Design of a Wearable Real-Time Hand Motion Tracking System Using an Array of Soft Polymer Acoustic Waveguides

Abstract

Robust hand motion tracking holds promise for improved human–machine interaction in diverse fields, including virtual reality, and automated sign language translation. However, current wearable hand motion tracking approaches are typically limited in detection performance, wearability, and durability. This article presents a hand motion tracking system using multiple soft polymer acoustic waveguides (SPAWs). The innovative use of SPAWs as strain sensors offers several advantages that address the limitations. SPAWs are easily manufactured by casting a soft polymer shaped as a soft acoustic waveguide and containing a commercially available small ceramic piezoelectric transducer. When used as strain sensors, SPAWs demonstrate high stretchability (up to 100%), high linearity (R² > 0.996 in all quasi-static, dynamic, and durability tensile tests), negligible hysteresis (<0.7410% under strain of up to 100%), excellent repeatability, and outstanding durability (up to 100,000 cycles). SPAWs also show high accuracy for continuous finger angle estimation (average root-mean-square errors [RMSE] <2.00°) at various flexion-extension speeds. Finally, a hand-tracking system is designed based on a SPAW array. An example application is developed to demonstrate the performance of SPAWs in real-time hand motion tracking in a three-dimensional (3D) virtual environment. To our knowledge, the system detailed in this article is the first to use soft acoustic waveguides to capture human motion. This work is part of an ongoing effort to develop soft sensors using both time and frequency domains, with the goal of extracting decoupled signals from simple sensing structures. As such, it represents a novel and promising path toward soft, simple, and wearable multimodal sensors.

Introduction

Human hands have unmatched dexterity and hold incredible importance in daily life as they grant us the ability to interact continuously with our environment. The first obvious and well-documented consequence is that damaged or deficient hands are devastating and lead to reduced quality of life.¹ A second consequence is that hand instrumentation can be highly beneficial by improving natural human hands in various ways, such as virtual reality,² robot control,³ and communication.⁴ However, capturing and measuring the minute hand motions, or more specifically finger motions, is no simple task. Indeed, hand size, user comfort, movement speed, and the hand's many degrees of freedom contribute to making this a challenging endeavor. Technologies used to capture hand gestures broadly fall into the categories of vision-based systems and wearable sensor systems.

State-of-the-art vision systems achieve impressive performance.⁵ However, vision-based methods suffer from optical occlusion, which is inevitable when manipulating objects and often depends on a controlled environment.⁶ Although multiple cameras can alleviate these issues, it also necessitates heavy computational power, additional costs, and further constraints on the surrounding environment. Furthermore, vision systems can also suffer from light changes, background image complexity, and privacy-preserving issues. Solutions based on wearable sensors do not rely on a specific environment and are usually immune to changes in external conditions.

Consequently, wearable systems may fit a much broader set of applications. Some commercial efforts such as the 5DT Glove (The Fifth Dimension Technologies) and Cyber Glove (The Cyber Glove Systems) have met commercial success. However, besides their high cost, their glove-inspired design limits customizability and reduces users' natural haptic interactions with their environment.⁷ Most commercial wearable devices rely on fairly established sensing technologies such as rigid resistive strain gauges and optical goniometers,⁸ which can barely stretch. Due to this limitation, they are fundamentally ill-suited to be used on our soft bodies. Optical fibers, for example, have long been used in the medical field to measure joint flexion reliably. Although relevant for use in a controlled medical environment, optical fibers are brittle and require complex electronics,⁸ which are hardly compatible with more generalized technology use.

Similarly, traditional rigid strain gauges not only suffer from time-dependent creep and a nonlinear relationship between curvature and resistance change,⁹ but most importantly, they can only stretch up to a few strains, thus relying on additional device integration.¹⁰ Finally, piezoelectric sensors¹¹ and inertial measurement units (IMUs)¹² capture motion rather than displacement, making static finger configuration hard to estimate over time.

Soft materials provide an interesting opportunity to create new wearable systems that adapt and conform to user morphology and motions without hindrance, leading to comfortable, small-form factor devices. However, as evidenced by the lack of widely available commercial products, soft sensors are not yet a mature technology. There is still no clear consensus on which soft sensing technology is the most appropriate for strain measurement. The soft technologies that are proposed so far have suffered from either (1) poor sensor intrinsic performance or from (2) mediocre scaling capabilities.

This first limitation is simply technological. Diverse types of sensors have been proposed, demonstrating varying performance levels. Probably the most common type of soft sensor is the piezoresistive sensor. Soft piezoresistive sensors are based on soft polymers loaded with conductive particles and suffer from creep and hysteresis.¹³ Innovative approaches using carbon nanotubes¹⁴ or graphene¹⁵ have demonstrated high sensitivity but rely on advanced manufacturing techniques. Microfluidic channels filled with conductive liquids, shaped to resemble traditional resistive strain gauges, and encapsulated between soft polymer layers can perform well.^16,17 However, these sensors are vulnerable to punctures and interface delamination. Soft capacitive sensors commonly have outstanding linearity and low hysteresis but typically suffer from low sensitivity and time response.¹⁸ Recently, soft optical waveguides have been introduced^19–23 and, although very promising, can suffer from poor linearity²⁴ and are also rather bulky.

The second limitation plaguing soft sensing systems is related to the sensor system manufacture and scaling. The human hand possesses 24 degrees of freedom.²⁵ Fully capturing finger motion therefore necessitates numerous sensors. Even in a modular system where all sensors can be replaced, manufacturing and demonstrating the simultaneous use of multiple sensors are more challenging than a single soft sensor. Issues such as complex electronics, sensor cross-talk (bending and stretching), overall system bulkiness, and sensor interconnects are relatively common. However, having multiple sensors is vital to deploying soft systems for motion tracking in real-time applications.

In response to both these challenges, we propose to use an array of soft polymer acoustic waveguides (SPAWs). These soft sensors are placed on the back of a user's hand so as not to hinder motion and actions (Fig. 1). These soft polymer waveguides have recently demonstrated the capability to measure both strains and bending in a decoupled manner.²⁶ Because these waveguides are made using an unmodified elastomer recipe, they are softer and more cost-effective than comparable piezoresistive and capacitive particle-loaded composites. Compared with microfluidic resistive devices, these sensors are easier to manufacture and cannot leak.

FIG. 1.

The proposed array of SPAWs: (a) the SPAW and flexible PCB connectors for a single finger. The scale bar is 10 mm. (b) The assembled SPAW array. The scale bar is 15 mm. (c) The SPAW array worn by a user. The scale bar is 14 mm. PCB, printed circuit board; SPAW, soft polymer acoustic waveguide.

Recently, soft pneumatic actuators have been equipped with acoustic actuators to allow them some proprioception and tactile sensitivity.^27,28 The SPAWs presented in this article are somewhat similar to the soft optical fibers presented above, the main difference being the propagation speed of the signal relied upon. Acoustic waves propagate several orders of magnitude slower than light and thus can be measured using various time and frequency-based techniques with commonly available electronics. Thanks to this feature, we rely on a time-based measurement technique that necessitates a simple but effective method for accurate strain measurement and, thus, hand motion detection.

We will first detail the system design, fabrication, and operating principles, then characterize the SPAWs for strain sensing and finger angle estimation. Then, we will demonstrate the system's capabilities in the hand motion tracking application. We will conclude with a discussion on our current prototype's limitations and possible research avenues.

System Overview, SPAW Sensor, SPAW Array

System overview

The sensing system consists of 10 SPAWs placed on a user's hand (Fig. 1) and connected to an electronic subsystem that generates or acquires voltage levels. The subsystem includes flexible printed circuit boards (PCBs) used as connectors, six analog multiplexers (CD74HC4067; Texas Instruments), two MAX14808 (Maxim Integrated Products) acoustic pulser evaluation boards (Maxim Integrated Products), an Analog Digilent 2 device (AD2; Digilent), laboratory power supplies, and a computer (Fig. 2a).

FIG. 2.

The proposed system layout: (a) the main system components and signal flow of the SPAW-based hand motion detection. (b) The output voltage pulses for a single MAX14808 board for a group of five SPAWs. Only one channel of MAX14808 will be selected during each 200 μs, thus, one corresponding SPAW's transducer is excited. (c) The filtered analog signal collected by a single oscilloscope channel from the AD2. The signal is divided into five 200 μs intervals. AD2, Analog Digilent 2 device.

SPAW sensor

The SPAWs use a square profile with 1.7 mm sides and measure 30 mm in total length. The SPAW fabrication process includes transducer placement and molding (Fig. 3a). The dimension design and fabrication details are shown in Supplementary Data S1.

FIG. 3.

SPAW fabrication and strain sensing mechanism: (a) SPAW fabrication steps, (b) $T O F_{0}$ obtained at the SPAW's initial length l₀, (c) $T O F_{1}$ obtained when the SPAW was stretched by $Δ l$ .

The transducer (AM1.2 × 1.2 × 1.7D-1F; Tokin) is first excited by four consecutive 15 V square pulses (f = 980 kHz) from MAX14808, thus generating an acoustic pulse train. The voltage (15 V) was lowered compared to previous articles^26,29,30 to ensure increased user safety and transducer life span. The transducer's excitation then generates acoustic waves in the surrounding soft polymer. Due to the significant acoustic impedance mismatch at the polymer/air boundary, the acoustic waves are reflected within the SPAW. The waves travel along the length of the SPAW. Upon reaching the end of the SPAW, the acoustic waves are then reflected toward the SPAW's origin. At the SPAW's origin, the piezoelectric transducer, now serving as a sensor, outputs a voltage responding to its mechanical deformation.

Stretching the SPAW increases the distance between transducer and waveguide's end, thus changing the time for the acoustic waves to travel from and to the transducer (Fig. 3b, c). The time interval between the pulse train generation and echo's peak is the SPAW's time of flight (TOF). By measuring TOF, one can estimate the SPAW's length. This imaging scheme, by which a waveguide impedance change is detected based on wave travel time, is known as time-domain reflectometry (TDR).³¹ The transducer is used to generate and measure the reflected acoustic waves. This imaging scheme is commonly referred to as the “pulse-echo” setup.^26,32

SPAW strain ( $ε$ ) is computed as presented in Equation (1), where l₀ is the SPAW initial length and $Δ l$ is the SPAW's length increment. $T O F_{0}$ and $T O F_{1}$ indicate TOF for the unstretched and stretched SPAW, respectively. Assuming a constant wave group speed (v) through the SPAW,^33–35 the TOF difference and the strain are linearly related. $ε = \frac{Δ l}{l_{0}} = \frac{v (T O F_{1} - T O F_{0}) ∕ 2}{v T O F_{0} ∕ 2} = \frac{T O F_{1} - T O F_{0}}{T O F_{0}}$ (1)

SPAW array

SPAW array electronics

An array of 10 SPAWs is used, each fixed on each side of the user's metacarpophalangeal (MCP) and proximal interphalangeal (PIP) digit joints, as well as on the thumb interphalangeal (IP) and MCP joints (Fig. 1). The array's placement on the hand is detailed in Supplementary Data S1. The SPAWs' transducers excitation is generated using two MAX14808 boards. Each MAX14808 can only service a maximum of eight transducers; two MAX14808 boards are used, each controlling five transducers. When the transducers act as receivers, the received analog signals are routed through the MAX14808 boards and measured by each of AD2's two oscilloscope channels. Both signal generation to control the excitation pulse timing and the echo-received channel selection are realized using the AD2 digital output channels and through multiplexers (Fig. 2).

SPAW array signal processing

Each AD2 oscilloscope channel captures a group of five SPAWs' analog voltage signals during a 1024 μs long window, divided into five 200 μs long periods (Fig. 2b, c). According to the Nyquist-Shannon theorem,³⁶ the sampling frequency (8 MHz) is sufficient. The digital data are delivered to a computer, where a real-time Python algorithm filters the signal (Chebyshev bandpass filter, fourth-order, 500 kHz to 4 MHz) with the SciPy package for Python.³⁷ The signal envelope was obtained by performing a Hilbert transformation^38,39 and used to detect the main acoustic peak.

The system's imaging frequency is estimated by timing the various steps required during the system operation. Given an elongated SPAW (100%), the pulse-echo time is ≈162.55 μs. Regarding electrical signal travel time, the AD2 data sampling and transferring time are about 1.5 ms. Python algorithm signal processing takes ∼12 ms (using an i7-8550U CPU), yielding a total acquisition and signal processing time of about 13.5 ms. We ensure a stable frame rate and longer transducer lifetime by adding a dead time of 6.5 ms. Consequently, the user's hand motion is estimated precisely every 20 ms, leading to an imaging frequency of 50 Hz. This has been further verified in the dynamic tensile test.

SPAW Characterization

Experiments were conducted to characterize the SPAWs' strain-sensing performance in hand motion detection. First, a SPAW was evaluated using a quasi-static tensile test, then a dynamic tensile test, and finally a tensile durability test. These results demonstrated SPAWs' stretchability, extreme durability, high linearity, and great repeatability. Second, a SPAW was positioned on a finger and its joint rotation tracking performances were evaluated, demonstrating SPAWs' high accuracy and good repeatability for hand motion tracking.

Quasi-static tensile test

A quasi-static tensile test was first conducted to demonstrate SPAWs' sensing capabilities and overall softness. The test setup is detailed in Supplementary Data S1.

Results show that stable echo signals were detected up to 100% strain, demonstrating the SPAW's high stretchability. When used as strain sensors, SPAWs' average echo TOF demonstrates low hysteresis (Fig. 4a). The bottom graph shows SPAW stress, establishing SPAW softness. The difference in hysteresis between the top and bottom graphs is significant in Figure 4a. Indeed, the TOF largely depends on SPAW longitudinal geometry, while its stress is due to polymer viscoelastic behavior.⁴⁰ This distinction is crucial since (1) it is well-known that soft elastomers often exhibit hysteresis, and (2) soft sensor measures are often coupled with the adopted materials' mechanical characteristics, such as in reported sensors.^41–43 By relying on SPAW geometry and selecting an ideal range of operation in which SPAW shape recovery is rapid for motion tracking, we mitigate measurement hysteresis, whose max value is 0.7410% under strain of up to 100%.

FIG. 4.

Experimental results for SPAW strain sensing. (a) The average TOF, stress, force, and corresponding standard deviations (error bars) for a SPAW under 10 consecutive quasi-static tensile tests. The SPAW's operational range, corresponding to a sensing region of improved linearity, is indicated by the light gray rectangle region. (b) SPAW TOF variation from 0% to 65% strain and under various cycling speeds (5, 10, 15, 20, 25, 30 mm/s). (c) SPAW TOF as a function of strain for the 10th cycle and under various cycling speeds (5, 10, 15, 20, 25, 30 mm/s). (d) Segments of TOF variation over 100,000 cycles from 0% to 65% strain and at a cycling speed of 30 mm/s. Magnified views of some cycles from each segment are on the upper part. (e) Detailed TOF versus strain curves at cycle number 1, 10, 10², 10³, 10⁴, 5 × 10⁴, and 10⁵, using cycling speeds of 30 mm/s. TOF, time of flight.

The TOF standard deviation is small (Fig. 4a), demonstrating excellent repeatability. It is worth mentioning that the most significant TOF deviation happened at 0% strain. TOF at 0% in the first stretching cycle was 73.19 μs but increased to 76.09 μs by the 10th cycle. This phenomenon can be explained by a slight increase in SPAW length at rest, due to the viscoelastic behavior of Ecoflex0010.

Using SPAW's TOF yields strain measures with negligible hysteresis and outstanding repeatability. This is mainly due to ultrasonic waves' stable propagation and reflection, allowing for easy and reliable peak detection.

The coefficients of determination (R²) at the full 0–100% strain range during SPAW stretching and releasing were 0.9968 and 0.9964, respectively (Fig. 4a). It is worth mentioning that in the 5–100% strain range, highlighted with the gray rectangle region, the linearity is improved to 0.9975 during both stretching and releasing cycles. Using a small prestrain (5%) allows the sensor to be operated within a zone with improved linearity. The slight nonlinearity in the measured data is likely because of a slight change in the wave group velocity during the waveguide strain.³³ Given our current model's simplicity and accurate results, we did not seek a more complete model, which could be done in future work if relevant.

Dynamic tensile tests

The SPAWs' capabilities under higher strain rates, such as those encountered during finger motion, have not yet been studied. Consequently, we devised three experiments to evaluate SPAW's dynamic measurement, including a cyclic stretching-releasing test at comparably high strain rates, a stair stretching-releasing test, and a sudden stretching-releasing impact test.

Cyclic stretching-releasing test

Before running the experiment, we chose six testing strain rates designed to mimic everyday hand motion, from slow to fast: 5, 10, 15, 20, 25, and 30 mm/s using the estimation (Supplementary Data S1).

The SPAWs exhibit excellent strain detection repeatability regardless of the strain rate (Fig. 4b). The SPAWs' hysteresis is negligible even at high strain rates and after 10 cycles (Fig. 4c).

Similarly to the quasi-static test, SPAWs display a region of lower linearity at low strains. Consequently, SPAWs' full range strain sensing linearity is degraded. However, using SPAWs in a slightly reduced strain range (5–65%) significantly improves performance. The measured strain R² values are 0.9977, 0.9973, 0.9975, 0.9975, 0.9983, and 0.9979, when elongating the SPAW, and under 5, 10, 15, 20, 25, and 30 mm/s, respectively. Similarly, during the relaxation cycle, the measured R² values are 0.9981, 0.9981, 0.9981, 0.9972, 0.9981, and 0.9976, respectively.

An interesting phenomenon occurs at relatively low strain rates (5 and 10 mm/s). Due to the use of a lower cycling rate and an equivalent data acquisition rate, the obtained data have higher spatial accuracy. A discrete TOF increment is observed during SPAW elongation and relaxation cycle. The TOF increment is very consistent and measures about 1.2 μs. This can be seen in Figure 4c as a “stairs-like” structure. This is likely due to the complex interaction between the acoustic wave and the soft continuously deforming waveguide. We expect this phenomenon to exist at all rates to some extent but is likely more significant at low strain rates where polymer viscoelasticity and acoustoelasticity impact SPAWs. A complete model and explanation of the phenomenon are beyond the scope of this article but will be investigated in future work.

Moreover, a dynamic characterization for the array of 10 SPAWs was performed to better verify the system's imaging frequency. The experimental setup was the same as in the one SPAW's dynamic tensile test mentioned above. An array of 10 SPAWs were stretched simultaneously by 5 mm at a stretching-releasing rate of 30 mm/s (Supplementary Movie S1). The TOF data were recorded in real time using Python script. Among the 10 SPAWs, 1 typical SPAW's TOF data (Supplementary Fig. S2 in the Supplementary Data S1) demonstrated that the system imaging frequency is 50 Hz (20 ms) under our system design.

Stair and abrupt stretching-releasing tests

Two additional tests have been conducted to further validate the dynamic performance of the SPAW. The results obtained from these tests provide additional evidence of the SPAW's exceptional dynamic stability and fast response (Supplementary Figs. S3 and S4 in the Supplementary Data S1). Furthermore, it is worth noting that no creep was observed in the SPAW during the experiments. This can be attributed to the stable propagation and reflection of ultrasonic waves, facilitating easy and reliable peak detection. This characteristic sets the SPAW apart from resistive and capacitive soft strain sensors. Moreover, the SPAW's TOFs at a specific strain level remained unchanged throughout the stair stretching-releasing test, consistent with the findings from previous experiments (Fig. 4a, c, e). This observation strongly supports the assertion that hysteresis is negligible in the SPAW. Other details regarding the tests have been added to Supplementary Data S1.

Durability tensile test

It is well-known that repeated motion over many cycles can cause fatigue and breaks in sensors. However, numerous applications will require motion capture over long periods. To demonstrate SPAWs' real-life capabilities, a durability test was devised.

A SPAW was continuously stretched and released with a speed of 30 mm/s, from 0% to 65%, for over 100,000 cycles. SPAWs can accurately measure strain over at least 100,000 cycles without breaking (Fig. 4d). SPAWs' extreme resilience is partly due to the soft silicone elastomer's extreme softness and the manufacturing method's extreme simplicity.

We quantify the differences in TOF measured at various cycle numbers during the durability test (Fig. 4e). Two important observations are made: (1)

The TOFs during elongation and relaxation for the 1st, 10th, 100th, 1000th, 10,000th, 50,000th, and 100,000th coincide closely. This testifies to SPAWs' outstanding long-term repeatability.

(2)

Some residual SPAW elongation is observed below 10% strain, rising rapidly during the first thousand cycles. The residual increment in SPAW length is insignificant at higher cycle numbers.

The SPAW residual length increment is attributed to viscoelastic behavior. This diminishes the SPAWs' linearity over the full strain range. However, a simple 10% prestretch of SPAWs allows us to use the sensors in a region of operation that is extremely repeatable and remarkably linear. In that region (10–65% strain) during elongation, the measured R² values are 0.9983, 0.9982, 0.9980, 0.9982, 0.9978, 0.9978, and 0.9975 for 1st, 10th, 100th, 1000th, 10,000th, 50,000th, and 100,000th, respectively. In the same region and during relaxation, the measured R² values are 0.9990, 0.9986, 0.9978, 0.9977, 0.9977, 0.9976, and 0.9974, respectively.

Continuous finger joint angle estimation test

Previous experiments also show SPAWs' great performance in strain sensing. Moreover, in line with previous research,^44–46 we chose to model the finger PIP and MCP joints as cylindrical joints (Supplementary Data S1), which can demonstrate that SPAWs have great potential for accurate and simple joint angle estimation and, thus, hand motion tracking. Therefore, SPAWs' finger motion detection performance needs to be further validated.

Experiment protocol

A user's finger joint was tracked simultaneously using a single SPAW and a state-of-the-art optical tracking system (Vicon, OML, Oxford, United Kingdom). Vicon is famously accurate even at a high frame rate and routinely used for human motion tracking.^47–49 Five Vicon cameras were used to record finger motion using three markers, each being 6 mm in diameter.

We recorded the users' index finger MCP and PIP joints (Fig. 5a).⁵⁰ Flexion–extension rates were separated into three levels corresponding to humans' daily life habits:^51,52 slow (<20°/s), medium (30–60°/s), and fast (>90°/s) rate. The span of the subjects is significant for testing the influence of finger size. Thus, five subjects (three males [subjects 1, 2, and 3] and two females [subjects 4 and 5]) with distinctive index finger lengths (Distance measured from the top of fingertip to MCP joint: subject 1:10.5 cm; subject 2: 11.2 cm; subject 3: 9.3 cm; subject 4: 7.8 cm; subject 5: 7.4 cm) were enrolled. Subjects also assessed their finger locomotion before the experiment to ensure their fingers could move freely. The subjects' index finger sizes were measured according to clinical guidelines and the measuring critics following that in literatures.^50,51 Moreover, they do not suffer from any finger disease and can freely control their finger joint movement. Ethical Approval and Consent to Participate have also been obtained. The experiment step is detailed in Supplementary Data S1.

FIG. 5.

Continuous finger joint angle estimation experiment. (a) Details of marker and SPAW positioning on the MCP joint (upper left: straight finger; upper right: bent finger) and PIP joint (lower left: straight finger; lower right: bent finger). The scale bar is 12 mm. (b) One trial's experimental data of MCP flexion angle estimated by both the Vicon system and the SPAW, as well as corresponding absolute error and SPAW strain levels. The three flexion rates are presented (data from subject 1). (c) One trial's experimental data of PIP flexion angle estimated by both the Vicon system and the SPAW, as well as corresponding absolute error and SPAW strain levels. The three flexion rates are presented (data from subject 1). (d) Eight trials' average RMSE and standard deviation of each subject at different flexion rates. MCP, metacarpophalangeal; PIP, proximal interphalangeal; RMSE, root-mean-square errors.

Experimental results

Data processing is detailed in Supplementary Data S1.

The finger flexion root-mean-square errors (RMSE) between the Vicon and SPAWs were calculated for each trial, and the maximum absolute error among all five trials' data at each flexion rate is presented in Table 1. Notably, the maximum error consistently remains relatively low among users, demonstrating the SPAW's capability for sufficient continuous tracking. The experimental data excerpts are shown in Figure 5b and c, displaying the SPAW strain levels.

Table 1.

The Max Estimated Index Metacarpophalangeal and Proximal Interphalangeal Angle Errors (Degrees)

	MCP			PIP
	Slow	Medium	Fast	Slow	Medium	Fast
S1	3.74	3.85	4.52	3.77	4.12	4.48
S2	3.59	3.99	4.76	3.76	4.21	4.54
S3	3.11	3.30	4.03	3.91	4.34	4.24
S4	3.20	4.01	4.65	3.62	3.85	3.99
S5	3.78	4.59	4.56	3.79	4.40	4.65

S1, S2, S3, S4, and S5 stand for subjects 1, 2, 3, 4, and 5, respectively.

MCP, metacarpophalangeal; PIP, proximal interphalangeal.

The average estimated angle of RMSE is within 2.00°, with a standard deviation below 0.40° for each subject and each flexion rate, indicating the high consistency of measures obtained using the SPAW system (Fig. 5d). A one-way analysis of variance test was performed to evaluate the variation of RMSE across all subjects and at different flexion rates. The results indicate that, at all flexion rates, the p-value (>0.05) validates the lack of statistical difference in SPAW performance among various users, indicating the versatility and adaptability of the SPAW array across a diverse range of users.

It is noteworthy that the flexion rate significantly impacts accuracy. Specifically, the maximum error tends to increase with higher finger motion speeds. This phenomenon can be attributed to the vibration of markers as fingers move,^53,54 causing the angles measured by the Vicon system to vary more as flexion speed increases. When examining the error distribution, discrepancies between the SPAW and Vicon systems are observed around the minimum and maximum flexion angles. This can be attributed to skin slip, which becomes more pronounced at extreme angles.^49,55

Application for Hand Motion Tracking

A first static hand gesture test was performed to demonstrate the system's ability to capture static positions. A subject was asked to perform 20 different preselected hand gestures from American sign language while wearing an array of 10 SPAWs (Fig. 6a). We measured the user's MCP and IP joints of the thumb and the other fingers' MCP joints and PIP joints. The SPAWs were attached to fingers with a 5% prestrain. The selected hand gestures are the 10 first digits (0–9), 9 alphabet letters (A, B, C, I, J, L, U, X, and Y), and the sign for “I love you.” The subject performed each gesture for about 5 s and quickly switched to another one. All the signals were steady and output distinctive differences under different finger states, demonstrating the system's stability and reliability for hand motion detection (Fig. 6b, c).

FIG. 6.

Hand motion tracking application. (a) The American sign language gestures for selected digits, alphabet letters, and the expression for “I love you.” The scale bar is 32 mm. (b) The corresponding SPAW TOF when performing American gestures of digits with about 5 s for performing each gesture. (c) The corresponding SPAW TOF when performing American gestures of alphabets and the expression for “I love you” with about 5 s for performing each gesture. (d) A picture shows the 3D virtual hand and its interaction with the real-human hand wearing the device. The scale bar is 30 mm. 3D, three-dimensional.

To demonstrate the system's ability to track the user's hand in real-time, a three-dimensional (3D) virtual hand was developed based on the work⁵⁶ using the Unity 3D game engine (Unity Technologies) (Fig. 6d). Ten of the modeled virtual hand joints are directly controlled by the 10 corresponding SPAWs. The user monitored joints are the MCP and IP thumb joints and the other fingers' MCP and PIP joints. Based on previous work, the Distal interphalangeal (DIP) finger joint angle was determined synergistically as 2/3 of the same finger's PIP joint angle.^57,58 Thus, 14 joints were actuated on screen. The SPAWs were attached to fingers under a 5% prestrain.

A two-step calibration was then conducted. First, the user was instructed to extend his fingers fully, and the captured angles were considered to correspond to joint angles of 0°. Then, user's fingers were recorded when maximally bent. The SPAW data were matched with joint angles previously recorded using a goniometer (187-101; Mitutoyo): the joint was positioned and stabilized correctly, and the joint's two ends and rotation center were determined. Then the goniometer was aligned according to the determined ends and center. Later we read the measuring instrument properly and obtained the joint angles. A linear fit was made using both extremum values and used to determine the joint angles at a given time. TOFs data were captured using the AD2-Python application programming interface and connected to the Unity 3D game engine with a C# script through user datagram protocol (UDP). The result of a user wearing the SPAW array can be seen in Supplementary Movie S2. The prototype demonstrated continuous real-time hand motion tracking with little delay, glitches, or erroneous finger position visually.

Discussion and Conclusion

Our laboratory's first work²⁶ focused on exploring and proving the waveguide's multimodal sensing ability. Strain sensing was not fully studied, and its application in hand motion tracking was not explored. Therefore, we have characterized SPAWs in strain sensing more comprehensively and exploited more potentials of SPAWs to measure strain. More exciting results have then been shown for hand motion detection in this article. More specifically, here are several main differences from our previous work: (1) The pulse voltage used here is 15 V (100 V previously), targeting the wearable application. (2) The pulse-echo technique is adopted here, reducing the transducer number to one. (3) The Ecoflex0010 elastomer with lower Young's modulus is chosen as the waveguide material in this work.

In this article we detailed the design, fabrication, and use of an array of stretchable strain sensors for hand motion tracking. Based on a novel acoustic sensing mechanism, SPAWs boast great linearity (R² > 0.996), ultra-low hysteresis (<0.7410% under strain of up to 100%), high stretchability (up to 100%), outstanding durability (>100,000 cycles), great repeatability, and dynamic response (<20 ms). When worn, the SPAWs could track finger angles with average RMSE smaller than 2.00° and max angle error of 4.76° among all subjects and under varied flexion-extension rates. Designed to be worn by the user, the device is soft, lightweight, and does not suffer from limitations such as optical occlusion.

SPAWs do not require cleanroom facilities or complex manufacturing processes, making them accessible and inexpensive to manufacture. Moreover, the measuring process and electronics used are inherently scalable. This is particularly attractive compared to most previously reported micro/nano-polymer, fiber, or hydrogel-based strain sensors,^59–61 and only further their relevance to the soft wearable and motion capture industries.

The work and results will serve as a foundation for exploring potential solutions to existing barriers in hand motion detection for virtual reality entertainment and clinical applications. They will also provide crucial insights for the design of soft, wearable prototypes as a part of an ongoing effort to develop soft sensors using both time and frequency domains to extract decoupled signals from simple sensing structures, representing a novel and promising path toward soft, simple but effective, wearable sensors. Furthermore, SPAW strain-sensing performance, SPAW array electronics, and a generalized framework will be discussed in the following parts.

SPAW strain-sensing performance

Table 2 compares our SPAWs' performance against that of other reported representative stretchable strain sensors. Resistive strain sensors commonly suffer from high hysteresis and poor linearity because of the intrinsic resistive response of soft materials, unstable connection upon stretching/releasing loads, or irreversible crack generation in conductive films.¹⁸ Furthermore, capacitive strain sensors possess better linearity and low hysteresis based on the more reliable geometrical effect. Research has also introduced micro/nanomaterials into a soft substrate and adopted advanced fabrication techniques to improve strain-sensing performance in some aspects or others. For instance, Tang et al. reported a highly stretchable (600%) resistive core-sheath fiber-based strain sensor using wet-spinning.¹⁴ Wu et al. proposed a resistive strain sensor with improved hysteresis and linearity using a maze-like vertical graphene network.⁴¹ An ionic nanocomposite-based capacitive strain sensor reported by Xu et al. exhibited excellent stretchability up to 1000%.⁶⁴

Table 2.

Performance Comparisons to Representative Stretchable Strain Sensors

Sensing principles	Stretchability (%)	Hysteresis	Linearity	Durability	References
Resistive	100	High	Two linear regions	6000	⁶²
	12	Unknown	Poor	1000	¹⁵
	1000	Unknown	0.97327 (0–600%)	>250	⁶³
	120	Negligible	0.99 (0–120%)	1000	⁴¹
	600	High	Two linear regions	10,000	¹⁴
Capacitive	1000	Low	Multiple linear regions	1000	⁶⁴
	300	Negligible	0.993	1000	⁶⁵
	50	Low	High	Unknown	⁶⁶
	100	Negligible	0.998 (0–100%)	3000	⁶⁷
Inductive	100	Negligible	Poor	Unknown	⁶⁸
Optical	100	Negligible	High	6000	⁶⁹
	300	High	Poor	100	²⁴
	100	Negligible	>0.999	Unknown	⁸
Acoustic	100	Negligible	>0.996	100,000	This work

However, some other performances might have been sacrificed, and the increasing complexity of fabrication and cost of materials further limit their widespread application. Recently, Xing et al. introduced a novel inductive-based strain sensor using a mechanical spring and achieved ultra-low hysteresis even though its linearity was insufficient.⁶⁸ Optical strain sensors have recently gained significant interest with outstanding linearity for Fiber Bragg Grating-based sensors and high stretchability⁸ for light transmittance-based sensors.⁶⁹ The SPAW we reported in this article has overall high performances, especially hysteresis and durability, mainly due to the simple material used and reliable ultrasonic propagation, which is intrinsically different from other reported strain sensors.

The max hysteresis is 0.7410% under strain of up to 100%, which is ultra low.¹⁸ The corresponding finger joint angle error the max hysteresis brings is about 1.4° (under the case of Subject 1), which is quite small and acceptable in our applications.^46,70,71 Therefore, in the current applications, there is little need to compensate for it. TOF significantly relies on the SPAWs' longitudinal geometry making the hysteresis behavior of SPAWs quite distinctive from other reported soft strain sensors whose hysteresis is mainly due to the inherent viscosity behaviors of the soft substrates and/or the interconnection between the soft matrix and the active materials. Therefore, the stable propagation and reflection of ultrasonic waves are the keys to realizing SPAWs' negligible hysteresis, allowing for reliable detection of echo peaks. So any undesired circumstances affecting the ultrasonic waves' propagation and reflection may impact the SPAWs' strain measurement accuracy and hysteresis:

(1)

Temperature fluctuations will alter the moduli of the waveguide material and subsequently bring propagating velocity changes,^33,72 which might cause different peak detection values under the same strain levels. Even though a dramatic temperature change or unbonded situation rarely occurs during the daily use of SPAWs, prevention and compensation should also be made to further extend its applications with higher hysteresis and accuracy requirements. Temperature-insensitive soft materials can be selected to fabricate waveguides and temperature compensation methods, such as integrating temperature-controlling modules within the waveguide to get uniform waveguide temperature, and the TOF can be amended using compensation algorithms if temperature changes.

(2)

The bonding robustness at the interface between the transducer and the waveguide will affect the transmission ratio, making the transmitted energy change, and subsequently might influence the peak detection. In the worst-case scenario, the transducer gets unbonded with the waveguide, making the SPAW fail to measure strain. The bonding strength at the transducer/waveguide interface will be more robust if the mechanical impedance difference is smaller.⁷³ So particle-filler composites as the waveguide material or a matching layer using a particle-filler composite will improve the bonding robustness.

Indeed, another concern one may raise is that the strain mismatch resulting from using common wearable devices, such as electronic skin, with human skin can lead to discomfort for users due to differences in Young's modulus or stiffness.⁷⁴ Although the Ecoflex series soft polymers have Young's modulus that is very close to that of human skin, it is important to clarify that our SPAWs are not directly attached to human skin. Instead, we have implemented a design where the SPAW unit is lifted by a spacing cylinder, with front and end elastic pads in place. This configuration creates a small gap between the SPAW and the human skin, alleviating concerns about discomfort caused by strain mismatch. And the SPAWs being at a distance from the joint mechanically increase the resulting SPAW strain compared to the skin strain. The decision to introduce this design was primarily driven by the need to address acoustic signal loss that may occur if the SPAW is attached directly to the skin.

However, it is worth noting that for better adhesion stability, it would be preferable to have the SPAW fully attached to the skin without any air gap. To achieve this, stretchable foam can be used in future iterations of the design, which would minimize acoustic energy loss. In addition, exploring softer materials with Young's modulus similar to that of human skin can enhance the wearability and comfort when wearing the SPAWs. By addressing these considerations, we aim to provide reassurance to users regarding any potential discomfort arising from strain mismatch while also acknowledging areas for future improvement in terms of adhesion stability and comfort during prolonged usage.

SPAW array electronics

A sampling frequency of 3 MHz can already ensure a complete capture of echo signal (Supplementary Fig. S6 in the Supplementary Data S1). Besides the Nyquist–Shannon theorem, the reason for choosing 8 MHz in this article is to let a single sampling of AD2's one oscilloscope channel just completely collect the signals from a group of five SPAWs (Sampling No. 8192, so each AD2 oscilloscope channel captures a group of five SPAWs' analog voltage signals during a 1024 μs long window [8192/8 = 1024], divided into five 200 μs long periods, then each period can fully cover one SPAW's TOF during stretching).

The SPAW array electronics used here can track hand motion tracking with high performance but are currently not portable. Therefore, it is of high importance to minimize the whole system into a wireless and portable one. Although our efforts focused on the SPAWs' compactness and cost-effectiveness rather than on the associated electronics, it should be noted that replacing the AD2 digital oscilloscope and integrating the various development boards (Max14808) on a custom PCB using a single field programmable gate array (FPGA) would lead to reduce costs and size, while improving performance.

After processing, the data can be transmitted wirelessly (through Wi-Fi or Bluetooth) to any host machine for storage or further analysis to develop applications. Several portable ultrasonic systems have been successfully developed, offering us useful related information and knowledge to make the SPAW array electronics portable and wireless. Yang et al. developed an ultrasound system (132 × 90 × 30 mm and 190 g) with a 40 MHz sampling rate and up to 100 Hz imaging frequency.²⁹ Yin et al. also designed a portable system (65 × 75 × 25 mm and 85 g) with a 5 MHz sampling rate and 70 ms response/imaging time.³⁰

Generalized framework and future work

We constructed a generalized framework in terms of the basic theories and methods for creating the SPAWs, and using them in other applications (Supplementary Fig. S7 in the Supplementary Data S1). The frame contains four modules: electronics, waveguide, signal, and wearable applications. The main functions of the electronics module are to generate ultrasonic vibration and to receive the echo. Usually, the ultrasonic vibration source and the detector can be integrated into one element, such as the piezoelectric transducer used in this work. In the waveguide module, different structures and materials will achieve various outcomes of TOF, attenuation, dispersion effect, and energy. A theoretical model is supposed to more effectively and efficiently guide waveguide design. Then, in the signal module, more algorithms can be introduced to extract features after basic signal processing and are ready for further input to the wearable applications, including facial expression, arm motion, hand motion, knee motion, and foot motion detection.

We have also included simple signal demonstrations in Supplementary Figure S8 in the Supplementary Data S1 to showcase the SPAW's capability for monitoring other parts of human motion. These additional illustrations aim to better highlight and validate the potential of the SPAW in wearable sensing. However, we acknowledge that further in-depth analysis is required, along with modifications and optimizations of the SPAW's structures and algorithms, to achieve more precise tracking of other human motions.

In the future, longer SPAWs may be required to measure other body parts' motion. To that extent, using different elastomers or creating composite structures, one might trade off system performance, softness, and manufacturing complexity. An obvious example would be creating an impedance matching layer⁷⁵ at the transducer's surface, potentially increasing the transducer/waveguide transmitted energy, but complexifying the device manufacture. Such an avenue is also a good candidate for either analytical or numerical modeling methods^76,77 to save time and optimize design parameters. Multiple echoes from a single emitter source may also open the path to multijoints with a single SPAW. Although this requires a high signal-to-noise ratio, it may also lead the way into multiaxis sensing and/or simplified electronics.

Moreover, there are two other exciting but challenging research domains about the SPAW. They are both quite challenging in-depth and worth exploring.

(1)

Theoretical modeling of the ultrasonic propagation, attenuation, and dispersion inside soft small-size isotropic waveguides. The theoretical model can guide SPAW structure design and provide abundant in-depth information about echoes for further signal analysis.

(2)

The current SPAW can only measure the strain in the longitudinal direction. The strain measurement in any direction within a plane can be potentially achieved using the electronic skin based on acoustic waveguides. Therefore, how to make the waveguide into a two-dimensional structure or the electronic skin is a promising research direction.

Ethical Approval and Consent to Participate

All study participants signed an informed consent form. Research protocols were conducted in accordance with the Declaration of Helsinki. Personal information and samples were deidentified and analyzed anonymously.

Availability of Data and Materials

The data generated during the current study are available from the corresponding author upon reasonable request.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant 52250610217.

Supplementary Material

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Supplementary Material

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