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2022-10-22 21:19:08 By : Mr. Jason Lee

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Scientific Reports volume  12, Article number: 1690 (2022 ) Cite this article

We present a miniaturised thermal acoustic gas sensor, fabricated using a CMOS microhotplate and MEMS microphone. The sensing mechanism is based on the detection of changes in the thermal acoustic conversion efficiency which is dependent on the physical properties of the gas. An active sensing element, consisting of a MEMS microphone, is used to detect the target gas while a reference element is used for acoustic noise compensation. Compared to current photoacoustic gas sensors, our sensor requires neither the use of gas-encapsulated microphones, nor that of optical filters. In addition, it has all the benefits of CMOS technology, including production scalability, low cost and miniaturization. Here we demonstrate its application for CO\(_2\) gas detection. The sensor could be used for gas leak detection, for example, in an industrial plant.

Gas sensors play an increasingly important role in environmental monitoring due to elevated levels of atmospheric pollutants in urban areas, or the need for the safety monitoring of numerous industrial processes1,2. These requirements have fueled the demand for robust, low-cost, gas sensors that can detect hazardous levels of pollutants, including nitrogen dioxide (NO\(_2\) ), carbon dioxide (CO\(_2\) ) and volatile hydrocarbons such as benzene (C\(_6\) H\(_6\) )1,2. Current gas sensing technologies utilise a range of transduction effects, including gas-induced changes in the electrical, optical, physical and thermal properties of materials. Each technology has performance advantages/disadvantages specific to the detection of individual analytes, with no one universal approach1,2. A widely used sensing technology is the chemiresistor which utilises changes in the electrical conductivity of a semiconducting metal oxide (MOx) layer when it is exposed to an oxidising or reducing gas. These types of sensors are commonly used in low-cost, low-power applications, including portable air conditioning units3. Chemiresistors offer high sensitivity to organic compounds, however, they have several disadvantages including poor selectivity, environmental drift/poisoning and are insensitive to CO\(_2\) 4. Optical sensors (including photoacoustic) can address some of these limitations, and are the tool of choice for monitoring CO\(_2\) , as well as a range of other gases5. Their operating mechanism is typically based on the detection of absorption lines in the mid-infrared (MIR) spectrum. They have enhanced selectivity compared to other approaches6 but are currently challenging to implement in a cost-efficient manner at chip-scale5. More recently, inexpensive alternatives have been reported based on CMOS thermal conductivity sensors which exploit changes in the thermal conductivity of the gas7,8.

Thermal acoustic systems are used to generate acoustic waves in a gas9. The effect was first investigated by F. Braun10 in 1898, who discovered that the electro-thermal modulation of a conductor could produce an acoustic wave in the surrounding air. An early example of such a device is the thermophone, developed in 1917 by H. D. Arnold and B. Crandall11, whose work helped establish the first theoretical understanding of its operation. Thermal acoustic systems are typically modelled as an electrically conducting plate, electro-thermally modulated by an alternating (AC) current12,13,14. These periodic electrical changes were thought to cause periodic fluctuations in the plate’s thermal energy and modulate the temperature (T [K]) of an air pocket adjacent to the plate in proportion to the periodical flow of heat (\(\frac{Q}{\Delta t}\) [\(\mathrm {\frac{J}{s}}\) ]). The contraction and expansion of air molecules in the heated zone was primarily attributed to the generation of an acoustic wave12,13,14. More recently, Daschewski15 has suggested that the thermal acoustic effect is caused by the exchange of momentum between the thermally modulated plate and gas molecules (rather than thermal expansion), with the molecules being rapidly ejected away from the thermally excited surface. To maximize the thermal-acoustic conversion efficiency (i.e. the ratio of acoustic to thermal power), it is important to minimize the thermal capacity (C [\(\mathrm {\frac{J}{K}}\) ]) of the heat source12,13,14,15. Early approaches used freestanding metallic films and more recent approaches have used other types of structure, including ultra thin metallic films supported with porous silicon16 or CNT layers17. However, some of these approaches present manufacturability challenges and are not scalable.

In practical applications, thermal acoustic systems have previously been used as transducers and as components to convert thermal acoustic power into electrical energy18, with their thermal-acoustic conversion efficiency known to be influenced by the thermophysical properties of the gas12,13,14,15. However, little work has been done to study their application as actual gas sensors, including, e.g., for CO\(_2\) gas sensing. CO2 is an asphyxiant gas, widely used in industrial processes and exposure to CO2 concentrations greater than 7% (70,000 to 100,000 ppm) may cause suffocation and unconsciousness within a few minutes to an hour. In this paper, we describe a miniaturised thermal acoustic sensor which utilizes a CMOS-based microhotplate chip and MEMS microphone and demonstrate its application for CO\(_2\) gas sensing. The sensor benefits from the use of CMOS technology which offers excellent manufacturing scalability, low-cost and low-power consumption19.

Device fabrication. (a) Structure of the CMOS microheater chip (not to scale) which employs a tungsten (W) heating element embedded in a \(\sim\) 4.6 \(\upmu\) m thick silicon dioxide (SiO\(_2\) ) membrane formed by deep reactive ion etching. A thermal diode is embedded in the centre of the heated membrane for temperature monitoring. (b) Optical image of the CMOS microheater chip, showing the multi-ring W heating elements and metal heatspreading plates embedded within a SiO\(_2\) membrane. Chip size = 1.08 mm \(\times\) 1.08 mm. (c) Temperature-power characteristics of the microheater up to 450 \(^{\circ }\) C at 60 mW. Inset: hotplate structure. (d) Schematic diagram showing the sensor’s construction. The microheater chip is mounted above the port of a MEMS microphone (TDK model ICS-40300) with a thermal acoustic cavity formed by the etched Si substrate. (e) Optical image of the fabricated thermal acoustic sensor, showing the microheater chip mounted on the MEMS microphone using die bonding film. The opening between the bonding films, to allow gas to diffuse into the thermal acoustic cavity, is visible (dark area).

Our miniaturised thermal acoustic gas sensor uses an in-house designed CMOS-based micro-hotplate chip, fabricated at a commercial MEMS foundry. A cross-section of the chip (not to scale) is shown in Fig. 1a, consisting of a circular 4.6 \(\upmu\) m thick SiO\(_2\) membrane (600 \(\upmu\) m diameter), with an embedded tungsten (W) microheater (300 \(\upmu\) m diameter). Tungsten metallisation is chosen due to its very high melting point (3400 \(^{\circ }\) C) and low susceptibility to electromigration, thus ensuring stable electro-thermal performance19,20. The heater track has an electrical resistance of 39 \(\Omega\) at room temperature. The membrane is formed by deep reactive ion etching (DRIE) and thermally isolates the heater from the Si substrate. The microheater chip also incorporates an p\(^+\) –n\(^+\) junction thermal diode, embedded in the SiO\(_2\) membrane, which is used to monitor the operating temperature. The forward bias voltage of the diode has a linear response to temperature to over 600 \(^{\circ }\) C21, with a temperature coefficient of − 1.34 mV/\(^{\circ }\) C. Figure 1b shows an optical image of the fabricated chip, showing the meandering heater track design (chip dimensions: 1.08 mm \(\times\) 1.08 mm \(\times\) 0.38 mm). The temperature-power characteristics of the heater are shown in Fig. 1c, determined by the thermal diode. The heater reaches a temperature of 300 \(^{\circ }\) C at an operating power of only 38 mW, and is characterised by a fast (\(\sim\) 9 ms) thermal time constant20.

To construct our sensor, we mounted the microheater chip above the port of an analogue MEMS microphone (TDK model ICS-40300), in a simple, miniature (non-resonant) configuration5, as depicted in Fig. 1d. The microphone has an extended frequency response of 6 Hz–20 kHz and a signal-to-noise ratio (SNR) of 63 dBA. Die mounting pads were used to mechanically secure the microheater chip to the microphone’s substrate. An acoustic cavity is thereby formed between the etched membrane of the microheater chip and the microphone port. To allow gas to diffuse into the cavity, a small opening (dimensions: \(\sim\) 500 \(\times\) 50 \(\upmu\) m) was created between the die mounting pads. For characterisation, both the microheater and microphone were mounted on a TO-8 metal package. An optical image of the fabricated sensor is shown in Fig. 1e.

Sensor interfacing. (a) Block diagram of the experimental setup. The microheater is electrically modulated using a custom current drive circuit. Signals from the active and reference MEMS microphones are amplified and their differential signal digitised using a National Instruments data acquisition unit, with a software based lock-in amplifier used to help remove noise. (b) Modulated acoustic signal showing the pressure changes which occur during electro-thermal modulation of the sensor at a frequency of 43 Hz. (c) Acoustic frequency response of the sensor, showing the rise in the acoustic signal with modulation frequency and gradual tail off in the response due to thermal inertia of the membrane which limits the thermal modulation depth. Inset: relative change in pressure with humidity. (d) Response of the sensor to pulses of ~ 20–60 % CO\(_2\) gas concentrations showing the drop in the thermal acoustic signal with increasing CO\(_2\) concentration.

To interface the sensor, we used a custom heater current drive and amplification electronics, as shown in Fig. 2a. The electronics were interfaced to a National Instruments (NI) data acquisition (DAQ) card, so that modulation and data acquisition could be done automatically using LabVIEW software. The microheater was sinusoidally modulated using a current source with a peak current of 30 mA at a frequency of 43 Hz, corresponding to a peak temperature of \(\sim\) 320 \(^{\circ }\) C. To compensate for background acoustic noise, the signal from a second ’reference’ microphone (acoustically isolated from the microheater), was subtracted from the active thermal acoustic signal, after voltage amplification (100\(\times\) ). The resulting differential modulated acoustic signal, generated by the thermal acoustic effect, is shown in Fig. 2b. A software based lock-in amplifier, with a time constant of 1 s, was used to process the recovered waveform and extract the amplitude of the acoustic response. The acoustic response across a range of modulation frequencies is plotted in Fig. 2c. As the heater modulation frequency (f [Hz]) increases [from near direct current (DC)], the level of the acoustic signal rises, as the rate of heat flow into the gas increases, peaking at around 43 Hz. At higher modulation frequencies, the microheater’s temperature modulation depth (\(\Delta T\) [K]) decreases due to its thermal inertia (or thermal effusivity, a measure of the rate at which it absorbs or releases thermal energy22), as shown in Fig. 2c, causing a shallow drop-off in the strength of the acoustic signal. The thermal acoustic sensor shows a change of around 1% in measured pressure from 0 to 70% relative humidity, as showed in the inset of Fig. 2c.

For gas tests, we mounted the sensor in a stainless steel chamber kept at 25 \(\pm 1\;^{\circ }\) C ambient temperature by a Dri-bloc™ heater. Mass flow controllers (MFCs) were used to regulate the flow of gas into the chamber. Gas tests were done with CO\(_2\) diluted in zero grade air at 0% relative humidity. The total flow of gas through the system was kept constant at 200 mL/min. The response of the sensor exposed to CO\(_2\) concentrations varying from 0 to 60% is shown in Fig. 2d. The sensor gives a relative change in amplitude response of 0.13% per 1% change in CO\(_2\) concentration, giving a limit of detection (3\(\sigma\) ) of 0.14% CO\(_2\) . These values are comparable to current state-of-the-art thermal conductivity based sensors7,8, and could be further improved by minimizing the thermal heat capacity of the heat source to reduce the heating time, i.e., maximise the transfer of kinetic energy into the gas, ultimately boosting the thermal acoustic signal. There is a small recovery period after each gas exposure, thought to be due to thermal stabilisation of the sensor.

Numerical analysis. (a) Simplified thermal model illustrating the heat flow from the microheater into the gas and chip due to their thermal capacities \(C_{th}\) and resistance \(R_{th}\) of the chip under DC heating. A temperature rise ΔT occurs on the microheater due to the flow of heat. (b) Experimental vs. numerical calculations showing the relative pressure change in the thermal acoustic cavity with varying volumetric fractions of CO\(_2\) , modelled with and without compensation for the photoacoustic effect. (c) Mid-infrared absorption spectrum with 20% CO\(_2\) in air at 0.1 mm absorption length, under standard conditions (296 K, 1 atm).

In order to better understand the response dynamics of our sensor, we performed numerical calculations based on a standard thermal circuit model23, accompanied by thermodynamics15,22. Thermal systems can be conveniently represented as electrically equivalent thermal circuits. Figure 3a shows a simplified electrical equivalent thermal circuit for our thermal acoustic sensor where the gas’s and chip’s thermal capacitances \(C_{th} = Q/ \Delta T\) [\(\mathrm {\frac{J}{K}}\) ] represent a measure of the heat needed to produce a change in temperature. The microheater chip’s thermal resistance Rth chip is also shown, signifying the temperature change per unit Watt of electrical power under DC heating. A current source I [A] is used to represent the heat flow \(Q/ \Delta t\) [W] that generates a temperature rise \(\Delta T\) [K] across the gas, equivalent to a voltage. In our case, the two gas volumes, either side of the heater, have the same thermal properties, and thus the same \(C_{th}\) . The heater is modulated by electrical excitation [\(I(t)= I_0 \cdot sin(\omega \cdot t)\) , with \(I_0\) the current magnitude, and \(\omega =2\cdot \pi \cdot f\) the angular frequency, where f [Hz] is the thermal modulation frequency], closely related to the supplied electrical power (\(I\cdot V\) [W] proportional to \(Q/\Delta t\) ), causing a temperature increase. Gas molecules receive thermal energy as momentum resulting in them being directed away from the heated surface15, with the velocity at which their ejection occurs dependent on the heating rate and therefore frequency of thermal modulation15,22,23.

A further mathematical description of our thermal acoustic system can be derived by thermodynamics15,22,23. The average change in acoustic pressure \(\Delta p\) [Pa] generated in our thermally modulated system of constrained volume V [m\(^3\) ] is proportional to the average change of internal thermal energy of the gas \(\Delta U\) [J], given by

where z is a constant to account for acoustic losses through the small opening of the cavity which increases its effective volume. From Fig. 3a, the heat \(\Delta Q\) [J] supplied into the gas, during a heating period of time \(t_{th}(f)\) [s], can be written as

where \(\Delta T\) [K] is the average change in temperature during the heating period \(t_{th}\) [s], and \(C_{th}\) [\(\mathrm {\frac{J}{K}}\) ] is the thermal capacity of the gas, given by

where the thermal penetration depth \(d_{th}(f) = \sqrt{ \frac{ \alpha _{diff} }{ 2 \cdot \pi \cdot f } }\) [m] is a function of f and the thermal diffusivity \(\alpha _{diff} = k \cdot \rho / c\) [\(\mathrm {\frac{m^2}{s}}\) ] of the gas, A [m\(^2\) ] is the area of the heat source, and k [\(\mathrm {\frac{W}{m \cdot K}}\) ], \(\rho\) [\(\mathrm {\frac{kg}{m^3}}\) ] and c [\(\mathrm {\frac{J}{kg \cdot K}}\) ] are the thermal conductivity, density and specific heat capacity of the gas, respectively. Substituting for \(d_{th}\) and rearranging we get

where \(e = \sqrt{ k \cdot \rho \cdot c }\) [\(\mathrm {\frac{J}{m^2 \cdot K \cdot \sqrt{s}}}\) ] is the thermal effusivity of the gas. The acoustic pressure change can now be expressed as

Momentum is propagated by the collision of the gas particles, as they move away from the heated surface, increasing the pressure. As the heater’s temperature decreases, the velocity of the gas particles decreases, causing them to return to their initial thermodynamic state15. At high thermal modulation frequencies f, the gas does not expand in volume due to self-heating and does not store the supplied \(\Delta Q(f)\) . In this scenario, a particle-velocity wave in the adjacent gas is formed which propagates at the speed of sound. If the heating time is long (seconds), the mechanism of operation is different and the gas layer close to the heated surface has time to store the kinetic energy as heat, increasing in volume. \(\Delta Q(f)\) supplied to the gas is then dissipated by convective gas flow, thermal diffusion and radiation15,22,23.

We use the model described above to calculate the relative change in pressure, caused by a gradual increase (from 0 to 100%) of CO\(_2\) concentration in air, with respect to air. Figure 3b (black line) shows a maximum \(\sim\) 28% relative decrease in pressure for 100% CO\(_2\) with respect to that of air. When compared to the experimental data, plotted in Fig. 3b (red line), a deviation (\(\sim\) 0.16 slope) from the numerical calculations can be observed. In this experiment, our microheater has a dual-effect. It provides the thermal modulation profile needed for thermal acoustic conversion, and, at the same time, acts as a MIR thermal source, responsible for an additional photoacoustic effect in the cavity24. With increasing the CO\(_2\) concentration, the thermal acoustic effect, described above, is responsible for a decrease in the acoustic pressure, which is related to the CO\(_2\) effusivity with respect to that of air. On the other hand, a competing photoacoustic effect is responsible for an increase in the acoustic pressure, proportional to the CO\(_2\) absorption cross section (\(\sigma (\lambda )\) [cm\(^2\) ], with \(\lambda\) [m] the optical wavelength) in the MIR (significantly higher than that of air)24. An expression for the photoacoustic signal, which is proportional to the optical power, can be derived from the Beer–Lambert law24:

where \(P_0\) and P are the optical power before and after the photoacoustic cell, respectively, N [cm\(^{-3}\) ] is the number of absorbing molecules per cubic centimeter, and l [cm] the absorption path length. In order to account for the additional photoacoustic effect, we use HITRAN data25 to calculate the optical absorption A (\(\lambda\) ) in the sensor’s cavity. An absorption spectrum for 20% CO\(_2\) in air is shown in Fig. 3c for a 1 mm absorption length. For our microhotplate we assume a grey body emitter profile G (\(\lambda\) ) with a defined 300 \(^{\circ }\) C temperature20. The absorbed power is calculated by numerical integration of the absorption data with that of the microheater’s profile:

which is then used to adjust \(\Delta Q\) [J] supplied into the gas to account for the additional photoacoustic effect. The new relative change in pressure is plotted in Fig. 3b (blue line) showing a reduced (\(\sim\) 0.04 slope) deviation from the experimental data. It is important to note that most current photoacoustic gas sensors employing MEMS heaters as MIR sources use MEMS microphones encapsulated with the target gas, thus minimizing any direct transfer of thermal to kinetic energy from the heater5,26. In our sensor, the heater is in direct contact with the gas to maximise the direct energy transfer.

In this paper, we have reported on a novel technique for gas sensing, exploiting changes in the thermal acoustic conversion efficiency of gases. By combining a CMOS MEMS microhotplate, as a thermal source, and a MEMS microphone, we demonstrate an ultra-compact gas sensor with a limit of detection of 0.14% to CO\(_2\) . We provide a theoretical model, to accompany the experimental results, showing the sensor's response is mostly dependent on the thermal effusivity of the gas, thus allowing for simple sensor design and optimization. We believe the thermal acoustic technique is a simple and cost-effective approach that can be used for a variety of applications. A further refinement would be to investigate approaches to decouple the thermal and photo acoustic effects respectively, for example, by minimising IR emission.

The micro-hotplate was fabricated using a commercial 1 \(\upmu\) m silicon-on-insulator (SOI)-CMOS process on 6 inch 375 \(\upmu\) m thick silicon (Si) wafers. Deep Reactive Ion Etching (DRIE) was used to form the membrane; utilising the first silicon dioxide layer as an etch-stop. The DRIE etching process creates near vertical side-walls. Si\(_3\) N\(_4\) is used as a passivation layer. The microheater area is ~ 0.07 mm2.

The microphone (model ICS-40300, acting as the acoustic sensor) was packaged in a surface-mount package, with a metal cap on top of a substrate layer (dimensions: 4.72 mm \(\times\) 3.76 mm \(\times\) 3.5 mm). The microheater was driven using a sinusoidal voltage signal via a buffer amplifier while op-amp based amplifiers (10 \(\times\) voltage gain) were used to amplify the microphonic signals prior to digitisation. The thermodiode was constant current biased at 100 \(\upmu\) A. The sensor was interfaced to a National Instruments DAQ card (model NI USB-6353), so that control and data acquisition could be done automatically using LabVIEW software. A lock-in amplifier was implemented in software to process the recovered waveform. The effect of background acoustic noise was reduced by digital noise cancellation and integration.

Data from additional sensors was collected during the gas tests, including pressure, temperature, humidity data from a Bosch BME680 sensor and CO2 concentration data from a SCD30 optical sensor. The sensors were interfaced for data logging using a Warp RevC board27.

Spinelle, L., Gerboles, M., Kok, G., Persijn, S. & Sauerwald, T. Review of portable and low-cost sensors for the ambient air monitoring of benzene and other volatile organic compounds. Sensors. (2017).

Article  PubMed  PubMed Central  Google Scholar 

Nazemi, H., Joseph, A., Park, J. & Emadi, A. Advanced micro- and nano-gas sensor technology: A review. Sensors. (2019).

Article  PubMed  PubMed Central  Google Scholar 

Burgués, J. & Marco, S. Low power operation of temperature-modulated metal oxide semiconductor gas sensors. Sensors. (2018).

Article  PubMed  PubMed Central  Google Scholar 

Dey, A. Semiconductor metal oxide gas sensors: A review. Mater. Sci. Eng. B 229, 206–217. (2018).

Popa, D. & Udrea, F. Towards integrated mid-infrared gas sensors. Sensors. (2019).

Article  PubMed  PubMed Central  Google Scholar 

Hodgkinson, J. & Tatam, R. P. Optical gas sensing: A review. Meas. Sci. Technol. 24, 012004 (2012).

Gardner, E. L. W., De Luca, A. & Udrea, F. Differential thermal conductivity CO\(_2\) sensor. In 2021 IEEE 34th International Conference on Micro Electro Mechanical Systems (MEMS), 791–794. (2021).

Struk, D., Shirke, A., Mahdavifar, A., Hesketh, P. J. & Stetter, J. R. Investigating time-resolved response of micro thermal conductivity sensor under various modes of operation. Sens. Actuators B Chem. 254, 771–777. (2018).

Rott, N. Thermoacoustics. vol. 20 of Advances in Applied Mechanics, 135–175. (Elsevier, 1980).

Braun, F. Notiz über thermophonie. Annalen der Physik 301, 358–360 (1898).

Arnold, H. & Crandall, I. The thermophone as a precision source of sound. Phys. Rev. 10, 22 (1917).

Vesterinen, V., Niskanen, A. O., Hassel, J. & Helistö, P. Fundamental efficiency of nanothermophones: Modeling and experiments. Nano Lett. 10, 5020–5024. (2010).

Article  ADS  CAS  PubMed  Google Scholar 

Hu, H., Wang, Y. & Wang, Z. Wideband flat frequency response of thermo-acoustic emission. J. Phys. D Appl. Phys. 45, 345401. (2012).

Xiao, L. et al. High frequency response of carbon nanotube thin film speaker in gases. J. Appl. Phys. 110, 084311 (2011).

Daschewski, M., Boehm, R., Prager, J., Kreutzbruck, M. & Harrer, A. Physics of thermo-acoustic sound generation. J. Appl. Phys. 114, 114903. (2013).

Article  ADS  CAS  Google Scholar 

Shinoda, H., Nakajima, T., Ueno, K. & Koshida, N. Thermally induced ultrasonic emission from porous silicon. Nature 400, 853–855 (1999).

Article  ADS  CAS  Google Scholar 

Barnard, A. R., Jenkins, D. M., Brungart, T. A., McDevitt, T. M. & Kline, B. L. Feasibility of a high-powered carbon nanotube thin-film loudspeaker. J. Acoust. Soc. Am. 134, EL276–EL281 (2013).

Article  ADS  CAS  Google Scholar 

Timmer, M. A. G., de Blok, K. & van der Meer, T. H. Review on the conversion of thermoacoustic power into electricity. J. Acoust. Soc. Am. 143, 841–857. (2018).

Article  ADS  CAS  PubMed  Google Scholar 

Ali, S. Z., Udrea, F., Milne, W. I. & Gardner, J. W. Tungsten-based SOI microhotplates for smart gas sensors. J. Microelectromech. Syst. 17, 1408–1417 (2008).

Ali, S. Z. et al. A low-power, low-cost infra-red emitter in CMOS technology. IEEE Sens. J. 15, 6775–6782. (2015).

Article  ADS  CAS  Google Scholar 

De Luca, A., Pathirana, V., Ali, S. & Udrea, F. Silicon on insulator thermodiode with extremely wide working temperature range. In 2013 Transducers & Eurosensors XXVII: The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII), 1911–1914 (IEEE, 2013).

Lienhard, J. H. IV., Lienhard, J. H. V. A Heat Transfer Textbook, Version 5.10, 5th ed. (Phlogiston Press, 2020).

Shabany, Y. Heat Transfer: Thermal Management of Electronics, 1st ed. (CRC Press, 2009).

Harren, F. J. & Cristescu, S. M. Photoacoustic Spectroscopy in Trace Gas Monitoring, 1–29 (American Cancer Society, 2019).

Gordon, I. et al. The hitran2016 molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transf. 203, 3–69. (2017) (HITRAN2016 Special Issue).

Article  ADS  CAS  Google Scholar 

Palzer, S. Photoacoustic-based gas sensing: A review. Sensors. (2020).

Article  PubMed  PubMed Central  Google Scholar 

Stanley-Marbell, P. & Rinard, M. Warp: A hardware platform for efficient multimodal sensing with adaptive approximation. IEEE Micro 40, 57–66 (2020).

We acknowledge funding from EPSRC Grants EP/S031847/1, EP/R022534/1, Alan Turing Institute Award TU/B/ 000096 under EPSRC Grant EP/N510129/1, and Royal Society Equipment Grant RG170136.

Department of Engineering, University of Cambridge, Cambridge, CB3 0FA, UK

Richard Hopper, Daniel Popa, Florin Udrea & Phillip Stanley-Marbell

Flusso Limited, Cambridge, CB4 0DL, UK

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R.H. and D.P. conceived and conducted the experiments, analysed the results and wrote the manuscript. All authors reviewed the manuscript.

The authors declare no competing interests.

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Hopper, R., Popa, D., Udrea, F. et al. Miniaturized thermal acoustic gas sensor based on a CMOS microhotplate and MEMS microphone. Sci Rep 12, 1690 (2022).


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fied using data-driven and metabolic approaches were similar. For example, optimized peak torque values were well correlated across methods (R2 = 0.76, P = 1.4 × 10−4, n = 9). On the second day, participants performed a standing rest condition followed by assistance conditions including Normal Shoes and walking with the exoskeletons under Zero Torque, Generic assistance, Metabolic Optimized assistance and Data-driven Optimized assistance. The assistance conditions for these validation tests were randomized and presented in a double-reversal order, as ABCDDCBA, to mitigate the effects of trial order related to within-day adaptation and fatigue. Each condition lasted for 6 min and included metabolic measurements.

The second experiment was used to evaluate the same set of assistance conditions at additional speeds and treadmill grades. A subset of healthy adult participants from the first experiment (n = 3, 3 men; age, 24.0 ± 2.0 yr; body mass, 66.0 ± 8.0 kg; height, 1.76 ± 0.05 m) completed the experiment. Participants completed the same experimental protocol used in the first tethered exoskeleton experiment for three additional walking conditions: walking at a slow speed of 0.75 m s−1, a fast speed of 1.75 m s−1, and on a 10° incline at 1.25 m s−1.

We developed a speed-adaptive controller that adjusted exoskeleton assistance based on walking speed. During real-world walking, people naturally vary their speed27. We hypothesized that adjusting exoskeleton assistance based on walking speed would provide larger metabolic reductions than a constant pattern of assistance. We estimated the walking speed of each step using a linear model, relating measured stride durations to measured walking speeds (Extended Data Fig. 2). Walking speed estimates from each step were used to interpolate exoskeleton assistance parameters from those optimized at a range of fixed speeds (Fig. 3a).

During speed-adaptive control, walking speed from one step was used to select the assistance parameters for the following step. We expect this approach to perform well when changes in walking speed occur slowly, or when there are rapid changes in speed but they constitute a small portion of total steps, as in natural human gait. Our experimental data are consistent with the observation that most acceleration and deceleration occurs within a few steps at the start and end of each walking bout. The expected stance duration was also adjusted based on speed estimates, following an approach established in previous research53. In future studies, the speed-adaptive controller could be improved to deliver more effective assistance during rapid changes in gait speed by incorporating instantaneous estimates of walking speed54,55 and stance duration. Acceleration regimes could also be considered, with a binning approach analogous to the one used for speeds in this study, to allow optimization of assistance specific to acceleration and deceleration phases. Other approaches, such as those using phase-based control55 or adjusting assistance based on changes in joint kinematics rather than walking speed56, may be beneficial for generalizing to a large set of activities.

We conducted a third tethered exoskeleton experiment to evaluate whether adapting assistance to variations in walking speed could provide larger reductions in metabolic cost than a fixed generic assistance profile. Healthy young adults (n = 3, 3 men; age, 24.0 ± 2.0 yr; body mass, 66.0 ± 8.0 kg; height, 1.76 ± 0.05 m) completed the experiment. These participants had previously completed the first two tethered exoskeleton experiments, providing Data-driven Optimized parameters for walking speeds of 0.75 m s−1, 1.25 m s−1, and 1.75 m s−1. Participants walked on a treadmill while the speed varied sinusoidally from 0.75 m s−1 to 1.75 m s−1 with a period of 30 s. Participants completed assistance conditions including walking in Normal Shoes and walking with the exoskeletons under Zero Torque, Generic assistance (which did not change in response to changes in speed) and Speed-adaptive assistance (using the optimized control parameters previously identified for each participant). The validation tests were randomized and presented in a double-reversal ABCDDCBA order to mitigate the effects of noise in the metabolics measurements and trial order.

The untethered exoskeleton was designed to provide the optimized assistance parameters from the tethered exoskeleton experiments under real-world conditions. The maximum peak torque magnitude for the optimized assistance during the tethered exoskeleton study was 54 Nm when walking at a moderately fast speed of 1.5 m s−1. The motor and power transmission elements were designed to robustly provide this level of assistance. A portable battery was selected to allow 30 min of continuous walking on a single charge. The device was designed to be lightweight to reduce the metabolic power required to carry the exoskeleton.

The untethered exoskeleton had a mass of 1.2 kg for each ankle. Many of the mechanical elements were the same as in the tethered exoskeleton, including the frame, shoe and pressure-sensor insole. New elements included the portable motor, drum-and-cable transmission, electronics, and battery (Extended Data Fig. 3). A set of computer-aided design files and a bill of materials are provided as Supplementary Data 2.

The brushless motor (AK80-9, CubeMars) contained a single stage 9:1 gear ratio and internal motor driver electronics. This gearmotor has a rated peak torque of 18 Nm, a no-load speed of 25 rad s−1, and a mass of 0.5 kg. We selected this motor based on simulations with a simplified model that predicted it would be capable of applying the patterns of ankle torque and velocity that corresponded to optimized assistance in the tethered exoskeleton experiments, assuming an additional 5:1 gear ratio from the drum to the heel spur.

The custom drum was machined from 7075 aluminium, with a radius of 0.020 m. A cable connected the heel spur to the motor drum. The heel spur had a maximum lever arm (the distance from the centre of the ankle joint to the rope tie-off point) of 0.115 m. The lever arm decreased as the ankle plantarflexion angle increased, with a singularity at a maximum plantarflexion angle of 55° ensuring that no ankle torque could be applied to hyperextend the ankle joint. The torque assistance profile of the exoskeleton was not impacted by changes in the lever arm because torque was measured directly at the ankle; strain gauges on the superior and inferior surfaces of the heel lever directly sensed bending moment independent of cable force. This allowed for accurate torque control without explicitly correcting for joint angle. When the motor applied torque to the drum, a force was generated in the cable, which then transmitted this force to the heel lever, creating a torque about the ankle joint of the exoskeleton. The drum-and-cable transmission had the added benefit of being backdrivable, avoiding the possibility of force spikes that can be produced by classically stiff actuators57,58. The cable could also be driven to a slack state to allow the person to move freely when desired, an important capability that prevents interference when not providing assistance59.

The untethered exoskeleton electronics consisted of a microcontroller, portable sensing elements, a motor driver integrated into the motor and a rechargeable battery. The untethered exoskeleton used a Raspberry Pi 4b microcontroller to read sensor data and perform real-time control and optimization at a rate of 200 Hz. A breakout board enabled sensors to interface with the microcontroller. A step-down voltage converter enabled the electronics to be safely powered by a portable battery. The portable sensing elements included a rotary encoder in the ankle joint that measured ankle angle and velocity, a pressure-sensing insole in the shoe, a set of strain gauges in a full Wheatstone bridge configuration applied to the heel spur to measure torque, and an amplifier (IAA100, Futek) to allow measurement of strain-gauge signals. The pressure-sensing insole had pressure sensors located at the heel, fifth metatarsal, distal phalanx of the great toe and the first metatarsal. Fusing information from these different sensors enabled robust estimation of stance and stride period while providing measurements to extract information for optimizing assistance. This choice of sensors was guided by the design heuristic that multiple modes of sensing are important for effective exoskeleton control60. Muscle electrical activity could have provided additional information for control, but with the added challenge of handling noise from sensors placed on the skin61. The total weight of electronics was 0.15 kg.

The entire system was powered by a lithium polymer battery with a nominal voltage of 24 V, a capacity of 1,300 mAh, and a weight of 0.3 kg. Battery life was experimentally evaluated under the most demanding assistance pattern, characterized by a peak torque of 54 Nm and late timing of peak torque. Tests were conducted while walking on a treadmill at a speed of 1.5 m s−1. The battery was initially charged to a maximum voltage of 25.2 V and the battery life experiment was stopped once the battery voltage reached 21.6 V, corresponding to a cell voltage of 3.6 V, the minimum safe level recommended for discharging a lithium polymer battery. During testing, cell voltage was monitored by a safety regulator and an audio alarm was played once the cell voltage reached 3.6 V. We found that the 0.3-kg battery used in real-world tests allowed 36.3 min of operation under these conditions.

The design of the untethered device was guided by previous laboratory-based ankle exoskeletons, incorporating design elements that allowed for large assistive torques while maintaining comfortable forces on the body43. The shoe, carbon fibre struts and calf spacers were designed to be interchangeable to fit different participants, following best practices for fitting62. The motor-and-drum transmission and heel spur were designed to be one size fits all, with interchangeable shoes and spacers accommodating differences in foot size and mediolateral dimensions of participants’ legs. It might at first appear that the force applied by the cable between the drum and heel spur would pull the exoskeleton down the leg, but the rigid exoskeleton frame allows the axial component of this force to be reacted out at the exoskeleton joint rather than as shear on the person’s skin43. Thus, only a normal force is applied to the shank of the leg, which allows for more comfortable application of high torques63. The carbon fibre frame of the exoskeleton used stiff material and a cross-section with a high-area moment of inertia to prevent meaningful deflection during loading. As the system regulated exoskeleton joint torque, rather than motor current or velocity, and as torque was measured directly at the joint, compliance and dissipation in the transmission, exoskeleton frame and human–exoskeleton interface did not affect the accuracy or consistency of the applied torque.

The design of the untethered exoskeleton required several trade-offs. The highest design priority was providing a peak torque of 54 Nm during walking at 1.5 m s−1, specified from previous optimization experiments, with the least mass possible. We considered several factors to ensure that the motor would provide 54 Nm during operation. We simulated the torque needed to provide the desired assistance, overcome transmission inefficiencies, and accelerate the mass of the motor rotor and drum as required to track ankle movements during walking at 1.5 m s−1. The motor had to operate at a safe steady-state temperature to prevent damage to the windings. A brushless motor was selected for its relatively high efficiency and peak torque. This untethered exoskeleton was designed for the optimized parameters of our experimental participant group, and other participants may require a different device with different balance between torque and weight to provide the same reductions in the metabolic cost of walking.

Another important decision was whether to place the motor and electronics near the assisted joint or closer to the torso. The energy cost of carrying mass at distal joints is high33, suggesting a relocated drive approach with heavy motors carried more proximal to the centre of mass of the body. We considered mounting the motor and electronics at the hip and using a Bowden cable to transmit forces to the ankle joint. Bowden cables have an inner cable that moves relative to an outer conduit like a bicycle brake. This introduces complex transmission dynamics, including stick–slip friction, history dependence and a dependence on leg posture, making torque control more challenging, reducing control bandwidth and decreasing energy efficiency. The cables and additional electrical wires also add to the weight of the system. For these reasons, we selected a drum-and-cable transmission located on the shank of the leg. Locating motors and electronics near the assisted joint resulted in more efficient power transmission, lower transmission compliance, better control bandwidth and less total weight.

Our untethered exoskeleton was designed to allow tests of real-world personalization and resulting mobility benefits during naturalistic walking in a community setting. A significant amount of additional engineering would be required to make this device ready for everyday use by consumers. Everyday use would require easier donning and doffing, a more comfortable interface, more robust electronics hardware and more intuitive, independent control, for example, utilizing a smartphone app. In addition, the exoskeleton would have to be tested to ensure functionality during additional common activities such as navigating stairs, and to ensure that it did not interfere with common activities such as sitting and driving. While we did not directly evaluate descending stairs in this study, we did notice that the long heel spur required participants to walk carefully to avoid hitting the previous step. This design choice was made for convenience, allowing us to use as many elements from our previous tethered exoskeleton design as possible. A less obtrusive transmission would be needed for a consumer device. The commercially available Dephy ExoBoot64 provides an example of a more streamlined design; it has no spur behind the heel of the shoe, has simple donning and doffing features, and has minimal structure on the medial side of the leg, making it a good candidate for extended use in a large range of activities. Other autonomous ankle exoskeletons10,17 demonstrate complementary ways of designing hardware that is more compatible with everyday use. With increased torque capacity, more accurate torque control and real-world personalization using the approach described here, we expect commercial devices could achieve similar reductions in metabolic rate.

We overcame the challenges of optimizing assistance during short bouts of walking at varying speeds by opportunistically accumulating data across many bouts and binning by speed. This opportunistic optimization approach used the same data-driven classification model and optimization method that were validated in the tethered experiments, with the addition of a check that sufficient consecutive steps had been collected for each control law and a method for addressing a wide range of speeds (Extended Data Fig. 4).

The opportunistic optimization method checked that sufficient steps had been collected before moving on to the next control law. We chose the requirement of 44 steps to approximate the durations used in the tethered data-driven optimization experiments. If sufficient continuous steps were not collected before the end of the walking bout, the optimizer would start over with the same controller on the next bout. Once sufficient strides were collected, the next control law was applied for that speed bin. As with the tethered experiments, the first six strides of data were discarded to avoid confounds related to rapid adaptation to a new exoskeleton control law.

The same data-driven classification model used in the tethered exoskeleton experiments was used for the real-world optimization, but a different set of assistance torque parameters were optimized. The torque parameters for peak time and fall time were fixed to the average values of the Data-driven Optimized parameters from the first tethered exoskeleton experiment (54.6% of the gait cycle and 10.0% of the gait cycle). We fixed the values of peak time and fall time because the optimized values changed little across speeds and participants, indicating that fixed values may be sufficient. The optimized values of peak torque and rise time varied substantially across speeds and participants, and so these parameters were optimized in untethered exoskeleton experiments. Optimizing two, rather than four, torque parameters reduced the dimensionality of the optimization, requiring only six, rather than eight, control laws to be collected for each generation of optimization. Reducing the number of control laws to be evaluated per generation allowed for more generations to be completed within a set experiment time, providing more frequent optimization updates and a better estimate of the optimal values. This may have come at the cost of suboptimal assistance timing parameters for some participants.

Once data for all the control laws in a generation were collected, the data-driven classification model ranked the control laws. The optimizer used this ranking to update its estimate of the optimal parameters and to adjust internal parameters, such as the convergence parameter (σ) that set the spread of the distribution from which to draw parameters for the next generation. Optimizations were performed for three bins of walking speed: less than 1.22 m s−1, between 1.22 m s−1 and 1.38 m s−1, and greater than 1.38 m s−1. These speeds were chosen based on the 33rd and 66th percentile of real-world walking speed distributions27, resulting in an equal expected likelihood for the participant to walk in each bin. Speed-adaptive control interpolated assistance based on the speed of each individual step (Extended Data Fig. 2). When a sufficient number of steps were collected for one control law, the estimated walking speeds for all steps during that control law were averaged, the corresponding speed bin was selected, and data were stored for the optimization process. When a complete generation of control laws were collected for a speed bin, control laws for that bin were ranked and the optimization parameters for that bin were updated. The estimate of the optimal assistance parameters for the other speed bins were also adjusted by a lesser amount, with the magnitude of the adjustment being proportional to the value of the convergence parameter, σ, for that bin (Extended Data Fig. 4). This allowed parameters in all speed bins to update more quickly at the beginning of the optimization, with decreased across-speed influences as the optimizations within each speed bin converged.

We chose to optimize a set of assistance parameters for each of three bins of walking speed, but it is possible to formulate this optimization in different ways. The data-driven classifier requires comparisons of control laws at similar walking speeds. A larger number of bins of walking speeds could be used to provide more granular speed-based adaptation, at the expense of additional time to optimize a larger number of assistance parameters. It may also be possible to simultaneously solve for a larger set of control parameters that fully define the speed-adaptive controller, but this would introduce challenges related to the larger parameter space, interaction effects between parameters, and poorly conditioned maps between parameters that have a strong effect on assistance at one speed and little effect on assistance at different speeds. Instead, we opted for a small set of speed bins, with a relatively simple approach to updating the optimal parameter estimates.

In the real-world optimization experiments, we used the untethered exoskeleton to optimize assistance during naturalistic bouts of walking and then evaluated the optimized assistance profiles under real-world and treadmill conditions.

Healthy adult participants (n = 10, 6 men and 4 women; age, 24.2 ± 1.8 yr; body mass, 67.0 ± 8.2 kg; height, 1.72 ± 0.07 m) completed a two-day protocol. On the first day, participants walked outside in a public setting along a path consisting of concrete, asphalt and brick sidewalks (Fig. 5b) for approximately 1 h while the untethered exoskeleton provided assistance and performed data-driven optimization. To emulate natural walking, the participants received audio cues to tell them to start and stop walking bouts. The durations of these bouts were randomly drawn from a preselected distribution (Fig. 5d) that matched naturally occurring bout durations34. Participants stood at rest between bouts for a randomized duration of 5 s to 10 s. To encourage a normal range of speeds, we provided participants with audio prompts, such as “Walk as if you were walking to catch a bus” and “Walk as if you were walking a small dog”, at the start of each bout. A previous study28 demonstrated that these prompts were associated with different self-selected walking speeds, and we expected that participants would adopt similar speeds. We randomly sampled from a distribution of speeds (Fig. 5c) that mimicked natural walking patterns measured in a previous study27.

On the second day, participants performed outdoor and treadmill validation tests to evaluate the benefits provided by Real-world Optimized assistance. For the outdoor validation, participants walked along a 566-m path in the same public setting with a fixed ordering of bouts of specific distances and corresponding speed prompt commands that were selected to match real-world distributions27,34. Distances were set using cones to mark stopping locations, which ensured consistent distances for each bout. Participants completed this outdoor course once for each condition, including Real-world Optimized assistance, Generic Speed-adaptive assistance and Normal Shoes. The ordering of the conditions was randomized to minimize effects of testing order (Extended Data Table 1). The double-reversal protocol, used in the first three laboratory experiments, was not used because the outdoor experiments took significantly more time owing to the longer trial time, varying self-selected walking speeds, short bouts of walking, and rest periods between bouts and conditions. Each real-world condition required about 15 min, compared with about 8 min for each treadmill condition. Outdoor and indoor tests of Real-world Optimized assistance were conducted on the same day to avoid confounding effects from differing respirometry system calibrations. The total walking time for these two experiments was about 1.5 h, and we found that participants were not able to complete the additional 1.5 h of walking that would have been required for a double-reversal approach without experiencing fatigue. For the 3 min following completion of the path, participants stood at rest while respirometry data were collected to capture the total metabolic cost of completing the course. The duration of walking for each bout was timed with a stopwatch. Walking speed for each bout was computed by dividing the fixed distance for that bout by the time spent walking during that bout. Walking speed for each condition was calculated as the total distance travelled divided by the total time spent walking while navigating the course.

The indoor validation consisted of a standing rest condition followed by six treadmill conditions, each lasting 6 min. Participants walked on a treadmill at 1.25 m s−1, at 1.5 m s−1, and on an incline of 10° at 1.25 m s−1. Participants completed each treadmill speed and grade twice, once with Real-world Optimized assistance, as identified during the outdoor optimization period, and once with Normal Shoes. The ordering of conditions was randomized, with a constraint that the exoskeleton would only be donned and doffed one time to reduce experiment time (Extended Data Table 2). We did not use the double-reversal protocol in these tests because we found that participants could not reliably complete the additional 1.5 h of walking that would have been required without experiencing fatigue, and so instead used the more typical approach of single presentations with randomized order.

One pilot participant completed additional indoor conditions, walking at 1.25 m s−1 with an incline of 5°, walking at 1.25 m s−1 with a load of 20% of their body weight carried in a weight vest, and stair climbing on a stairmill at 50 steps per minute. The results (Extended Data Fig. 6) were used to test the generality of the approach. Owing to the small sample size (n = 1), this figure and the numerical results for change in metabolic rate are not included in the main text.

We performed a naturalistic overground experiment in an outdoor, suburban community setting. People require assistance in many different settings and for a variety of additional activities, and future work should extend the approaches presented in this study to optimize assistance and evaluate assistive device benefits for a wider range of tasks. For example, future devices could sense, adapt to and optimize assistance for various grades55, during stair navigation17 and over rough terrain54. These future studies will provide additional translational impact for daily mobility.

We compared the benefits of Real-world Optimized assistance with the untethered exoskeleton to the best results of comparable previous studies10,11,12,13,14,15,16. To allow direct comparison, we considered only studies that tested untethered devices, report data for normal walking, tested similar walking conditions, tested sufficient participants and used standard data-processing techniques. For untethered exoskeletons, the most relevant outcome is the percent change in the energy cost of walking with exoskeleton assistance to walking in normal shoes without the exoskeleton. Changes in walking conditions can affect outcomes, so we considered studies conducted at within 10% of the speeds and inclines that we tested. Before conducting our final experiment, we selected the speeds (1.25 m s−1 and 1.5 m s−1) and inclines (10°) that captured the largest percent reductions in metabolic rate that had previously been observed for any exoskeleton study in the literature. We compared with previous exoskeleton studies with at least five participants, because studies reporting data from fewer tests are difficult to interpret owing to measurement noise and inter-participant variability. We compared with previous studies in which the metabolic cost of walking was calculated using standard techniques, by averaging respirometry measurements during the last 2 min or 3 min of a 5-min or 6-min steady-state treadmill condition. One previous exoskeleton study65 was excluded because steady-state metabolic cost was computed by taking the median of respirometry measurements. We found that using the median rather than the mean to compute metabolic rate in our untethered exoskeleton study increased the magnitude of the reductions in metabolic cost by an average of 7% across participants. This is a large amount compared with the total improvement of 23%, indicating that the median and mean measurements are not equivalent. We were not able to obtain the data from the previous study that would have allowed computation of the mean percent change in metabolic rate.

To keep Extended Data Fig. 5 legible, we only depict studies reporting results within a 5% change in metabolic rate of the best previous value for that condition category. There are several other untethered exoskeletons that have provided some reduction in metabolic rate under conditions similar to those tested in this study. For example, the Dephy ExoBoot, the commercially available exoskeleton with the most similar features to the prototype tested in this study, can provide a 5.2% reduction in metabolic energy consumption compared with walking with Normal Shoes while walking on a treadmill with time-varying speed64. Another technologically mature untethered exoskeleton, the MyoSuit Beta, has shown that hip assistance during outdoor uphill walking can reduce metabolic rate compared with wearing the exoskeleton in Zero Torque mode37. Sufficient data are not yet available to estimate the benefits compared with walking without the exoskeleton. In the interests of clarity, we did not include the results of all previous exoskeleton experiments in Extended Data Fig. 5.

We compared the results of this study against all types of lower-limb exoskeleton, including devices that assist the knees and hips, to provide the clearest understanding of the relative benefits of this design and personalization approach. Considering instead only ankle exoskeletons would allow for a more mechanistic comparison of system components and biomechanics outcomes, at the cost of reduced generality of the high-level findings. As exoskeleton technologies mature and address more tasks and populations, joint-specific benefits or restrictions related to specific conditions may make it more sensible to apply joint-specific comparisons in some contexts.

Our untethered exoskeleton provided the largest reductions in the metabolic cost of walking primarily owing to the way it personalized assistance to individual users, but hardware design differences may also have contributed to its efficacy. Design differences between the untethered exoskeleton and some previous devices include: directly measuring joint torque, rather than inferring it from motor current; providing slack in the transmission to avoid interference during leg swing and Zero Torque mode; and larger peak torque capabilities, such that benefits were limited more by the user’s ability to accept assistance than by limitations in the hardware. Directly measuring joint torque requires additional electronics hardware for sensing and signal processing but enables more precise control of applied torques, which eliminates errors owing to model mismatch and power losses in the transmission and interface with the body. This helps provide users with a consistent assistance pattern. Placing slack in the transmission cable during periods when zero torque is desired prevents the inadvertent application of the small damping torques needed for linear feedback control. Although they may seem small, these damping torques can substantially increase user effort. Allowing for larger peak torques, in this case approximately twice the value of previous untethered ankle exoskeletons10,17,64,66, allowed for a larger range of possible assistance parameters. This makes it more likely that the global optimum for a given participant and walking speed lie within the range of hardware-feasible control. Larger torques require a rigid frame to react out transmission forces in the exoskeleton joint43, rather than through shear on the skin63, to maintain user comfort. The present results would therefore seem to favour devices that can apply higher torques to achieve greater benefits from assistance, at the cost of greater worn mass. This relationship, however, will be sensitive to the populations and tasks that are assisted. The above design decisions enabled the untethered ankle exoskeleton in this study to provide accurate, reliable and substantial assistance to the user, which enabled participants to obtain large net benefits from real-world personalized assistance.

Participants completed a series of surveys to evaluate the ease of use, comfort and functionality of the untethered exoskeleton after completion of all the experiments. Participants completed a System Usability Scale survey67 to determine how easy it was to operate the untethered exoskeleton. Users reported that the exoskeleton was relatively easy to use, with an overall score of 72.5 (Extended Data Table 3), placing it in the 65th percentile of 5,000 devices previously surveyed42. Participants also completed surveys adapted from the Orthotics and Prosthetics Users’ Survey68, which acts as a self-report instrument for evaluating the outcomes of prosthetics and orthotics services in a clinically useful manner. Among comfort-related outcomes, participants were most likely to agree that the weight of the device was manageable, that it was easy to put on and that their clothes were free of wear (Extended Data Table 4). Participants were more likely to be neutral or to disagree that the exoskeleton would be comfortable throughout the day. Among outcomes related to functionality, participants found standing, walking indoors and outdoors, and donning and doffing the exoskeleton to be easy or very easy (Extended Data Table 5). Participants found picking objects up from the ground and walking up steep ramps to be slightly difficult. When asked whether they would prefer to use the exoskeleton or normal shoes if they had to complete the outdoor walking course again, six out of the ten participants reported that they would prefer to use the exoskeleton.

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

All study data necessary to replicate this work are available in the Source Data included with the paper. Computer-aided design files and a bill of materials for the untethered ankle exoskeleton are provided in Supplementary Data 2. Source data are provided with this paper.

Optimization code samples are provided in Supplementary Data 1. This code uses Python version 3.6.1. The required python packages are numpy (1.17.4), scikit-learn (0.21.3), scipy (1.3.2) and matplotlib (2.0.2).

Song, S. & Collins, S. H. Optimizing exoskeleton assistance for faster self-selected walking. IEEE Trans. Neural Syst. Rehabil. Eng. 29, 786–795 (2021).

Article  PubMed  PubMed Central  Google Scholar 

Zhang, J. et al. Human-in-the-loop optimization of exoskeleton assistance during walking. Science 356, 1280–1284 (2017).

Article  ADS  CAS  PubMed  Google Scholar 

Kim, M. et al. Bayesian optimization of soft exosuits using a metabolic estimator stopping process. In IEEE/RAS International Conference on Robotics and Automation (ICRA) 9173–9179 (IEEE, 2019).

Poggensee, K. L. & Collins, S. H. How adaptation, training, and customization contribute to benefits from exoskeleton assistance. Sci. Robot. 6, eabf1078 (2021).

Studenski, S. et al. Gait speed and survival in older adults. JAMA 305, 50–58 (2011).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Enoka, R. M. & Duchateau, J. Translating fatigue to human performance. Med. Sci. Sports Exerc. 48, 2228 (2016).

Article  PubMed  PubMed Central  Google Scholar 

Tudor-Locke, C., Leonardi, C., Johnson, W. D. & Katzmarzyk, P. T. Time spent in physical activity and sedentary behaviors on the working day: the American time use survey. J. Occup. Environ. Med. 53, 1382–1387 (2011).

Lee, H. J. et al. A wearable hip assist robot can improve gait function and cardiopulmonary metabolic efficiency in elderly adults. IEEE Trans. Neural Syst. Rehabil. Eng. 25, 1549–1557 (2017).

Awad, L. N., Kudzia, P., Revi, D. A., Ellis, T. D. & Walsh, C. J. Walking faster and farther with a soft robotic exosuit: Implications for post-stroke gait assistance and rehabilitation. IEEE Open J. Eng. Med. Biol. 1, 108–115 (2020).

Mooney, L. M., Rouse, E. J. & Herr, H. M. Autonomous exoskeleton reduces metabolic cost of walking. J. Neuroeng. Rehabil. 11, 80 (2014).

Article  PubMed  PubMed Central  Google Scholar 

Collins, S. H., Wiggin, M. B. & Sawicki, G. S. Reducing the energy cost of human walking using an unpowered exoskeleton. Nature 522, 212–215 (2015).

Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

Seo, K., Lee, J., Lee, Y., Ha, T. & Shim, Y. Fully autonomous hip exoskeleton saves metabolic cost of walking. In IEEE/RAS International Conference on Robotics and Automation (ICRA) 4628–4635, (IEEE, 2016).

Seo, K., Lee, J. & Park, Y. J. Autonomous hip exoskeleton saves metabolic cost of walking uphill. In IEEE International Conference on Rehabilitation Robotics (ICORR) 246–251 (IEEE, 2017).

Lee, T. et al. A flexible exoskeleton for hip assistance. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 1058–1063 (IEEE, 2017).

Kim, J. et al. Reducing the metabolic rate of walking and running with a versatile, portable exosuit. Science 365, 668–672 (2019).

Article  ADS  CAS  PubMed  Google Scholar 

Sawicki, G. S., Beck, O. N., Kang, I. & Young, A. J. The exoskeleton expansion: Improving walking and running economy. J. Neuroeng. Rehabil. 17, 25 (2020).

Article  PubMed  PubMed Central  Google Scholar 

Fang, Y., Orekhov, G. & Lerner, Z. Improving the energy cost of incline walking and stair ascent with ankle exoskeleton assistance in cerebral palsy. IEEE Trans. Biomed. Eng. 69, 2143–2152 (2021).

Selinger, J. C. & Donelan, J. M. Estimating instantaneous energetic cost during non-steady-state gait. J. Appl. Physiol. 117, 1406–1415 (2014).

Seth, A. et al. OpenSim: simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. PLoS Comput. Biol. 14, e1006223 (2018).

Article  PubMed  PubMed Central  Google Scholar 

Ijspeert, A. J. Biorobotics: using robots to emulate and investigate agile locomotion. Science 346, 196–203 (2014).

Article  ADS  CAS  PubMed  Google Scholar 

Rosenberg, M. C., Banjanin, B. S., Burden, S. A. & Steele, K. M. Predicting walking response to ankle exoskeletons using data-driven models. J. R. Soc. Interface 17, 20200487 (2020).

Article  PubMed  PubMed Central  Google Scholar 

Lee, D., Kang, I., Molinaro, D. D., Yu, A. & Young, A. J. Real-time user-independent slope prediction using deep learning for modulation of robotic knee exoskeleton assistance. IEEE Robot. Autom. Lett. 6, 3995–4000 (2021).

Slade, P., Kochenderfer, M. J., Delp, S. L. & Collins, S. H. Sensing leg movement enhances wearable monitoring of energy expenditure. Nat. Commun. 12, 4312 (2021).

Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

Matijevich, E. S., Volgyesi, P. & Zelik, K. E. A promising wearable solution for the practical and accurate monitoring of low back loading in manual material handling. Sensors 21, 340–265 (2021).

Article  ADS  PubMed Central  Google Scholar 

Wu, W., Saul, K. R. & Huang, H. H. Using reinforcement learning to estimate human joint moments from electromyography or joint kinematics: an alternative solution to musculoskeletal-based biomechanics. J. Biomech. Eng. 143, 044502 (2021).

Hansen, N. in Towards a New Evolutionary Computation (eds Lozano, J. A. et al.) 75–102 (Springer, 2006).

Baroudi, L. et al. Estimating walking speed in the wild. Front. Sports Act. Living 2, 583848 (2020).

Article  PubMed  PubMed Central  Google Scholar 

Brinkerhoff, S. A., Murrah, W. M., Hutchison, Z., Miller, M. & Roper, J. A. Words matter: instructions dictate “self-selected” walking speed in young adults. Gait Posture 95, 223–226 (2019).

Brown, G. L., Seethapathi, N. & Srinivasan, M. A unified energy-optimality criterion predicts human navigation paths and speeds. Proc. Natl Acad. Sci. USA 118, e2020327118 (2021).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Caputo, J. M. & Collins, S. H. A universal ankle-foot prosthesis emulator for human locomotion experiments. J. Biomech. Eng. 136, 035002 (2014).

Moisio, K. C., Sumner, D. R., Shott, S. & Hurwitz, D. E. Normalization of joint moments during gait: a comparison of two techniques. J. Biomech. 36, 599–603 (2003).

Zhang, J., Cheah, C. C. & Collins, S. H. in Bioinspired Legged Locomotion: Concepts, Control and Implementation (eds Sharbafi, M. & Seyfarth, A.) Ch. 5 (Elsevier, 2017).

Browning, R. C., Modica, J. R., Kram, R. & Goswami, A. The effects of adding mass to the legs on the energetics and biomechanics of walking. Med. Sci. Sports Exerc. 39, 515–525 (2007).

Orendurff, M. S., Schoen, J. A., Bernatz, G. C., Segal, A. D. & Klute, G. K. How humans walk: bout duration, steps per bout, and rest duration. J. Rehabil. Res. Dev. 45, 1077–1090 (2008).

Schmuckler, M. A. What is ecological validity? A dimensional analysis. Infancy 2, 419–436 (2001).

Stolze, H. et al. Gait analysis during treadmill and overground locomotion in children and adults. Electroencephalogr. Clin. Neurophysiol./Electromyogr. Motor Control 105, 490–497 (1997).

Haufe, F. L., Duroyon, E. G., Wolf, P., Riener, R. & Xiloyannis, M. Outside testing of wearable robots for gait assistance shows a higher metabolic benefit than testing on treadmills. Sci. Rep. 11, 14833 (2021).

Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

Bastien, G. J., Willems, P. A., Schepens, B. & Heglund, N. C. Effect of load and speed on the energetic cost of human walking. Eur. J. Appl. Physiol. 94, 76–83 (2005).

Article  CAS  PubMed  Google Scholar 

Perera, S., Mody, S. H., Woodman, R. C. & Studenski, S. A. Meaningful change and responsiveness in common physical performance measures in older adults. J. Am. Geriatr. Soc. 54, 743–749 (2006).

Lloyd, R. & Cooke, C. B. The oxygen consumption with unloaded walking and load carriage using two different backpack designs. Eur. J. Appl. Physiol. 81, 486–492 (2000).

Article  CAS  PubMed  Google Scholar 

Young, A. J. & Ferris, D. P. State of the art and future directions for lower limb robotic exoskeletons. IEEE Trans. Neural Syst. Rehabil. Eng. 25, 171–182 (2016).

Sauro, J. A Practical Guide to the System Usability Scale: Background, Benchmarks, and Best Practices (Measuring Usability LLC, 2011).

Witte, K. A. & Collins, S. H. Wearable Robotics 251–274 (Elsevier, 2020).

Brockway, J. M. Derivation of formulae used to calculate energy expenditure in man. Hum. Nutr. Clin. Nutr. 41, 463–471 (1987).

Seethapathi, N. & Srinivasan, M. The metabolic cost of changing walking speeds is significant, implies lower optimal speeds for shorter distances, and increases daily energy estimates. Biol. Lett. 11, 20150486 (2015).

Article  PubMed  PubMed Central  Google Scholar 

Blokland, I. J. et al. Estimation of metabolic energy expenditure during short walking bouts. Int. J. Sports Med. 42, 1098–1104 (2021).

Article  CAS  PubMed  Google Scholar 

Witte, K. A., Fiers, P., Sheets-Singer, A. L. & Collins, S. H. Improving the energy economy of human running with powered and unpowered ankle exoskeleton assistance. Sci. Robot. 5, eaay9108 (2020).

Snaterse, M., Ton, R., Kuo, A. D. & Donelan, J. M. Distinct fast and slow processes contribute to the selection of preferred step frequency during human walking. J. Appl. Physiol. 110, 1682–1690 (2011).

Article  PubMed  PubMed Central  Google Scholar 

Jackson, R., Dembia, C. L., Delp, S. L. & Collins, S. H. Muscle-tendon mechanics explain unexpected effects of exoskeleton assistance on metabolic rate during walking. J. Exp. Biol. 220, 2082–2095 (2017).

PubMed  PubMed Central  Google Scholar 

Nuckols, R. W. et al. Individualization of exosuit assistance based on measured muscle dynamics during versatile walking. Sci. Robot. 6, eabj1362 (2021).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Galle, S., Malcolm, P., Collins, S. H. & De Clercq, D. Reducing the metabolic cost of walking with an ankle exoskeleton: interaction between actuation timing and power. J. Neuroeng. Rehabil. 14, 35 (2017).

Article  PubMed  PubMed Central  Google Scholar 

Moltedo, M. et al. Walking with a powered ankle-foot orthosis: the effects of actuation timing and stiffness level on healthy users. J. Neuroeng. Rehabil. 17, 98 (2020).

Article  PubMed  PubMed Central  Google Scholar 

Sun, D., Fekete, G., Mei, Q. & Gu, Y. The effect of walking speed on the foot inter-segment kinematics, ground reaction forces and lower limb joint moments. PeerJ 6, p.e5517 (2018).

Zihajehzadeh, S. & Park, E. J. Experimental evaluation of regression model-based walking speed estimation using lower body-mounted IMU. In Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) 243–246 (IEEE, 2016).

Quintero, D., Lambert, D. J., Villarreal, D. J. & Gregg, R. D. Real-time continuous gait phase and speed estimation from a single sensor. In IEEE Conference on Control Technology and Applications (CCTA) 847–852 (IEEE, 2017).

Martinez, A., Lawson, B. & Goldfarb, M. A controller for guiding leg movement during overground walking with a lower limb exoskeleton. IEEE Trans. Robot. 34, 183–193 (2017).

Ham, R. V., Sugar, T., Vanderborght, B., Hollander, K. & Lefeber, D. Compliant actuator designs. IEEE Robot. Autom. Mag. 3, 81–94 (2009).

Vanderborght, B. et al. Variable impedance actuators: a review. Robot. Autom. Syst. 61, 1601–1614 (2013).

Dollar, A. M. & Herr, H. Lower extremity exoskeletons and active orthoses: challenges and state-of-the-art. IEEE Trans. Robot. 24, 144–158 (2008).

Novak, D. & Riener, R. A survey of sensor fusion methods in wearable robotics. Robot. Autom. Syst. 73, 155–170 (2015).

Lenzi, T., De Rossi, S. M., Vitiello, N. & Carrozza, M. C. Intention-based EMG control for powered exoskeletons. IEEE Trans. Biomed. Eng. 59, 2180–2190 (2012).

Article  CAS  PubMed  Google Scholar 

Stirling, L. et al. Static, dynamic, and cognitive fit of exosystems for the human operator. Hum. Factors 62, 424–440 (2020).

Yandell, M. B., Quinlivan, B. T., Popov, D., Walsh, C. & Zelik, K. E. Physical interface dynamics alter how robotic exosuits augment human movement: implications for optimizing wearable assistive devices. J. Neuroeng. Rehabil. 14, 40 (2017).

Article  PubMed  PubMed Central  Google Scholar 

Shepherd, M. K., Molinaro, D. D., Sawicki, G. S. & Young, A. J. Deep learning enables exoboot control to augment variable-speed walking. IEEE Robot. Autom. Lett. 7, 3571–3577 (2022).

Lim, B. et al. Delayed output feedback control for gait assistance with a robotic hip exoskeleton. IEEE Trans. Roboy. 35, 1055–1062 (2019).

Mooney, L. M., Rouse, E. J. & Herr, H. M. Autonomous exoskeleton reduces metabolic cost of human walking during load carriage. J. Neuroeng. Rehabil. 11, 151 (2014).

Article  PubMed  PubMed Central  Google Scholar 

Brooke, J. in Usability Evaluation in Industry (eds Jordan, P. W.) 189–194 (Taylor & Francis, 1996).

Heinemann, A. W., Bode, R. K. & O’Reilly, C. Development and measurement properties of the Orthotics and Prosthetics Users’ Survey (OPUS): a comprehensive set of clinical outcome instruments. Prosthet. Orthot. Int. 27, 191–206 (2003).

Article  CAS  PubMed  Google Scholar 

We thank G. R. Tan, D. Miller and V. Chiu for assistance with exoskeleton hardware; K. Poggensee for assistance with accessing previous experimental data; W. Peisch for assistance with mechanical design; and W. Gu, O. Chaudhuri, A. Okamura, B. Roth, S. Slade and L. Lau for editorial suggestions. Funding: National Science Foundation Graduate Research Fellowship DGE-1656518 (P.S.), Stanford Graduate Fellowship (P.S.), Wu Tsai Human Performance Alliance Postdoctoral Fellowship (P.S.), NIH Grant P41EB027060 (S.L.D.) and National Science Foundation Grant No. CMMI-1734449 (S.H.C.).

Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

Patrick Slade, Scott L. Delp & Steven H. Collins

Department of Bioengineering, Stanford University, Stanford, CA, USA

Patrick Slade & Scott L. Delp

Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, USA

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P.S. contributed to conceptualization, methodology, investigation, visualization and writing. M.J.K. contributed to conceptualization and writing. S.L.D. contributed to conceptualization and writing. S.H.C. contributed to conceptualization, methodology, visualization, and writing.

Correspondence to Steven H. Collins.

S.H.C. is an inventor on a patent application (US patent no. 10,537,283) that covers the emulator systems used in this study.

Nature thanks Carlos Rodriguez Guerrero, Zachary Lerner and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The data-driven classifier decoded latent information from human movement that was not otherwise interpretable, allowing exoskeleton assistance to be optimized without laboratory-based measurement equipment. Top row: Model weights and mean inputs. The model compares data from two control laws at a time and associates inputs with higher or lower metabolic rate to estimate which control law resulted in a lower metabolic rate. Inputs comprised differences in ankle angle and ankle angular velocity at 30 different points in the gait cycle and differences in the four control law parameters of peak torque magnitude, peak time, rise time, and fall time. The data-driven model weights that multiply these differences are shown as a background colour of blue or red. Blue indicates that a positive difference is associated with lower metabolic rate, while red indicates that a positive difference is associated with higher metabolic rate. Darker colours indicate greater influence. Black lines depict the average, across all training data, of the differences in inputs. To generate this average, we ordered each pair-wise comparison by metabolic rate, such that inputs from the control law with a higher metabolic rate were always subtracted from those with a lower metabolic rate. Typical values of the model inputs differ, in part because of differences in units, and so the magnitudes of model weights do not correspond well to the contributions of those terms to the classification overall. Bottom row: The classification contributions of each term in the model, averaged over the entire training set. The percent contribution is calculated as the absolute value of the product of the model weight and the input difference, summed over all pair-wise comparisons, divided by the sum over all model terms. For the x-axes, 0% and 100% of the gait cycle refer to the instant of heel strike of the assisted limb at the beginning and end of one stride. Toe-off occurs at about 62% of the gait cycle. For a discussion of the intuitive meaning of the weights and contributions, please see the Methods subsection “Data-driven optimization”.

a, To calibrate the walking speed estimator, data are collected while the participant walks at several prescribed speeds, each within the range of speeds associated with a set of assistance parameters to be optimized. The measured stride durations and ground-truth speed measurements from those tests are used to fit an affine equation with linear regression. b, The resulting model can then be used to estimate walking speed based on measurements of stride duration alone. c, The speed-adaptive controller relates estimated walking speed to exoskeleton assistance parameters by interpolating between assistance parameters specified at a set of chosen speeds. In this case, there are three sets of optimized parameters corresponding to three different walking speeds.

These computer-aided design drawings depict the hardware elements of the untethered exoskeleton. The primary components are labelled. An image of the entire device, including textile components, can be found in Fig. 4b. A running shoe (not pictured) is attached to the toe strut with pins that extend from the tip of the toe strut into a carbon fiber plate embedded in the sole of the shoe. The heel of the running shoe is attached to the heel spur by a rope (not pictured) tied into holes on either side of the heel spur and passing through a plastic tube embedded in the sole of the shoe. A Vectran transmission cable (not pictured) transmits force from the drum to the tip of the heel spur. At the top of the calf strut, Velcro straps (not pictured) are connected to the strut through slots. These straps adhere to a separate Velcro strap (not pictured) worn on the shank of the leg, just below the knee. A complete bill of materials and set of computer-aided design files for this untethered exoskeleton assembly is included as Supplementary Data 2.

The exoskeleton applied speed-adaptive control, which adjusted exoskeleton assistance parameters on each step. Stride duration (tstride) was used to estimate walking speed (v) as described in Fig. 3. While the participant walked, portable sensor data (d) were collected, which included ankle angle (θ), ankle velocity (\(\dot{{\boldsymbol{\theta }}}\) ), and the control law defining exoskeleton assistance torque (C). If sufficient continuous strides (z) were not collected before the bout finished, the data were discarded and evaluation of the same control law began anew on the next walking bout. If sufficient continuous strides were collected, then data were stored for the associated control law number (n) and walking speed bin (b), selected based on the average walking speed for the collected strides. The control law number was incremented and the next control law was applied to the user. After six control laws had been applied for a given walking speed bin, forming one generation for the optimizer, the stored data were used to update the optimization parameters associated with that speed bin. When any bin performed an update, the estimate of the optimal parameter values (μ) for the other bins were also updated. Bins that were closer to convergence, indicated by a small value of the convergence parameter (σ) for that bin, were adjusted less. This approach allowed the optimizer to rapidly adapt to the participant early in the optimization, then to fine-tune the speed-specific parameters as the optimization progressed. Following the update, the optimizer selected a promising set of new control laws to be sequentially evaluated in the next generation for the associated walking speed bin.

We compared the benefits of Real-world Optimized assistance from the untethered exoskeleton under standardized laboratory conditions to those of prior untethered exoskeletons10,11,12,13,14,15,16. We considered only the results of tests that: compared exoskeleton-assisted outcomes to walking in normal shoes without an exoskeleton; used standard indirect respirometry procedures; had sufficient sample sizes; and applied walking conditions within 10% of the chosen walking speeds and inclines in this study, which were chosen to allow comparison to the largest prior improvements in metabolic rate. For legibility, in this figure we depict only results within a 5% reduction in net metabolic cost of the best prior results for each category. Please see the Methods subsection “Comparison to other untethered exoskeletons” for a complete explanation of the methods used to select amongst prior exoskeleton experiments. Real-world Optimized assistance from the untethered exoskeleton resulted in large improvements in energy cost.

For one pilot participant (n = 1), walking with Real-world Optimized assistance reduced the metabolic cost of walking compared to Normal Shoes during several additional treadmill conditions. These results suggest that Real-world Optimized assistance may perform well during a wide range of common walking activities. The conditions were walking at 1.25 m s−1 on a 5° incline, walking at 1.5 m s−1 while wearing a vest weighing approximately 20% body weight, and climbing stairs at a rate of 50 steps per minute. These results are not included in the main text due to their preliminary nature compared to the primary study outcomes.

Sample code consisting of functions used with the opportunistic optimization approach. This simulates an optimization of the exoskeleton torque parameters over multiple generations. This code uses Python version 3.6.1. The required python packages are numpy (1.17.4), scikit-learn (0.21.3), scipy (1.3.2) and matplotlib (2.0.2).

The computer-aided design files and bill of materials needed to render and replicate the untethered exoskeleton. These computer-aided design files depict the individual hardware elements of the untethered exoskeleton and a complete assembled structure. These files can be used to manufacture and assemble a replica of the system for full reproduction of our untethered ankle exoskeleton.

A close-up of the untethered exoskeleton assisting a person walking in a public setting. The video is slowed down by a factor of four to allow better visualization of the motor-and-drum transmission applying torque about the ankle joint to assist the person as they extend their ankle and push off of the ground with their toes.

Real-world optimization of exoskeleton assistance during one hour of walking. Every 44 steps, a new set of assistance parameters were provided to the person. This allowed the optimizer to quickly evaluate many possible assistance parameters. Audio cues provided to the participant through an earpiece prompted them to self-select a naturalistic range of walking speeds. The prompts for each bout of walking are shown as text. Participants also received audio cues to stop walking, the timing of which were chosen to produce a naturalistic distribution of bout durations. Playback is at 15 times the actual speed.

Validation of Real-world Optimized exoskeleton assistance. The video shows 7 of the 15 outdoor walking bouts used to determine the real-world benefits exoskeleton assistance. Participants completed all walking bouts under three walking conditions: Real-world Optimized exoskeleton assistance, Generic Speed-adaptive exoskeleton assistance and Normal Shoes. Participants walked between yellow cones whose separations were chosen to provide a natural distribution of bout lengths. Different verbal prompts were given to the participant to elicit a naturalistic range of walking speeds. A portable respirometry system measured the ground-truth energy expenditure during movement. The humming of the respirometry air sampling system is audible in the video.

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Slade, P., Kochenderfer, M.J., Delp, S.L. et al. Personalizing exoskeleton assistance while walking in the real world. Nature 610, 277–282 (2022).


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