Novel low-cost approach to build large-scale flexible sensors for spatially distributed ground reaction force measurements

Introduction

Rehabilitation exercises are crucial following surgery, stroke, sports injuries, and various other medical conditions, as they are integral to the recovery process. These exercises help restore muscle strength, proprioception, and joint functional ability, enabling patients to regain independence and improve their quality of life. Post-surgical rehabilitation prevents complications such as stiffness and muscle atrophy, while stroke rehabilitation focuses on neuroplasticity to recover motor skills and cognitive functions. For sports injuries, tailored rehabilitation protocols ensure a safe and effective return to athletic activities, reducing the risk of re-injury. Overall, rehabilitation exercises are essential for maximizing recovery outcomes, facilitating a smooth transition back to daily activities, and promoting long-term health and wellness.

Rehabilitation exercises are defined by physiotherapeutic personnel and usually done under their direct supervision. To increase effectiveness performing rehabilitation exercises at home is decisive. It is critical in the continuum of care for patients recovering from injuries, surgeries, or chronic conditions [1], 2]. These exercises, tailored to individual needs, play a vital role in enhancing recovery out-comes. Home-based rehabilitation not only provides the convenience of exercising in a familiar environment but also empowers patients to take an active role in their recovery process. Moreover, with the rising accessibility of telehealth and digital tools, the effectiveness of home physiotherapy can be bolstered, ensuring adherence to prescribed routines and timely professional guidance [2]. This paper explores the design of sensor technology for a physiotherapy mat supposed to measure spatially distributed ground reaction forces (GRF).

Measuring GRF during rehabilitation exercise, decubitus prevention, or patient fall situations, distributed over areas up to 2 m², is a challenging task. Furthermore, information about the spatial GRF distribution can be used to improve the quality of rehabilitation exercises, as they can be used to provide feedback to patients about the execution of exercises.

Commercially available systems for large area, spatially distributed GRF measurements are either rigid or expensive or both. These systems are based on a resistive (Tecscan, Inc.) or capacitive (novel GmbH, or zebris Medical GmbH) sensing technology. SENSING TEX, S.L. offers development kits for large area GRF measurements based on a piezo resistive technology. Table 1 gives a brief overview about the specifications of the different systems. They all have in common, that different sensor system sizes are available depending on the desired application. Generally speaking, the rigid systems rely on a capacitive sensing technology and provide a higher spatial resolution and accuracy compared to the flexible systems. The rigid systems are primarily used for gait analysis whereas the flexible ones are used for measurements on uneven and/or compliant surfaces. Depending on the manufacturer the measurement range differs by up to a factor of 10 even for the same application.

Recent research investigated the construction of flexible and stretchable capacitive force sensors. They all have in common, that electrodes are applied on flexible substrates. A force acting on the sensor results in a change of the distance between the electrodes and thus a change in capacitance. Even though high sensitivity and accuracy can be achieved, careful engineering of the used material combinations, coating and substrate doping is fundamental [17]. This requires the use of special machinery for sensor fabrication [18] and results in a commercial unavailability of low-cost ready-to use capacitive sensors for integration in devices for large area GRF measurement. Furthermore, capacitive force sensing is subject to disturbance by environmental influences such as electrical fields resulting in noise and parasitic capacitances [19].

Another approach for building flexible force sensors is the use of piezoresistive materials. These change their resistance dependent on the acting strain. Usually, polymer foams are used for building resistive force sensors. To obtain the piezoresistive behavior, conductive particles are added [18]. Recent research focuses on the use of metal nanowires [20], 21] or carbon nanotubes [22], 23] as well as advanced material geometries [23], [24], [25] to achieve high sensitivity and accuracy. Additionally, to this research aiming to optimize sensor characteristics, low-cost, commercially available materials for building a resistive force sensor were evaluated regarding their performance. ESD packing foam was identified as the most suitable material showing the best trade-off between sensing performance an cost [26]. ESD foam based force sensors presented in the literature require a flexible PCB as electrode in contact to the foam for resistance measurement [26], 27]. This limits the maximal sensor size and increases the production cost. Furthermore, the large lateral stiffness of flexible PCB reduces the compressibility of the sensor. Lastly, the flexible PCB can be damaged by repeated bending or folding [28].

This work presents a low cost, non-rigid, and rollable resistive sensing technology for GRF measurements over application specific areas up to several square meters. It relies on a robust, long term stable sensing setup and can be manufactured without expensive special machinery. The sensing technology used is based on discrete, resistive sensor modules. These sensor modules are characterized regarding their force-resistance sensitivity depending on the loaded area, their inter-module variability, inter-day variability and the influence of a covering foam.

System design

The sensing system is built from multiple discrete resistive sensor modules distributed over an area of 60 × 180 cm². Each sensor module provides a distinct force value. Using these, the spatial GRF distribution over the whole sensor system can be captured. ESD packing foam is used as resistive sensing material and conductive textile is used as electrodes [29], 30].

The proposed system offers a spatial resolution of 7.5 × 7.5 cm² (equals 17.8 GRF measurements per m²), allows to measure forces up to 330 N, and has a weight of 1.5 kg/m². It can appear as a sports mat and can be operated with a mobile device via an USB-cable without an external power supply.

Force sensor module

Each discrete sensor module was defined to have a quadratic shape with an edge length of 7.5 cm. This size was chosen to enable to distinguish between the GRFs of each foot of a person during normal, erect standing. Anthropometric data for the size calculation was taken from DIN 33402 [31]. Figure 1 shows the sensor module, composed of a sensing material and two electrodes, sewn on each surface of the sensing material. The sensitive surface of a sensing module is bounded by the seams, attaching the electrodes on the foam and results in an area of 6.5 × 6.5 cm².

Figure 1:

Left: assembled sensor module. Right: cross-sectional representation of the sensor module. 1: resistive foam (signal-construct PE 553), 2: electrodes based on conductive textile (Shieldex Technik-tex P180 + B), 3: copper braid, 4: copper cable, 5: conductive yarn, 6: polyester yarn, 7: encapsulating foam (displayed in Figure 2B).

Conductive ESD packing foam (PE 553, 5 mm thickness, Signal-Construct GmbH, Niefern-Öschelbronn, DE) was used as the sensing material. Conductive polymer foams like this show piezo-resistive characteristics, leading to reduced electrical resistance during compression [26], 32]. To build the sensor modules, quadratic pieces with an edge length of 7.5 cm were cut out of the foam.

To measure the resistance over the foam’s thickness on the whole area of the sensing module the top and bottom surface were electrically connected. For this purpose, flexible electrodes made of conductive textile and copper braid were used. To form the electrodes, the conductive textile (Shieldex Technik-tex P180 + B, Statex Produktions-und Vertriebs GmbH, Bremen, DE) was cut in quadratic, 7 cm edge length patches with a laser cutter (Speedy 100, TROTEC Laser GmbH, Marchtrenk, AT). The electrical connection of the textile patches to the measurement circuit was performed with a flexible, 6.5 cm long and 0.5 cm wide copper braid and a cable. The braid was sewn on the textile patch using a conductive yarn (Steel-tech 100, Amann & Söhne GmbH & Co. KG, Bönnigheim, DE) and a cable was soldered to the braid.

Demonstrator

A demonstrator sized 31 × 33 cm² was built to show the functionality of the developed sensing concept. Therefore, 16 identical sensor modules were built as described above. The sensor modules were arranged in a 4 × 4 matrix setup. A 4 mm thick yoga mat (Yogamatte Essential, Decathlon S.A., Villeneuve-d’ Ascq, FR) was used as a base and top material to encapsulate the sensor modules. The sensor modules were fixed on the yoga mat using thin double-sided adhesive tape (folia 55022, Max Bringmann KG, Wiesbaden, DE). All bottom electrodes were connected to a common ground and each top electrode was connected to an input pin of a measurement circuit. Figure 2A shows the arrangement of the sensor modules and Figure 2B shows the completed demonstrator. To evaluate and visualize the resistances of all 16 sensor modules a GUI was designed using MATLAB App Designer (version R2022a, The MathWorks, Inc., Natick, MA, US). It uses a color-coded map to visualize the resistance value of each sensor module.

Figure 2:

Assembly of the demonstrator. A: Sensor modules mounted on a yoga mat to build a demonstrator (top mat removed for better visibility). B: Completed demonstrator, side view. 1: yoga mat, 2: sensor modules.

Measurement equipment

To measure the resistance of the sensor modules a custom PCB (Figure 3) was designed and manufactured. Resistance measurements were carried out using a Wheatstone bridge circuit. To perform a measurement, one of the 16 sensor modules was connected in series to one of the four fixed-value resistors of the Wheatstone bridge circuit using a two-stage cascade of analogue multiplexers (TMUX 1208, Texas Instruments, Dallas, TX, US), which was controlled by an Arduino Nano micro-controller (Arduino S.r.l., Monza, IT). The bridge voltage was amplified to 5 V full scale using an instrumentation amplifier (INA 122, Texas Instruments). Analogue voltage signals were digitized using a single analogue input pin and the inbuilt ADC of an Arduino Nano microcontroller (10 bit). This arrangement enabled to measure the resistance of one specific and selectable sensor module at a time and switching between the modules with more than 1 kHz to gather the spatial resistance distribution. The circuit diagram and the PCB layout are shown in the supplementary material.

Figure 3:

Custom PCB for resistance measurement with 1: Arduino nano microcontroller, 2: instrumentation amplifier, 3: Wheatstone bridge and a 4: two-stage cascade of analogue multiplexers.

The microcontroller software enabled to set the number of sensor modules of which the resistance was measured and the sampling frequency. Using a timer function the resistance measurements were repeatedly triggered based on the sampling frequency. During each measurement cycle each of the previously defined sensor modules was successively connected to the bridge circuit for resistance measurement by setting the analogue multiplexers. After setting the multiplexers the signal was allowed to settle for 450 µs before the amplified voltage was measured with the microcontroller. The measurement value was written to the serial communication interface followed by a delimiter. After the resistance measurement of all selected sensor modules was performed, the microcontroller paused until the timer function triggered the next measurement.

Data acquisition and processing was performed on a PC with Matlab (version R2022a, The Math-Works). This included receiving the microcontroller’s data stream, converting the voltage measurements to resistance values and storing the measurement data on the PC.

Resistance values ΔR of the sensor modules were calculated based on the amplified bridge voltage V _bridge,amp which was measured by the ADC of the microcontroller according to the following equations.

The amplified bridge voltage V _bridge,amp depends on the bridge voltage V _bridge and the gain factor of the amplifier G _INA .

(1) V b r i d g e , a m p = V b r i d g e   · G I N A

G _INA depends on the gain resistor R _G according to equation (2) [33].

(2) G I N A = 200   k Ω R G − 5 , w i t h   R G = 9.08   k Ω , G I N A = 17.03

The sensor module’s resistance ΔR is calculated based on the resistance of the bridge resistors R _bridge , the excitation voltage V _CC and the bridge voltage V _bridge according to equation (3).

(3) Δ R = 4 R b r i d g e V C C · V b r i d g e − 1 − 2

With R _bridge =1000Ω, equation (1) and equation (2) ΔR is given by

(4) Δ R = 4 · 1000 Ω V C C · 17.03 · V b r i d g e , a m p − 1 − 2

As the bridge circuit is powered by the microcontroller used for voltage measurement, V _CC corresponds to the maximum value of the ADC V _CC =1023 (10 bit ADC). According to this, the calculation executed with Matlab to obtain resistance values is given by equation (5).

(5) Δ R = 4 · 1000 Ω 17.03 · 1023 · V b r i d g e , a m p − 1 − 2

The accuracy of the measurement circuit was evaluated with several fixed value resistors in the range of 20…140 Ω. The deviation of the resistances measured with the custom measurement circuit from the reference values was in the range of ±0.7 %.

Materials and methods

To characterize the piezoresistive behavior of the sensor modules several forces in the range of 1.6 N … 330 N were applied on the sensor modules and the module’s resistance was measured. 330 N was chosen as maximal force, as this corresponds to the force acting on one sensor module, when a 120 kg person is standing on the demonstrator (each foot stands on two modules).

Selected forces out of this range were distributed over four different circular, flat areas with the diameters 2.0 cm (=3.1 cm²=1 A), 4.5 cm (=15.7 cm²=5 A), 6.0 cm (=28.3 cm²=9 A), and 7.2 cm (=40.8 cm²=13 A), creating pressures in the range of 5 kPa (pre-tension) to 275 kPa.

To perform the measurements a test stand was built (Figure 4). The forces were generated by placing weights on a platform, which transferred the force on a cylindrical adapter with one of the above specified diameters. The sensor module under test was positioned underneath the cylindrical adapter.

Figure 4:

Test stand to apply defined forces on defined areas of the sensor module. 1: sensor module under test, 2: cylindrical adapter, 3: platform, 4: weight. Colored circles indicate the different sizes of the cylindrical adapters; red: 13 A, green: 9 A, yellow: 5 A, blue: 1 A. Blue circle on the lower left corner of the figure indicate positions of the force application on a sensor module. “center”, “north” and “north-east” were investigated, dashed circles are exemplary.

With this setup, the resistance of the sensor module dependent on the applied force and the area the force was acting on, was investigated. Furthermore, the influence of the position, where the force is acting was studied. Figure 4 shows the three different positions which were investigated.

Preliminary tests showed a temperature dependency of the resistive foam’s resistance. Therefore, the lab temperature was kept in the range of 20.0 °C–21.5 °C. The humidity was tracked and was between 37 % and 43 %.

Several combinations – subsequently named conditions – of applied force, area and position were investigated. For each condition, n=5 repeated measurements were executed. Acquisition of the resistance of the sensor-module automatically started, as soon as the force was applied on the sensor module and lasted for 3 s. The resistance was acquired with a sampling frequency of 100 Hz. After the measurement, the force was removed, and the sensor module was given 3 min to relax.

Selected conditions were measured repeatedly using two different sensor modules to investigate the variance between them. Furthermore, selected conditions were repeatedly measured on n=5 different days using the same sensor module to investigate the inter-day variability.

For each measurement the mean resistance of the sensor module was calculated based on the recorded single values, excluding the values recorded in the first 0.5 s. Based on these values for each of the five repetitions of similar conditions, mean and standard deviation were calculated.

Results

The 16 sensor modules manufactured had different resistances in unloaded condition and their mean resistance was 103 ± 6 Ω. The sensor module “M13” was chosen for the performance of the characterization tests, because of its resistance in unloaded condition of 102 Ω. In total, 115 measurements were performed with sensor module “M13” during force application on the central position. These measurements were recorded by applying multiple different forces on five different circular areas, using the cylindrical adapters with the areas 1 A, 5 A, 9 A and 13 A. Taking together all these measurements, a non-linear decrease in the sensor module’s resistance with increasing force applied is visible (Figure 5). An exponential fit on the data resulted in a R²=0.97 and RMSE of 4 Ω.

Figure 5:

Resistances of the “M13” sensor module measured under different test conditions, plotted against the impressed force. The given equation is the result of an exponential fitting on the data to calculate the sensor modules resistance R in Ω based on the impressed force F in N.

Furthermore, the investigations regarding the influence of the force application position on the resistance of the sensor module were performed with sensor module “M13”. For this purpose, n=5 additional measurements were performed at each of the positions “north” and “north-east” with 6.3 N and 12.6 N using the cylindrical adapter with area 1 A. The results showed the largest differences between the positions for an applied force of 6.3 N as displayed in Figure 6A. The largest deviation relates to the corner position north-east compared to the two other positions. This deviation was 2.6 % full scale (resistance of the sensor module in unloaded condition). Comparing the other measurements, the deviations were smaller.

Figure 6:

Results of characterization measurements. A: Mean values and standard deviations of the resistance measurements carried out on sensor module “M13” to investigate the influence of the force application position. n=5. B: Mean values and standard deviations of the resistance measurements carried out on sensor module “M13” to investigate the inter-day variability. n=5. C: Mean values and standard deviations of the resistance measurements carried out on sensor modules “M8” and “M13” to investigate the inter-module variability. n=5. D: Mean values and standard deviations of the resistance measurements carried out on the covered and un-covered sensor module “M13” to investigate the influence of two additional foam layers. n=5.

To investigate the inter-day variability of the measured resistances, n=5 measurements were repeated on five different days using sensor module “M13”. These were carried out for the conditions 12.6 N, cylindrical adapter area 1 A and 62.8 N, cylindrical adapter area 5 A with central force application. Figure 6B shows the measurement results. The deviation between the measured resistances was below 5.7 % (12.6 N, contact area 1 A) and 3.1 % (62.8 N, contact area 5 A) full scale.

As the sensor-modules were manually crafted, they showed different resistances in unloaded condition. Their mean resistance was 103 ± 6 Ω. To investigate the differences in resistance when forces are applied, measurements were carried out on two different sensor modules, having resistances of 109 Ω (sensor module “M8”) and 102 Ω (sensor module “M13”). With both modules 6 conditions with central force application were investigated as displayed in Figure 6C. Comparing the resistances measured under the same conditions, their deviation was below 3.8 % regarding full scale span of sensor module “M13”.

The results presented previously were all measured with bare sensor modules, as shown in Figure 1. As in the demonstrator (Figure 2) the modules were covered with a yoga mat on both sides, the influence of this additional foam on the module’s resistance was studied. Using the same sensor module (“M13”), once uncovered, and once covered, six conditions with central force application were investigated as displayed in Figure 6 D. Comparing the resistances measured under the same conditions, their deviation was below 3.5 % regarding full scale span of the tested sensor module “M13”.

Figure 7 shows the functionality of the demonstrator together with the GUI to visualize the sensor modules’ resistances. The resistance values of each of the 16 modules are updated with a frequency of 71 Hz and calculated according to equation (5). For visualization, the resistance value of each sensor module was displayed in a color-coded representation using Matlabs imagesc function with the turbo color map. The color map ranges from dark red (corresponding to a resistance of 0 Ω) to dark blue (corresponding to a resistance greater than 120 Ω). Changes in weight distribution are visualized without a noticeable time delay. The application of the demonstrator during different types of loading and unloading by a human are visible in the video in the online supplementary material.

Figure 7:

Complete system consisting of the demonstrator, the measuring circuit in its housing and a screen for visualizing the measurement results.

Discussion

In this paper a novel approach for a design of a flexible mat to measure ground reaction forces during rehabilitation exercise is presented. It was shown, that the conductive packing foam “Signal-Construct PE553” is a suitable material to build a large area resistive force sensor. The use of a conductive textile enabled to electrically contact the foam. By this process, discrete sensor modules can be built. Measurement results showed that increasing loads result in decreasing resistances of these sensor modules. The range of measurement is sufficient for a typical human body weight of 65 kg as even standing on one foot or tip toe leads to always at least two sensor modules being loaded. In addition, overload will lead to measurement saturation but not to damage of the sensor modules.

It was shown that the position of the load application point on the sensor module has a small influence within the standard deviation on the resistance measured at five of the six tested conditions. A higher difference in resistance (2.6 % full scale) was only observed for a force of 6.3 N at the position “north-east” acting on the cylindrical adapter of size 1 A. This behavior might be caused by the presence of two seams underneath the loaded area, used to sew the textile electrode on the foam. These seams cause a local pre-compression of the foam. The application of load on these areas may causes a more distinct height reduction of the foam, than in the other positions. When applying a load of 12.6 N, the compression of the foam is higher. In relation to this, the pre-compression effect of the seams on the sensor module’s resistance might be of lower order and therefore causing smaller differences in the measured resistances.

Repeated measurements of identical conditions on a single sensor module on different days showed a deviation of the measured resistances of 5.7 % full scale. The resistances measured at day 3 and later were all higher than on the first two days. A reason for this can be, that after the measurements on day 2 a 330 N load condition resulting in a 210 kPa pressure, was carried out on the sensor module. This caused a circular bend, having the shape of the cylindrical adapter used to apply the force, to stay present in the textile electrode and the copper braid. This may have led to an increased contact resistance between electrode and foam.

Furthermore, ambient temperature has an influence on the resistance of the sensor module. Even though the room temperature was kept in the range of 20 °C–21.5 °C these temperature deviations may have also caused deviations in the measured resistances. The influence of the temperature might be compensated in future using a calibration curve based on an ambient temperature measurement. In the application as a training mat the absolute force values are of secondary importance. To provide feedback about differences in force distribution it is sufficient to relatively compare the resistances of different sensor modules. Changes of the sensor modules’ force-resistance characteristics caused by temperature or humidity affect all sensor modules in the same way and consequently are regarded as uncritical for the envisioned application.

The deviation of the resistances measured on different sensor modules at the same conditions was below 3.8 %. This is most likely caused by manufacturing tolerances of the sensor modules caused by the manual crafting process. However, further investigations should evaluate if the resistances of the conductive textile and the conductive foam are uniformly distributed over the raw material. Furthermore, the measurements of the different modules were not carried out on the same day. Because of this it remains unclear, to which extent the observed deviation is caused by the inter-day variability or actual inter-module differences.

The observed inter-day and inter-module differences in the measured resistances are in a comparable range as the 10–15 % measurement accuracy of the commercially available (piezo-) resistive sensor systems.

Covering the sensor module with additional foam on both sides also causes changes in the measured resistance, which were below 3.5 % full scale. As previously discussed regarding the inter-module variability also these measurements were carried out on different days, resulting in an unclearness to which amount the observed resistance deviations are caused by the additional foam or by the different measurement day. However, calibration of the sensor modules should be carried out using the same sensor setup as in the envisioned application.

The foam used to build the sensor is a commercially available ESD-packing foam, not designed for sensor applications. According to this, preliminary tests regarding the resistive behavior of the foam showed deviations from ideal conditions. As mentioned before, the resistance is temperature de-pendent. Furthermore, during long term measurements, it was observed, that the foam is creeping under static load. Future material development may be carried out with the objective to receive a conductive foam with lower creeping and faster relaxation when removing load. The slow relaxation of the foam resulted in a dependency of the measured resistance from previously applied loads, when not allowing the foam to relax for several minutes.

The manufacturing process developed and used to build the sensor modules is easily adjustable to different shapes and sizes of sensor modules. Only the cutting size of the foam and the textile electrodes need to be adjusted to meet individual requirements towards spatial resolution and module shape. Furthermore, the manufacturing process relies mainly on sewing, which is a well-known, cheap, mass-production suitable technique in textile industry. Even though the manufacturing of the sensor modules needs several manual work steps. Production complexity may be reduced by the use of a different electrode material, e.g., a flexible polymer sheet, coated with an electrically conductive layer using a roll-to-roll process.

To further decrease the complexity of the sensor modules’ manufacturing process as well as their electrical connection and readout electronics, line electrodes can be used. Using this concept, a large area sheet of the foam can be used, on which line electrodes are applied. The electrode-lines on the top and bottom side are rotated by 90° towards each other. By addressing one electrode line on each side of the foam, the local resistance at the intersection of the lines can be measured.

Conclusions

This work shows a novel way to build low-cost, flexible resistive sensors for GRF measurements on large areas. A process for the manufacturing of discrete sensor modules based on conductive ESD packing foam and conductive textile as electrode material was presented. The dependency of force and resistance of the sensor modules was characterized. A demonstrator was built, showing the functionality of the developed sensor system.