure 4 shows different depths where FSR 402 were located and, it shows the average load (kg) in those locations. It can be observed that deepest locations (1 mm, 1.5 mm or 2 mm) have a problem to detect lower loads as we commented previously. On the other hand, outer locations saturate the signal when higher load values are applied (0.15 mm, 0.2 mm or 0.3 mm). For these reasons, we selected 0.2 mm and 1 mm as a combination that deals successfully with low and high load on cane simultaneously.

**Figure 4.** Sensor calibration for different sensor depths. Different static loads have been measured using the sensor electronic board (Figure 2) with one FSR 402 connected (the other one was bypassed).

Once both locations were selected (0.2 mm and 1 mm), we applied the same procedure to find the relation between applied weights and corresponding sensors readings, now with both FSR 402 connected. Figure 5 shows the obtained relation. It can be observed that readings below 2.5 kg present a bigger mean squared error (0.1389) than measurements over this value (0.0323). This is an effect of the rubber tip pressure distribution, as low weights only affect—partially—the outermost sensor. The obtained curve can be approximated by the following quadratic equation: 8.74 · <sup>10</sup>−11*x*<sup>4</sup> − 1.21 · <sup>10</sup>−7*x*<sup>3</sup> + 2.11 · <sup>10</sup>−5*x*<sup>2</sup> + 3.61 · <sup>10</sup>−2*<sup>x</sup>* + 0.5191.

**Figure 5.** This figure shows the relation between the ADC connected to the sensor electronic board (Figure 2) and the load on the cane in kilograms when only one sensor is connected (the other one is bypassed). A 4th order polynomial has been used to estimate that transformation: 8.74 · <sup>10</sup>−11*x*<sup>4</sup> <sup>−</sup> 1.21 · <sup>10</sup>−7*x*<sup>3</sup> <sup>+</sup> 2.11 · <sup>10</sup>−5*x*<sup>2</sup> <sup>+</sup> 3.61 · <sup>10</sup>−2*<sup>x</sup>* <sup>+</sup> 0.5191. The mean squared error on the estimation is 0.0515 kg.

The designed 2-sensors piece output range grows up to 45 kg (hardware reading equal to 1023) for the best depth difference. This means that a healthy contralateral user could weigh as much as 500 kg. Even though persons with disabilities support significantly more than 9% on the cane, this upper bound is high enough for most cases.
