Human Gait Entrainment to Soft Robotic Hip Perturbation During Simulated Overground Walking

Entraining human gait with a periodic mechanical perturbation has been proposed as a potentially effective strategy for gait rehabilitation, but the related studies have mostly depended on the use of a fixed-speed treadmill (FST) due to various practical constraints. However, imposing a constant treadmill speed on participants becomes a critical problem because this speed constraint prohibits the participants from adjusting the gait speed, resulting in significant alterations in natural biomechanics as the entrainment alters the stride frequency. In this study, we hypothesized that the use of a variable-speed treadmill (VST), which enables the participants to continuously adjust their speed, can improve the success rate of gait entrainment and preserve natural gait biomechanics. To test this hypothesis, we recruited 15 young and healthy adults and let them walk on a conventional FST and a self-paced VST while wearing a soft robotic hip exosuit, which applied hip flexion perturbations at various frequencies, ranging from the preferred walking frequency to a 30% increased value. Kinematics and kinetics of the participants’ walking under the two treadmill conditions were measured on two separate days. Experimental results demonstrated a higher success rate of entrainment during VST walking compared to FST walking, particularly at faster perturbation frequencies. Furthermore, walking on VST facilitated the maintenance of natural biomechanics, such as stride length and normalized propulsive impulse, better than walking on FST. The observed improvement, primarily attributed to allowing an increase in walking speed following the increase in the perturbation frequency, suggests that using a self-paced VST is a viable method for exploiting the potentially beneficial therapeutic effects of entrainment in gait rehabilitation.


I. INTRODUCTION
G AIT disorders, common among individuals with neu- rological impairments such as stroke or Parkinson's disease, have a significant impact on their quality of life [1], [2], [3].Stroke survivors often experience reduced walking speed and impaired inter-limb coordination [2], [4].Similarly, individuals with Parkinson's disease exhibit gait asymmetry and instability [5].Past clinical studies focusing on these disorders have suggested that improvements in walking speed and propulsion could potentially aid in the gait rehabilitation process [6], [7].
Conventional physiotherapy approaches have been widely used for gait rehabilitation in these populations.One approach involves the constant assistance of a therapist or two to correct gait patterns while the patient receives stimuli passively [8], [9], [10].Another approach is the motor-learning technique, which requires active participation from the patient [11].In this method, patients learn specific tasks that can be generalized to their daily activities [12].However, these conventional techniques face challenges such as the lack of standardized outcome measures and the need for coordinated efforts by large teams [13], [14], [15].
In recent years, there has been a growing interest in robot-aided gait rehabilitation, particularly utilizing active exoskeletons.These advanced robotic systems offer unique capabilities for assisting and enhancing the gait rehabilitation process.The control strategies employed in robot-aided gait rehabilitation can be broadly classified into two categories: kinematics-based approaches and dynamics-based approaches.
Kinematics-based approaches involve programming the lower-limb exoskeletons to follow predefined joint trajectories [16], [17], [18].These trajectories are often derived from recorded gait data of healthy individuals and may be optimized or adjusted online to improve performance [19], [20], [21].However, one limitation of this approach is that it forces patients to conform to a rigid gait pattern that may not be easily generalized to various walking conditions.
To address the limitations of kinematics-based approaches and accommodate natural gait dynamics, impedance control has been proposed in the context of wearable exoskeletons [22], [23], [24], [25].Impedance control analyzes the interaction between the human and the robot and provides joint torques to assist walking.This approach can also be extended to generate adaptive position trajectories based on desired force trajectories.By incorporating interaction forces and adapting to the user's needs, impedance control offers a more flexible and responsive approach to gait assistance.However, it should be noted that although dynamics-based approaches address some of the drawbacks of kinematics-based approaches, they may not fully account for the complexity of the natural biomechanics of walking.
Gait entrainment refers to the synchronization of human walking with an external periodic perturbation within a certain frequency range, known as the basin of entrainment [26].This phenomenon allows humans to modulate their gait frequency to align with the perturbation while maintaining control over their walking dynamics.Previous studies have demonstrated successful gait entrainment in humans using ankle and hip exoskeletons that applied periodic torque perturbations, particularly when the perturbation frequencies closely align with the individual's natural gait frequency [27], [28], [29], [30].These findings have been further extended to improve gait cadence and address locomotor deficits in patients with neurological impairments such as stroke and multiple sclerosis [31].While these studies have shown promising results in gait rehabilitation, the use of heavy and rigid exoskeletons has reported a limited clinical impact due to a relatively small basin of entrainment, which accounts for less than 10% of the natural walking frequency.To address this limitation, recent studies have employed lightweight soft robotic devices attached to the ankle and hip joints [32], [33], resulting in a larger basin of entrainment (approximately 15% of the natural walking frequency) [34], [35].
Although several studies in the past have highlighted the potential therapeutic effects of gait entrainment, it should be noted that these studies were typically performed on treadmills with a fixed belt speed.This conventional experiment setup inevitably restrained the participants from changing their walking speed, distorting the natural biomechanics as the entrainment increased the stride frequency at high perturbation frequencies.Acknowledging this critical problem of using a conventional fixed-speed treadmill in entrainment studies, Ochoa et al. compared entrainment characteristics during treadmill walking and overground walking and reported a preference for overground walking [27], highlighting the importance of preserving natural biomechanics to achieve a higher success rate of entrainment, especially at faster perturbation frequencies.
The objective of this study was to examine whether simulated overground walking could enhance the success rate of gait entrainment beyond the outcomes of previous studies conducted on fixed-speed treadmills while preserving natural gait biomechanics.This study utilized a pneumatically-actuated, lightweight, soft hip exosuit to deliver periodic hip flexion perturbations, which has been verified to not interfere with the participant's natural biomechanics during walking [33].Additionally, an active self-paced treadmill algorithm was utilized to control the speed of the treadmill, matching it with the participant's walking speed and position [36].
This study involved two treadmill walking conditions: Variable-Speed Treadmill (VST) and Fixed-Speed Treadmill (FST) walking.The constraint of treadmill speed modification was the distinguishing feature between these two treadmill walking conditions.FST is a simple speed control mode where the treadmill speed is maintained constant throughout the experiment.On the other hand, VST refers to an adaptive speed control algorithm that converges to the participants' motion, allowing them to change their walking speed as needed.
The study hypothesized that the success rate of entrainment would be higher during VST walking compared to FST walking.Furthermore, it was hypothesized that VST would preserve the natural gait biomechanics of the participants better than FST, particularly at higher perturbation frequencies, due to its closer simulation of overground walking.

A. Soft Robotic Hip Exosuit (SR-HExo)
The Soft Robotic Hip Exosuit (SR-HExo) [33] is a soft robotic hip device that utilizes a dual flat fabric pneumatic artificial muscle (ff-PAM) actuator to generate either flexion or extension torque at the human hip joint through the application of compressed air.In this study, the device is worn on the right leg, with its actuator aligned with the rectus femoris muscle, enabling it to provide flexion torque at the hip joint.
The device comprises a waist belt (X3, RDX Inc., Manchester, UK) and a custom-made thigh belt equipped with adjustable tightness mechanisms to prevent slipping at these points (Fig. 1A).The dual ff-PAM actuator is securely fastened at the top end near the waist belt and at the bottom end near the thigh belt using straps that allow for tension adjustments along the actuators.Weighing only 0.64 kg, the device can be easily donned and doffed by the user in under one minute.Its lightweight nature and fabric-based design ensure a comfortable experience during dynamic activities such as walking.
To assess the peak impulse force and operating frequency of the device, a characterization test was performed in a condition similar to walking experiments.The device was actuated using a continuous pulse with a desired duration (D) of 150 ms utilizing a closed-loop low-level control system.It was secured between anchors positioned at each end (Fig. 1B).One of the anchors was equipped with a low-profile load cell (LRF 350, Futek Advanced Sensor Technology Inc., CA, USA) to measure force along the axis of the actuator.This characterization test served as a reference for determining the force response of the actuator from the pressure sensor-only setup utilized during the walking experiments.
The pressure control system for the device incorporates a dual 3-port 2-way solenoid valve (153378012VDC, Humphrey Products Company, MI, USA) and an analog pressure sensor (ASDX-AVX001PGAA3, Honeywell, MN, USA) (Fig. 2A).Based on the configuration described in [37], the dual solenoid valves offer three distinct states for controlling the actuator using pulse width modulation signals: Inflate, Hold, and Deflate (Fig. 2B).During the Inflate state, which is initiated at the beginning of the pulse when the measured pressure ( p m ) is below 95% of the desired pressure ( p d ), the valve system allows air from the compressor (Model 8010A, California Air Tools Inc., CA, USA), regulated at 200 kPa, to inflate the actuator.Following the Inflate state, the Hold state is activated when p m ≥ 0.95• p d .In this state, the valve system temporarily pauses the inflation and deflation actions of the actuator to hold the air inside the actuator.The Hold state is triggered at 95% of the desired pressure ( p d ) to ensure that the average p m in this state remains within ±10% of p d .At the end of the 150 ms pulse, the Deflate state is activated, allowing the release of air from the actuator through the valve system into the surrounding environment.The system remains in the Deflate state until the next pulse activates the Inflate state.

B. Other Experimental Setup
The walking study was conducted using an instrumented split-belt treadmill (Bertec Inc., OH, USA) equipped with a multi-axis force plate underneath each belt.Two experimental conditions were explored in this study: a) FST walking and b) VST walking.The main distinction between these two conditions lies in the nature of treadmill speed control.
During FST walking, the treadmill was set to a fixed speed that matched the participant's preferred walking speed (PWS).In contrast, during VST walking, the treadmill speed was actively adjusted to match the participant's position and velocity.This adjustment was made possible through the utilization of an algorithm originally introduced by [36], with necessary modifications implemented to ensure compatibility with the current system.The central component of the VST algorithm was a state estimator, which accurately estimated the participant's anterior-posterior center-of-mass (CoM) position and velocity [36].
To evaluate the accuracy of the VST state estimator, the ground truth data for the anterior-posterior CoM position was obtained using a motion capture system.The system consisted of eight Bonita cameras and utilized Nexus software (Vicon Motion System Ltd., Oxford, UK), and data were collected at a frequency of 200 Hz.For capturing the CoM position, four reflective markers were placed on the participant's pelvis: two markers on the anterior side (left and right) and two markers on the posterior side (left and right).The positions of these markers were tracked and averaged in the anterior-posterior direction to obtain the precise CoM position information.Additionally, the motion capture system was used to measure the participant's stride length based on a set of three reflective markers placed on the toe, ankle, and heel of each foot.
The multi-axis force plates of the instrumented treadmill measured the ground reaction forces (GRF) exerted by the participant's left and right legs during walking.The normal component of the GRF (F z ) was used to segment the gait cycle.Specifically, the initial contact was defined at the moment when F z exceeded 4.5% of the participant's body weight [38].The shear component of the GRF (F y ) was used to measure propulsive impulse [Ns].The data from the force plates were filtered using a 2 nd order low-pass Butterworth filter with a 20 Hz cutoff frequency in real-time.
The data collection from sensors (the pressure sensor and multi-axis force plates) and actuators (dual solenoid valves) was managed by Speedgoat Baseline Target Machine equipped with IO183 modules (Speedgoat GmbH, Liebefeld, Switzerland).The target machine operated a Simulink Real-Time (MathWorks Inc., MA, USA) application for data acquisition and control at 2 kHz.To ensure synchronization, the target machine triggered the motion capture system to start and stop data collection.Moreover, pertinent information regarding the internal pressure of the dual ff-PAM actuator in SR-HExo as well as the state of the valve system was also collected for further data analysis.

C. Experiment Protocol
The study consisted of two separate walking experiments, which were evaluated on two distinct days, with a minimum Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
gap of five days between them.On each of the two days, the participants took part in a total of 12 walking sessions, each lasting 180 s.Additionally, an extra calibration session was conducted on the first day.
1) Calibration Session: The calibration session consisted of two short experiments conducted on the first day for each participant, aimed at collecting the necessary information for the main walking experiments.The first calibration experiment required the participant to walk on the VST for 180 s without the device while maintaining their natural cadence and stride length.Once sufficient time was provided for the treadmill speed to stabilize, the average of the mean treadmill speed during the last 120 s was computed and regarded as the participant's PWS.
The second calibration experiment involved the participant walking on the treadmill for 90 s at a fixed speed equal to the PWS.In this experiment, the average gait frequency (f gait ), average stride length, and average propulsive impulse of the participant were calculated.Subsequently, the participant performed either the FST walking or VST walking experiment on the same day, while the remaining experiment was conducted on a different day.Both walking experiments consisted of 12 treadmill walking sessions, each lasting 180 s.In each session, the perturbation frequency of the SR-HExo pulse, with a pulse duration of 150 ms, was changed to one of the following 4 frequencies: 1.0•f gait (+0%), 1.08•f gait (+8%), 1.18•f gait (+18%), and 1.30•f gait (+30%).The p d for all sessions was set at a fixed value of 125 kPa, providing a sufficient stimulus (≈ 11% of peak hip flexion torque during normal walking) for entrainment while ensuring safety.
The 12 sessions were divided into 3 blocks, each with 4 unique perturbations.The order of the sessions within each block was fully randomized to avoid any bias in the obtained results.To further randomize the experiment, the periodic pulse was initiated at a random gait phase of either 20%, 50%, or 80% of the gait cycle in each session.A 20 s buffer period at the beginning of each session, without any perturbations, allowed all hardware to initialize before data collection.A mandatory rest period of at least 5 minutes was provided between blocks.
To minimize external influences on gait entrainment, the participants were equipped with noise-cancellation headphones (Quite Comfort 45, Bose Corporation, MA, USA).These headphones emitted white noise at a reasonable volume to prevent any auditory entrainment caused by the periodic ticking of the valves.Furthermore, the participants were instructed to avoid focusing on their feet to prevent potential visual entrainment.Instead, they were advised to gaze at a visual mark positioned at eye level on the wall before them while walking.

D. Participants
Fifteen healthy young adults (8 males and 7 females; age: 21.9±2.2years; height: 1.8±0.1 m; weight: 76.6±13.7 kg) were recruited for this study.Prior to the experiments, all participants provided written informed consent.The experimental protocol was reviewed and approved by the

Institutional Review Board of Arizona State University (STUDY00015183).
To prevent any potential ordering effect in the study, half of the participants started with the VST experiment on the first day, while the remaining participants started with the FST experiment as their first-day experiment condition.None of the participants were informed about the specific purpose of the experiment.

E. Data Processing
In both walking experiments, the entrainment characteristics were analyzed based on several parameters.These parameters included the success rate of entrainment, the percentage change in walking speed, the percentage change in stride length, and the percentage change in normalized propulsive impulse (NPI).
A session was labelled as a success if the perturbation phase of at least 80% of the final 30 strides was confined within the range of ±10% of the mean perturbation phase of the final strides.The perturbation phase was defined as the gait phase at which the Hold state is initiated within a stride.This criterion ensured consistency in assessing the success of the entrainment (as illustrated in Fig. 3).All perturbation phases were placed between 0-100% gait cycle (GC) for representation convenience.Discontinuities in the perturbation phases near 0% and 100% GC were addressed through phase unwrapping, which allowed for a continuous representation of the phase change.
Walking speed [m/s] was determined by calculating the ratio of the distance covered by the heel marker during one complete gait cycle to the duration of that gait cycle.Stride length [m] was determined by measuring the distance between successive points of heel contact made by the same foot.NPI [s] was calculated by integrating the positive portion of the shear force curve (F y ) throughout the propulsive phase, i.e., from heel-strike to toe-off, and then normalized by the participant's weight to account for differences in body size and weight among participants.Since the major spatiotemporal gait parameters, specifically, stride length and stride duration, exhibit symmetry between the left and right legs, and treadmill walking is spatially constrained to a straight line, each parameter reported in this study was the average of the left and right values.
For each participant, the mean of the parameters was reported based on the specific perturbation condition and treadmill condition, considering only the entrained sessions.In the group analysis, the estimated modelled means and standard deviation of the participants' parameters were reported and categorized by perturbation condition and walking condition.
Additionally, to investigate whether entrainment in VST walking preserves the natural biomechanics more effectively than FST walking, human walking data without the robot was obtained from the treadmill walking experiment in [39].Stride length and NPI measurements were interpolated at different walking speeds, corresponding to the perturbation conditions applied in the VST walking experiment.A subset of 10 participants from [39], whose physical attributes closely represented the population of the current study, was selected for data analysis (reported as NAT).

F. Statistical Analysis
The primary objective of this study was to compare the success rate of entrainment between VST walking and FST walking across different perturbation conditions (+0%, +8%, +18%, and +30%).The Wilcoxon Signed Rank test, a nonparametric equivalent to the t-test, was used as the data did not meet the assumption of a normal distribution.
The secondary objective was to determine whether VST walking preserves natural gait biomechanics more effectively than FST walking under different perturbation conditions, due to its capability for adaptive speed changes.To test this hypothesis, walking speeds in VST walking were compared to those in FST walking under different perturbation conditions.Alongside, stride length and NPI in FST and VST walking were compared with those observed in NAT walking across perturbation conditions.This was accomplished using Linear Mixed Effect modelling where the perturbation conditions (+0%, +8%, +18%, and +30%) and walking conditions (FST, VST, and NAT) were chosen as fixed effects.The 15 subjects that participated in the FST and VST experiments and 10 subjects adopted from literature (representing NAT) were chosen as random effects.Paired t-tests were performed to evaluate whether the walking speeds between FST and VST at each perturbation condition were different.Other paired t-tests were conducted to investigate whether the estimated modelled means of stride length and NPI in the FST-NAT pair and VST-NAT pair were different across perturbation conditions.
Baselines for response variables such as walking speed, stride length, and NPI were used to report percentage change during the FST and VST experiments compared to NAT walking.The baseline for walking speed was the population mean of PWS and it remained constant across perturbation conditions.The baselines for stride length and NPI were the estimated mean during NAT walking that were unique to each perturbation condition.
All statistical tests were performed with a significance level of 0.05, and the corresponding p-values are reported to indicate the statistical significance of the results.

A. System Validation: SR-HExo and Self-Paced Variable-Speed Treadmill
The actuator system was subjected to 18 perturbation cycles during the SR-HExo validation experiment.The parameters for the perturbations were set at a peak pressure of p d = 125 kPa, a pulse duration of 150 ms, and a period of 1 s.The peak impulse force generated by the dual pneumatic actuators was 122.1±0.8N (Fig. 4).The system produced a flexion torque of 7.4 Nm about the hip joint center (moment arm ≈ 6.1 cm).For an average participant weighing 72.8 kg, this torque corresponded to ≈11% of their peak hip torque of 67 Nm during natural pace walking [40].
The operating frequency of the actuator was determined from the time required to complete one cycle of actuation, which was found to be approximately 3 Hz (Fig. 4).This is sufficiently fast to accommodate the frequency observed during human walking [41].
The root-mean-square error calculated for the VST state estimator was 2.4±0.5 cm for mean position error and 2.0±0.2cm/s for mean speed error.These evaluations were performed on three participants walking at speeds ranging from 1.0 -1.5 m/s for 180 s.These results confirm the reliability of the VST in realizing self-paced variable speed walking on a treadmill.

B. Representative Participant Results
Representative participant results demonstrate the difference in the success rate of entrainment and gait characteristics between FST and VST walking experiments.During FST walking, this particular participant achieved 100% success of entrainment in the +0%, +8%, and +18% perturbation conditions.However, the success rate decreased to 0% in the +30% perturbation condition (Fig. 5A).In contrast, during VST walking, the participant achieved the perfect 100% success rate in all perturbation conditions (Fig. 5B).Thus, VST walking provided consistent success in entrainment across a wider range of perturbation conditions than FST walking.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
The differences in walking speeds between the FST and VST experiments were significant in every perturbation condition: +0% (p = 0.018), +8% (p < 0.001), +18% (p < 0.001), and +30% (p < 0.001).While the mean walking speed remained constant during the FST experiment, it increased in the VST experiment with an increase in the perturbation frequency (Fig. 7B).The population mean PWS, referred to as the baseline speed, was 1.2 m/s.The change in mean FST speed compared to the baseline was 0.0±0.2%across perturbation conditions.On the contrary, the increase in VST walking speed compared to the baseline was 3.0±6.1% at +0%, 13.2±6.0%at +8%, 25.3±6.2% at +18%, and 40.2±6.2% at +30% frequency condition.Thus, the gap in walking speed between the FST and VST walking widened as the perturbation frequency increased.
The mean VST walking speed at different perturbation conditions served as the reference walking speeds for calculating natural (NAT) stride length and NPI.The reference walking speeds for NAT were: 1.2, 1.4, 1.5, and 1.7 m/s at +0%, +8%, +18%, and +30% conditions, respectively.Stride length and NPI obtained from the NAT data were interpolated at these reference speeds and were represented in their natural scale alongside the FST and VST data (Fig. 7C-D).At each perturbation frequency, NAT served as a baseline for comparing the changes in stride length and NPI during FST and VST walking.

IV. DISCUSSION
This study was motivated by the unnatural biomechanics of entrained gaits on fixed-speed treadmill (FST) systems.The ideal solution for this problem is to entrain human gait on the ground using lightweight yet effective devices.However, applying proper periodic perturbations during overground walking while simultaneously monitoring the resulting gait biomechanics is costly in terms of space, infrastructure, and human resources.In contrast, a treadmill-based system offers the advantage of providing mechanical perturbation and utilizing stationary equipment without the need for excessive space; the stationary equipment includes not only the device that measures the participant's motor outcomes but also the heavy components of the actuation system, such as a compressor and valves.Therefore, entraining gait on a variable-speed treadmill (VST) emerges as a practical solution.This system capitalizes on the evident benefits of a treadmill setup while mitigating the unnatural biomechanics induced by FST.It serves as a feasible and viable alternative to overground gait entrainment.
A pneumatically-actuated soft robotic device was utilized to provide unilateral hip flexion perturbations at various frequencies, ranging from the natural walking frequency to a 30% increased frequency.Walking speed is strongly and positively correlated to several kinematic and kinetic aspects of gait in the healthy and the neurologically impaired populations [42], [43], [44], [45], [46], [47], [48], [49].Studies in the past that utilized the auditory cueing technique successfully improved walking speed in humans by modulating the frequency of metronome beats [50], [51].Sensory cueing, similar to this study, is also capable of modulating walking speeds in humans through the synchronization of periodic perturbations to the walking cadence [52], [53].Since an increase in walking cadence is associated with an increase in walking speed [42], this study only focused on perturbation frequencies higher than natural walking frequencies.These perturbation frequencies were evaluated for their entrainment performance using two treadmill systems: a conventional treadmill system (FST) set at a constant speed of the participant's PWS, and a simulated overground system (VST) that adjusted the treadmill speed to match the participant's walking speed.
Performance indicators such as entrainment success rate (%), walking speed (m/s), stride length (m), and NPI (ms) were evaluated in FST and VST walking at various perturbation frequencies.Despite the application of unilateral (right side) perturbations, the participants in this study exhibited bilateral (left and right side) symmetry in the stride length and stride duration.The comparison of left and right stride lengths during FST and VST walking, respectively, under +0% (p = 0.75 and 0.77), +8% (p = 0.11 and 0.45), and +30% (p = 0.092 and 0.44) conditions showed no significant differences.Under +18% condition, stride lengths between the left and right side during FST walking were significantly different (p = 0.030) while VST walking showed symmetric stride lengths (p = 0.33).The bilateral stride durations during FST and VST walking, respectively under +0% (p = 0.12 and 0.18), +8% (p = 0.33 and 0.28), +18% (p = 0.32 and 0.06), and +30% (p = 0.69 and 0.21) conditions demonstrated no significant differences.In contrast, the NPI on the perturbed side showed a higher reduction compared to the unperturbed side.While the bilateral NPIs during FST and VST walking were symmetric (p = 0.053 and 0.14) under +0% condition, they were significantly different under +8% (p = 0.003 and 0.029), +18% (p <0.001 and p = 0.004), and +30% (p <0.001 and p <0.001) conditions.However, as treadmill walking is restricted to a straight path, human walking speed is proportional to the overall (left and right averaged) CoM propulsion per stride and vice versa.Hence, the study reported the average stride length and NPI of both the left and right sides, rather than distinguishing between the bilateral contributions for each participant.
In both the FST and VST walking experiments, the success rate of entrainment was very high (>95%) for perturbations up to an 18% increase from the natural walking frequency (+18%).Notably, previous studies utilizing heavy rigid exoskeleton robots have only achieved successful entrainment within a narrow range close to the natural walking frequency, specifically below an 8% increase [28], [30].The larger basin of entrainment observed in the current study can be attributed to the use of the lightweight, low-inertia, soft robotic device, which minimally interfered with human walking and ensured entrainment even during FST walking [35].
While there was no statistically significant difference in the success rate of entrainment between FST and VST walking up to the +18% perturbation condition, there was a noticeable distinction in walking biomechanics.During FST walking, as the perturbation frequency increased beyond +0%, a consistent reduction in stride length and NPI was observed.Since the treadmill speed was fixed to the participant's PWS, the only way to achieve entrainment to faster perturbations was by decreasing the stride length, which is also associated with a decreased NPI [54], [55], [56].Maintaining normal NPI in human walking is important as it contributes to maintaining stability and balance and optimizing walking efficiency [57], [58].Although some trials at the +30% perturbation condition were still successful, the overall success rate of entrainment significantly dropped to below 70%.This underscores the significance of preserving natural gait biomechanics to achieve successful gait entrainment.
During VST walking, all participants exhibited an increase in walking speed rather than adopting shorter strides when subjected to faster perturbations.Notably, the stride lengths observed across the four different perturbation conditions were statistically similar to those in NAT walking.Conversely, beyond the +0% condition, the NPI decreased significantly compared to NAT walking as the perturbation frequency increased.Unlike the FST condition, this reduction in NPI cannot be explained by the change in the stride length because entrainment during VST walking did not alter the stride length.Therefore, it is plausible that the observed reduction in NPI during VST walking resulted from other factors, including the sensory cues from the periodic perturbations.The periodic perturbations during entrainment lasted for very short intervals (150 ms) and converged near the propulsion phase of gait (≈50% GC).These transient perturbations inevitably generated sensory cues that may have interrupted the leg extension and motivated the participants to move it towards flexion.In such a case, the overall leg extension during propulsion could be restricted, which might reduce the NPI during VST walking [59], [60], [61].However, the reduction in NPI during VST walking was far less than that during FST walking compared to NAT walking.Despite the reduction in NPI, VST walking demonstrated a consistently high success rate of entrainment (93.3%), even under the most challenging perturbation condition (+30%) examined in this study.This suggests that relaxing the fixed speed constraint and preserving the natural or inherent gait biomechanics are crucial factors in increasing the success rate of gait entrainment, particularly under high-frequency perturbation conditions.
The experimental results in this study are in line with the findings of a previous study that investigated the entrainment of overground human walking using a wearable ankle robot [27].The previous study by Ochoa et al. demonstrated that gait entrainment occurred more frequently and at a faster pace in overground walking compared to treadmill walking, supporting the idea that gait entrainment can be improved when a constant speed constraint is removed.However, in studies investigating overground locomotion, quantification of the kinematic and kinetic variables like stride length and NPI is inevitably limited; the extent to which the entrained gait preserves the natural biomechanics in the absence of the constant speed constraint could not be assessed in previous studies.In contrast, we could measure the detailed kinematics and kinetics by virtue of the system with VST and the motion capture device.The results of this study conclude that allowing volitional changes in walking speed clearly contributes to preserving the natural biomechanics of typical walking.This achievement is particularly important in that the therapeutic effects of any intervention should be eventually assessed under a circumstance similar to daily overground walking.
On a related note, to enhance the practical therapeutic benefits of gait entrainment on daily walking activity, it might be necessary to increase the success rate and basin of entrainment without overriding the natural biomechanics of overground walking.For example, although the basin of entrainment could be significantly expanded when a soft ankle robot applied periodic perturbations to a participant on a treadmill whose belt speed increased in proportion to the perturbation frequency [34], it is unclear whether such interventions will increase eventual therapeutic effects on daily walking more than the gait entrainment on VST or overground.While it is possible to achieve a higher entrainment basin by manipulating the treadmill speed, such manipulations may put forth additional artificial kinematic constraints.Considering the discrepancy between natural overground walking and imposed treadmill walking, the assessment of success rate and basin of entrainment should be accompanied by the assessment of biomechanical variables.
Several limitations of this study should be acknowledged.First, the self-paced treadmill algorithm used for VST walking provides a close approximation of overground walking but is not a complete replacement, as it cannot replicate the full range of human walking speeds with a constant error margin [36].Moreover, factors such as visual information and psychological effects during treadmill walking [62], [63], as well as inherent non-ideal behaviours of the treadmill [64], contribute to disparities between self-paced VST walking and overground walking.Nevertheless, these limitations can be outweighed by the advantages of using VST, including the reliable collection of multi-modal data and safety features that mitigate fall risks.Second, this study examined gait entrainment only up to a frequency increase of +30% from the natural walking frequency, without exploring the upper bound or basin of entrainment.Further research is required to investigate these aspects.Third, it is important to note that this study exclusively included young, healthy participants.Future studies should be conducted to examine whether the findings of this study hold true for elderly individuals or patients with neurological impairments such as stroke, multiple sclerosis, and Parkinson's disease.
This paper emphasizes the advantages of relaxing the speed constraint in gait entrainment studies.The utilization of a self-paced treadmill for simulated overground walking not only increases the likelihood of successful entrainment but also helps maintain natural gait biomechanics.These findings have the potential to enhance gait rehabilitation by addressing the limitations of conventional physiotherapy and current robotic gait rehabilitation approaches and providing a simple yet effective solution for modulating gait.This study improves on a recently introduced rehabilitation technique, gait entrainment, to produce clinically relevant results in the future.

Fig. 1 .
Fig. 1.A: Experimental setup.A human participant wearing the SR-HExo while walking on an instrumented treadmill.B: Experimental validation setup.Dual ff-PAM actuators anchored for impulse force and operating frequency testing.L represents the free length of the actuator in the deflated state.∆L represents the change in length due to contraction under pressure.F represents the corresponding tensile force generated by the actuator.

Fig. 2 .
Fig. 2. A: Schematic diagram of the SR-HExo actuation system.B: Three states of the dual solenoid valves setup: Inflate, hold, and deflate.

Fig. 3 .
Fig. 3.The perturbation phase during the last 30 strides of a representative participant in A: an entrained trial and B: a not entrained trial.

Fig. 4 .
Fig. 4. Characterization of the actuators at p d = 125 kPa and D = 150 ms.The state transition in the desired pressure controller is also shown.

Fig. 5 .
Fig. 5. Perturbation timing variation with strides for a representative participant at different perturbation frequencies during a A: Fixed-Speed Treadmill experiment and a B: Variable-Speed Treadmill experiment.Bold lines represent successfully entrained trials.

Fig. 6 .
Fig. 6.Walking biomechanics of a representative participant at different perturbation conditions during A: FST walking and B: VST walking.Nominal data represents the average value at the participant's PWS.

Fig. 7 .
Fig. 7. Group averaged results for A: success of entrainment, B: mean treadmill speed, C: stride length, and D: normalized propulsive impulse (NPI).NAT represents the stride length and NPI interpolated at reference walking speeds observed at different perturbation frequencies in the VST experiment.