Dynamic stability is tied to gait assistance when walking with a hip exoskeleton

Abstract

As age increases, factors such as visual impairments, joint instability, muscle weakness, and unreliable postural reflexes contribute to reduced stability and a higher risk of fall. Weak hip abductors/adductors further increase this risk. Hip flexors and extensors, which govern sagittal-plane limb advancement and propulsion, also play a critical role in dynamic walking stability. While traditional assistive devices support mobility, exoskeleton technology may improve walking stability and reduce fall risk. This study examines the effects of five exoskeleton assistance timings and two torque magnitudes on gait stability and step characteristics. We hypothesized hip assistance would increase MoS (particularly in the ML direction) through changes in foot placement and that nonlinear COM metrics would change in a direction consistent with stability adaptations. Ten healthy young adults (four males, six females; age: 27.6 ± 5.9 years, body mass: 65.3 ± 13.1 kg, height: 1.66 ± 0.08 m) were assessed for Margin of Stability (MoS), step characteristics, and center of mass nonlinearity. Statistical analyses included linear mixed-model ANOVAs, paired t-tests, and Wilcoxon signed-rank tests. Exoskeleton assistance increased MoS in medial-lateral (ML) and anterior-posterior (AP) directions. Wider, more variable steps and increased gait irregularity suggest extensive adaptation is required. While hip exoskeletons improve walking stability, further research is needed to understand long-term adaptation and daily use. Future studies should explore larger clinical populations and the long-term implications of exoskeleton-assisted walking.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1038/s41598-026-61659-4.

Introduction

Aging increases fall risk due to declines in sensory function, joint stability, muscle strength¹, and unreliable postural reflexes². The hip abductors and adductors are crucial for maintaining balance, and their weakness increases the risk of falling³. However, the hip flexors and extensors, which act primarily in the sagittal plane, are equally important for stable walking. Because gait progression occurs along the anterior–posterior direction, weakness or fatigue in these muscles can disrupt propulsion and limb control, leading to compensatory movements that also affect stability. Thus, deficiencies in either frontal-plane or sagittal-plane hip muscles can compromise dynamic balance and increase fall risk in older adults and individuals with gait limitations. Traditional assistive devices like wheelchairs and canes play a crucial role in mobility support, but they are typically introduced after significant functional decline has occurred. Advancements in exoskeleton design and development offer a promising opportunity to intervene earlier, by improving walking stability and reducing fall risk in older adults before reliance on more restrictive mobility aids⁴. It should be noted, however, that exoskeletons themselves may impose mechanical constraints, including added mass and altered joint loading, which can influence gait mechanics and user comfort. However, despite technological advances in assistive technologies, it remains unclear how specific assistance strategies affect dynamic balance control, which is critical for preventing falls and for translating exoskeleton use to older populations.

Quantifying walking stability requires measures that capture how the body responds in demanding situations. Walking stability is commonly quantified using step variability measures, nonlinear dynamic stability metrics, and biomechanics-based measures such as the margin of stability (MoS)⁵. MoS is a biomechanical measurement of stability during walking based on the relationship between the moving center of mass and foot placement⁶. In the anterior-posterior (AP) direction, the MoS is usually negative due to the forward fall condition necessary for continuous walking and transitioning to the next steps. The larger the negative MoS value, the more it indicates that the center of mass moves outside the base of support during walking, leading to an unstable condition until the next step is taken. In contrast, in the mediolateral (ML) direction, MoS is typically positive during double support but may become negative during single-limb support when the extrapolated center of mass moves beyond the lateral boundary of the base of support, requiring active control from the central nervous system⁷. A larger MoS suggests more margins for maintaining stability during walking, while a smaller MoS in the ML direction is the opposite. Other biomechanical measures of stability focus on step characteristics for regulating body movement⁷ and nonlinear techniques like linear and nonlinear gait variability^5,8. The Lyapunov Exponent (LyE) quantifies the rate of divergence of adjacent movement trajectories; higher values indicate greater local instability. Sample entropy (SampEn) measures signal regularity, with lower values reflecting more periodic motion and higher values indicating greater complexity or irregularity. Together, these measures provide a comprehensive assessment of walking stability by capturing spatial margins and dynamic adaptations in gait patterns.

Lower-body robotic exoskeletons assist walking in various populations, including patients with mobility impairments^9,10, soldiers¹¹, and industrial workers¹². By delivering mechanical power support, these devices can reduce muscle activation¹³ and metabolic cost^{14,16–19,19}, increase walking speed^20,22,23,23. Prior studies examining stability found that ankle exoskeleton assistance did not affect stability during walking in healthy older adults²⁴. On the other hand, compared to conventional methods, rehabilitation with a hip exoskeleton led to significant improvements in maximum walking speed and step length²⁵. Hip exoskeletons are especially promising for stability because the hip is central to step-to-step regulation and whole-body balance control¹. Also, it led to significantly positive balance improvements among stroke patients compared to those not using this device²⁶. During the weight acceptance phase of gait, the monoarticular hip extensors (gluteus maximus and adductor magnus) stabilize the hip as body weight transfers onto the outstretched limb. During the swing phase of gait, the hip flexors lift and advance the leg^27,29,29.

Alili et al. (2024) developed a bilateral hip exoskeleton that applied powered abduction and adduction torque through adaptive control, enabling active modulation of step width during treadmill walking³⁰. By adjusting the amount of assistance applied to side-to-side hip motion, the researchers were able to make participants take wider or narrower steps within just a few strides. Similarly, Park et al. (2022) evaluated a passive back-support exoskeleton that provided mechanical torque at the hip and lumbar region during level walking³¹. Although the main purpose of the device was to reduce low-back strain, it also changed how people walked, reducing hip motion and decreasing both forward–backward and side-to-side stability margins. These results suggest that external hip torque, even when passively applied, can meaningfully affect multi-joint coordination and dynamic balance, reinforcing the sensitivity of stability metrics to hip-assistive interventions. Lee et al. demonstrated that varying assistance timing in a hip exoskeleton significantly influenced metabolic cost, assistance power, and spatiotemporal gait parameters during treadmill walking. However, the effects of hip assistance timing on biomechanical stability measures such as margin of stability and nonlinear COM dynamics remain unexplored^32,33. In a clinical context, Ishmael et al. (2023) examined a powered hip exoskeleton that provides unilateral assistance to individuals with above-knee amputations³⁴. The exoskeleton reduced the work required from the hip muscles on the prosthetic side by up to 80%, without altering balance measures such as body sway or the relationship between the body’s center of mass and the center of pressure.

Reducing muscular demand and delaying fatigue can indirectly improve postural stability, as fatigue is known to compromise coordination and increase fall risk during prolonged walking. Hsua et al. (2023) reported that no trials to date have examined the orthotic effects of wearing exoskeletons on stability outcomes, and that evidence in healthy and clinical groups remains incomplete³⁵. Liac et al. (2024) highlighted that there is currently no global consensus on measurement methods for functional ability, limiting the broad application and comparison across exoskeleton studies³⁶. They emphasized that future research should consider variations in locomotor capacity to improve the effectiveness and user acceptance of assistive technologies. Therefore, this study systematically varied hip exoskeleton assistance timing (five conditions) and torque magnitude (two levels) to quantify effects on: (i) margin of stability in the AP and ML directions, (ii) step characteristics, and (iii) nonlinear COM dynamics. Because assistance timing alters when mechanical support is delivered relative to stance and swing phases, we hypothesized that earlier and later assistance timings would produce distinct adaptations in walking stability. Specifically, earlier timing conditions were expected to influence anterior–posterior COM progression and propulsion-related stability mechanisms, whereas later timing conditions were expected to more strongly affect mediolateral balance regulation through foot-placement adaptations. We further hypothesized that higher torque magnitudes would amplify these timing-dependent effects.

Results

Ten participants completed all walking conditions, including five timing and two torque-magnitude levels, along with no-exoskeleton and powered-off reference trials. Outcome variables included: (i) MoS in the anterior–posterior and mediolateral directions, (ii) step characteristics (length, width, time, and velocity), and (iii) nonlinear measures of center-of-mass motion (Lyapunov exponent (LyE) and sample entropy (SampEn)). Statistical analyses were performed using a linear mixed-model Analysis of Variance (ANOVA) with subject as a random effect and torque magnitude or timing as fixed effects, as described in the Methods. Outcome variables, such as the mean and standard deviations of the margin of stability measures, step characteristics, and nonlinear measures of the center of mass, were quantified across various conditions and compared to the no-exoskeleton or powered-off conditions. The results are detailed in the following sections. Experimental conditions were administered in randomized order within each protocol block to minimize order and learning effects. To support full transparency, Appendix Table S1 provides the raw values for all MoS, step, and nonlinear metrics across conditions, including baseline values. Percentage changes are presented in the main figures to emphasize the relative increases or decreases associated with each assistance condition, which aligns with the primary aim of this study. Table 1 presents the raw values of anterior–posterior (MoS AP) and medial–lateral (MoS ML) margin of stability (mean and variability), spatiotemporal parameters, and COM nonlinear dynamics across assistance timing conditions (0%, 21%, 28%, 35%, 42%, and 49% of the gait cycle). Figure 1 presents the commanded hip assistance torque profiles and corresponding sagittal-plane hip kinematics across the gait cycle. Across all conditions, the hip remained in net flexion relative to the upright-standing reference throughout the gait cycle, consistent with the predominance of the passive flexion-spring force over the actively commanded extension torque (Fig. 1B-C); nonetheless, the assisted conditions achieved measurably greater hip extension excursion during late stance relative to the No-Exo and Powered-Off conditions. Frontal-plane hip kinematics (Fig. 1D-E) showed a similar pattern across all conditions, with hip adduction of approximately 3 to 4 degrees during early-to-mid stance followed by a peak in hip abduction of approximately 7 to 9 degrees during the late-stance-to-swing transition (approximately 60% to 70% of the gait cycle); assisted conditions showed a descriptive trend toward slightly greater peak hip abduction relative to the No-Exo condition, although this was not formally tested.

Table 1.

Raw values of anterior–posterior (MoS AP) and medial–lateral (MoS ML) margin of stability (mean and variability), spatiotemporal parameters, and COM nonlinear dynamics across assistance timing conditions (0%, 21%, 28%, 35%, 42%, and 49% of the gait cycle). The numbers are formatted in the (Mean ± Standard Deviation) style.

MOS AP Mean (mm)	Low Earliest	Low Early	Low Medium	Low Late	Low Latest	High Earliest	High Early	High Medium	High Late	High Latest	No Assist	No Exo
	−102.03 ± 40.40	−98.07 ± 42.51	−102.60 ± 42.48	−109.14 ± 40.66	−103.47 ± 42.26	−95.42 ± 36.55	−105.95 ± 38.10	−102.16 ± 42.93	−106.79 ± 41.79	−108.66 ± 44.43	−99.40 ± 29.87	−90.19 ± 35.88
MOS AP Variability (mm)	12.48 ± 1.54	20.07 ± 15.48	12.49 ± 1.49	16.77 ± 7.90	13.77 ± 2.06	17.43 ± 10.26	14.52 ± 4.82	13.37 ± 2.17	13.24 ± 1.70	14.60 ± 3.91	15.24 ± 7.71	13.25 ± 2.67
MOS ML Mean (mm)	54.62 ± 20.10	50.18 ± 17.38	53.21 ± 21.76	54.23 ± 19.96	51.48 ± 18.58	50.65 ± 16.46	53.25 ± 18.61	58.03 ± 19.95	53.88 ± 20.10	52.69 ± 17.02	43.93 ± 14.76	49.92 ± 16.71
MOS ML Variability (mm)	19.87 ± 7.14	19.87 ± 7.28	19.07 ± 6.60	19.73 ± 6.95	19.09 ± 6.51	19.03 ± 4.23	18.34 ± 3.93	20.21 ± 5.18	21.06 ± 8.01	19.16 ± 6.09	18.26 ± 5.36	20.28 ± 7.64
Step time Mean (s)	0.49 ± 0.03	0.49 ± 0.04	0.49 ± 0.03	0.49 ± 0.03	0.49 ± 0.04	0.49 ± 0.03	0.49 ± 0.03	0.49 ± 0.03	0.49 ± 0.03	0.48 ± 0.04	0.49 ± 0.03	0.49 ± 0.03
Step width Mean (mm)	171.64 ± 47.46	168.00 ± 43.61	169.45 ± 50.76	177.98 ± 52.08	173.83 ± 45.37	167.74 ± 43.70	174.52 ± 41.55	177.86 ± 47.68	173.81 ± 51.18	175.13 ± 41.00	143.36 ± 40.53	161.49 ± 41.08
Step length Mean (mm)	575.58 ± 42.18	587.34 ± 47.80	575.26 ± 41.35	563.52 ± 48.18	577.53 ± 50.21	573.44 ± 58.74	582.56 ± 40.05	578.04 ± 44.74	576.89 ± 42.18	574.43 ± 55.75	569.03 ± 42.66	582.43 ± 36.61
Step velocity Mean (mm/sec)	1182.07 ± 14.01	1196.21 ± 61.03	1178.49 ± 15.05	1154.68 ± 62.14	1178.81 ± 16.34	1167.23 ± 75.57	1183.61 ± 15.68	1182.77 ± 15.22	1184.00 ± 14.76	1183.35 ± 20.16	1162.23 ± 65.96	1182.43 ± 15.53
Step time Variability (s)	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00	0.01 ± 0.00
Step width Variability (mm)	17.29 ± 2.98	18.20 ± 2.82	17.17 ± 3.39	18.89 ± 2.74	18.25 ± 4.55	20.43 ± 4.18	17.97 ± 3.57	17.09 ± 3.68	19.11 ± 4.32	18.14 ± 6.07	17.97 ± 3.76	19.73 ± 5.09
Step length Variability (mm)	19.82 ± 3.08	24.69 ± 8.01	20.49 ± 3.35	22.25 ± 2.98	20.41 ± 3.54	20.67 ± 4.49	21.59 ± 4.33	19.25 ± 4.14	19.14 ± 3.71	20.63 ± 3.63	19.11 ± 3.24	20.22 ± 4.82
Step velocity Variability (mm/s)	17.87 ± 2.99	25.55 ± 20.27	17.95 ± 3.26	21.36 ± 5.34	18.29 ± 3.41	18.70 ± 5.57	19.05 ± 4.50	19.58 ± 3.41	18.95 ± 3.20	20.00 ± 5.56	17.59 ± 3.28	18.68 ± 5.21
COM AP LyE (bit/s)	2.40 ± 1.30	3.37 ± 0.82	2.15 ± 1.47	2.48 ± 1.78	2.67 ± 1.40	2.55 ± 1.10	3.25 ± 1.64	2.77 ± 1.48	3.00 ± 1.77	2.87 ± 1.33	2.79 ± 2.12	3.20 ± 1.63
COM ML LyE (bit/s)	1.97 ± 0.88	1.72 ± 0.47	1.63 ± 0.49	1.78 ± 0.63	1.68 ± 0.39	1.62 ± 0.37	1.66 ± 0.43	1.71 ± 0.61	1.60 ± 0.73	1.65 ± 0.49	2.22 ± 1.08	1.98 ± 1.12
COM Vertical LyE (bit/s)	0.63 ± 0.24	0.63 ± 0.49	0.73 ± 0.36	0.70 ± 0.29	0.57 ± 0.31	0.66 ± 0.34	0.66 ± 0.48	0.45 ± 0.25	0.75 ± 0.82	0.57 ± 0.14	1.17 ± 1.15	1.02 ± 1.39
COM AP SpEn	0.07 ± 0.03	0.09 ± 0.04	0.07 ± 0.02	0.08 ± 0.04	0.09 ± 0.05	0.08 ± 0.03	0.08 ± 0.02	0.07 ± 0.03	0.10 ± 0.05	0.08 ± 0.04	0.07 ± 0.04	0.08 ± 0.03
COM ML SpEn	0.20 ± 0.01	0.19 ± 0.01	0.19 ± 0.02	0.20 ± 0.01	0.19 ± 0.02	0.19 ± 0.02	0.19 ± 0.01	0.19 ± 0.02	0.18 ± 0.03	0.19 ± 0.02	0.16 ± 0.03	0.19 ± 0.02
COM Vertical SpEn	0.32 ± 0.03	0.32 ± 0.03	0.32 ± 0.02	0.33 ± 0.03	0.32 ± 0.02	0.32 ± 0.02	0.32 ± 0.02	0.30 ± 0.08	0.33 ± 0.03	0.32 ± 0.02	0.33 ± 0.04	0.32 ± 0.03

Fig. 1.

Assistance torque profiles and corresponding hip sagittal-plane kinematics across the gait cycle. (A) Commanded hip torque profiles for all 10 assistance conditions, combining five assistance timing windows (Earliest, Early, Medium, Late, and Latest timing: %0, %21, %28, %35, %42, and %49 of the stride time of the gait cycle) and two peak torque magnitudes of Low and High (0.06 and 0.12 Nm·kg⁻¹). Each condition is represented by a different color as indicated in the legend. (B) Mean hip sagittal-plane angle trajectories across the gait cycle for the low-torque conditions (0.06 Nm·kg⁻¹). (C) Mean hip sagittal-plane angle trajectories across the gait cycle for the high-torque conditions (0.12 Nm·kg⁻¹). All curves are plotted over 0–100% of the gait cycle. Hip joint angles are reported relative to the anatomical upright standing position; positive values denote flexion. Because the reference is set at quiet standing, values during walking may remain positive throughout the gait cycle, reflecting the degree of flexion relative to that upright posture. The torque magnitudes listed in the Methods (0.06 and 0.12 Nm/kg) refer to the commanded end-point magnitude of the sinusoidal profile; the visual peak amplitude of the waveform in the figure may differ due to the sinusoidal shape of the torque curve. The passive flexion springs are not represented as separate torque curves in panel A, as their magnitude varies passively with hip joint position and is not independently commanded. The torque profiles displayed in panel A represent actual measured torque values recorded during each assistance condition; the ‘Low’ (0.06 Nm·kg-1) and ‘High’ (0.12 Nm·kg-1) designations refer to the desired (commanded) target peak magnitudes. Shaded bands in panels A-C represent +/−1 standard deviation across participants. The device provides active hip extension torque through dorsal cable actuation together with passive hip flexion assistance through anterior spring (bungee-cord) elements; because the passive flexion-spring force typically exceeded the actively commanded extension torque achieved during stance, the group-mean hip angle trajectory remained in flexion relative to the upright-standing reference across most of the gait cycle. The standard-deviation bands show that, for some participants and trials, hip angle approached or briefly crossed the upright reference, indicating that hip extension did occur even though the group mean remained flexion-biased. This flexion-dominant pattern reflects a recognized characteristic of the original device design³⁷ and is discussed further in the Discussion and Limitations. (D) and (E) present the corresponding mean hip frontal-plane (ab/adduction) angle trajectories across the gait cycle for the low- and high-torque conditions, respectively. Hip ab/adduction angle is reported relative to the same upright-standing calibration trial; positive values denote abduction and negative values denote adduction. Shaded bands in panels D-E represent +/−1 standard deviation across participants, as in panels B-C.

• i.MoS

The magnitude of mean MoS AP increased by 7 to 24% across all assisted conditions compared to the powered-off condition. However, no significant differences were observed between the assisted and No-Exo conditions. Walking with higher torque assistance applied at 28% of the gait cycle resulted in a 19.5% increase in MoS AP compared to the powered-off condition (p = 0.006) (Fig. 2). Among the tested timing conditions, the significant improvement in MoS AP was concentrated at this earlier timing window (28% of the gait cycle), while later timing conditions (42% and 49%) showed smaller, non-significant changes, suggesting that earlier-stance assistance may more directly influence the forward-progression dynamics underlying MoS AP.

Fig. 2.

(A) anterior-posterior margin of stability (MoS AP) mean, (B) MoS AP variability, (C) medial-lateral margin of stability (MoS ML) mean, and (D) MoS ML variability. The red and blue bars represent the low torque and high torque-assisted conditions compared to the Powered-Off condition. In contrast, the green and yellow bars represent the low torque and high torque-assisted conditions compared to the No-Exo condition. Black bars represent the No-Exo condition. Asterisks (*) and plus signs (+) indicate significant differences < 0.05 and < 0.1, respectively.

Compared to the No-Exo condition, all assisted conditions showed a significant increase in mean MoS ML ranging from 15% to 36%. The assistance provided by the exoskeleton resulted in a slight increase in the mean MoS ML compared to the powered-off condition. Additionally, the No-Exo condition showed a significantly greater mean MoS ML compared to the powered-off condition (p = 0.035) The increase in MoS ML was broadly consistent across all timing conditions, suggesting that mediolateral foot placement adaptation may represent a generalized response to exoskeleton presence rather than a timing-dependent mechanism within the tested range. Among the timing conditions, the 35% high-torque and 42% low-torque conditions showed the largest descriptive increases in ML MoS, suggesting that later assistance timings may have more strongly influenced mediolateral foot-placement regulation, although these differences did not reach statistical significance. (Fig. 2).

• ii.Step characteristics

Step velocity did not vary significantly across assisted conditions compared to the powered-off state. Step length increased modestly (0.6–3.5%) across most assisted conditions compared to the no-exoskeleton condition and by about 2% in the powered-off (no-assistance) condition. Although these differences were not statistically significant, the consistent trend indicates that wearing the exoskeleton may slightly lengthen step distance, potentially due to its structural support.

In contrast, step width increased by 19% to 27% across all assisted conditions compared to the No-Exo condition. However, these increases were not significant, as the p-values fell between 0.07 and 0.1 (Fig. 3).

Fig. 3.

Percentage changes in (A) step time mean, (B) step width mean, (C) step length mean, (D) step velocity mean. The red and blue bars represent the low torque and high torque-assisted conditions compared to the Powered-Off condition. In contrast, the green and yellow bars represent the low torque and high torque-assisted conditions compared to the No-Exo condition. Black bars represent the No-Exo condition. Asterisks (*) and plus signs (+) indicate significant differences < 0.05 and < 0.1, respectively.

Compared to the No-Exo condition, all assisted conditions resulted in increased step time variability. However, this change of 5% to 22%, did not reach statistical significance. Linear variability increased for step length (5.5% to 30%) and step velocity (3.2% to 50%) compared to the No-Exo condition, though these increases did not reach statistical significance (Fig. 4).

Fig. 4.

Percentage changes in (A) step time variability, (B) step width variability, (C) step length variability, and (D) step velocity variability. The red and blue bars represent the low torque and high torque-assisted conditions compared to the Powered-Off condition. In contrast, the green and yellow bars represent the low torque and high torque-assisted conditions compared to the No-Exo condition. Black bars represent the No-Exo condition. Asterisks (*) and plus signs (+) indicate significant differences < 0.05 and < 0.1, respectively.

Timing-dependent differences in step characteristics were modest. However, later assistance conditions generally demonstrated slightly greater increases in step width, whereas earlier timing conditions showed smaller changes in mediolateral stepping behavior.

• iii.Nonlinearity of center of mass

Compared to the No-Exo and powered-off conditions, the LyE of anterior-posterior center of mass (COM) motion during assisted walking increased (up to 113% and 223%, respectively), as did sample entropy (up to 71% and 51%, respectively). However, these differences did not achieve statistical significance. In contrast, the LyE of medial-lateral COM motion exhibited a different trend, increasing during assisted walking compared to the powered-off condition but decreasing compared to the No-Exo condition. Similarly, compared to the No-Exo and powered-off conditions, the LyE of vertical COM motion during assisted walking slightly decreased (7% to 27%), while the sample entropy of vertical COM motion slightly increased (9% to 15%) Nonlinear COM measures demonstrated direction- and timing-dependent trends, although none reached statistical significance. Earlier timing conditions tended to show larger increases in AP LyE, whereas later timing conditions showed smaller changes in mediolateral nonlinear variability.(Fig. 5).

Fig. 5.

This figure illustrates the percentage of changes in the Lyapunov exponent of COM motion in the anterior-posterior (A), medial-lateral (B), and vertical (C) directions. Also, it illustrates the percentage of changes in the sample entropy of COM motion in the anterior-posterior (D), medial-lateral (E), and vertical (F) directions. None of the changes in any of the subplots reached statistical significance.

Discussion

This study examined the effects of five assistance timings and two torque magnitudes on multiple measures of walking stability. The primary finding was that hip exoskeleton assistance significantly increased MoS ML, indicating a widening of the base of support, primarily driven by small increases in step width. These results suggest that exoskeleton assistance influenced step-to-step regulation by altering foot placement. In contrast, MoS AP showed changes in magnitude, but these effects were modest and should be interpreted cautiously given the inherent forward progression of steady walking. Step characteristics remained largely unchanged across conditions, and nonlinear measures showed trends toward increased variability during assisted walking; however, these changes were not statistically significant. Overall, the most robust adaptation observed was the ML MoS increase associated with altered foot placement strategy.

The pattern of results also suggests that assistance timing differentially influenced the direction of stability adaptation. The significant improvement in MoS AP was concentrated at earlier assistance timing (high torque at 28% of the gait cycle), while later timing conditions (42% and 49%) showed smaller, non-significant changes in MoS AP. In contrast, MoS ML increased across all timing conditions, with the 35% high-torque and 42% low-torque conditions showing the largest descriptive increases. This distinction may reflect the phase-specific role of hip extension assistance: earlier-stance torque coincides with the weight-acceptance phase, where anterior-posterior momentum is actively regulated, and may therefore more directly influence the forward-fall dynamics captured by MoS AP. The descriptive trend toward larger ML MoS increases at later timing conditions, in turn, suggests that later assistance timings may have more strongly influenced mediolateral foot-placement regulation, though this pattern did not reach statistical significance in this pilot sample. This timing-dependent pattern addresses the central research question and underscores the value of systematically varying assistance timing rather than evaluating a single profile.The mean MoS AP increased by 7 to 19% across all assisted conditions compared to the powered-off condition. When the COM moves faster in the AP direction, it results in a greater negative value of MoS in the AP direction under assisted conditions. This occurs because the extrapolated center of mass is located further outside the anterior boundaries of the base of support. In this scenario, the whole-body momentum, driven by passive dynamics, supports the “fall forward” gait mechanism, leading to stepping and continued walking. While the MoS in the AP direction may not fully capture overall stability, it can indicate confidence in maintaining stability during a fall-forward condition³⁸. This interpretation is consistent with the sagittal-plane hip kinematics shown in Fig. 1: although the hip remained flexion-biased relative to the upright-standing reference across the gait cycle - reflecting the predominance of the passive anterior flexion-spring force over the actively commanded dorsal extension torque - the assisted conditions still achieved measurably greater hip extension excursion during late stance relative to the No-Exo and Powered-Off conditions. Because this additional extension excursion occurred during the weight-acceptance-to-propulsion phase, it may have contributed to the forward-progression dynamics underlying the AP MoS increases, particularly the significant improvement observed with high-torque assistance at 28% of the gait cycle. The persistent flexion bias observed across all conditions, including No-Exo, reflects a feature of the original device’s spring-based flexion-assistance design³⁷ rather than an artifact specific to a single assistance condition.

Consistent with previous literature, exoskeletons have the potential to enhance user stability, agility, and gait robustness³⁹. However, there is limited evidence on the impact of hip exoskeletons on walking stability, with more focus on the ankle^40,41. This study showed increased walking stability in the ML direction, as evidenced by an increase in MoS ML mean (15% to 36%) across all assisted conditions compared to the no-exoskeleton condition. An increase in MoS ML may reflect a compensatory widening of the base of support rather than a direct enhancement of intrinsic stability. In the present study, the ML MoS change was primarily associated with small but consistent increases in step width, with minimal alterations in XCoM motion. This suggests that participants adjusted foot placement to regulate balance while adapting to the device. Such findings are consistent with prior work indicating that ML stability during steady walking is predominantly controlled through foot placement strategies rather than through direct reductions in center-of-mass sway⁷. For example, Fang and Lerner (2023) reported that ankle exoskeleton assistance increased ML MoS primarily via step width changes, while AP MoS and COM dynamics remained largely unaffected²⁴. Their results further demonstrated that different stability metrics can respond independently to exoskeleton assistance, indicating that increases in MoS do not necessarily reflect direct stabilization of whole-body motion. In this context, our findings suggest that hip exoskeleton assistance influenced the control strategy used to regulate mediolateral balance, likely by altering mechanical or proprioceptive conditions that biased foot placement selection. Rather than directly constraining XCoM motion, the device appears to have prompted participants to adopt a slightly wider base of support, thereby increasing ML MoS through step-to-step regulation. Although we understand that assistive devices can influence gait patterns, the present study extends prior work by systematically isolating the effects of assistance timing and torque magnitude on stability-related outcomes. Rather than simply demonstrating that gait changes occur, our results identify how specific assistance profiles modulate stability control strategies, particularly through mediolateral MoS and associated foot placement adjustments. Importantly, prior studies have shown that stability metrics do not necessarily change in parallel with general gait or metabolic alteration²⁴. In this context, the present findings provide insight into which aspects of gait stability are sensitive to hip assistance timing and magnitude, thereby informing controller design beyond generic device-induced gait modifications.

This increase suggests that active exoskeleton assistance may increase ML stability during walking This could be attributed to the physical support and structure offered by the exoskeleton, or the presence of the orthotic device in the groin/medial thigh region could have influenced limb positioning during the exoskeleton conditions, which might help stabilize the wearer. This is particularly relevant for populations such as post-stroke survivors, older adults, or individuals with neuromuscular disorders, for whom enhanced stability can reduce the risk of falls and improve mobility independence⁴. Previous studies found that using the exoskeleton adds extra weight and decreases the hip range of motion⁴², which can alter foot positioning and walking mechanics, potentially affecting overall stability and user comfort. Moreover, reducing muscular power generation⁴³ could be another reason for walking with larger ML MoS to minimize the risk of falls. Furthermore, the relatively lower MoS ML in the powered-off condition compared to the No-Exo condition likely reflects mechanical constraints imposed by the device structure — including added mass and altered limb positioning — which may have slightly narrowed step width when the device was worn but not actively assisting. This aligns with prior work showing that wearing lower-limb exoskeletons can alter limb kinematics even when unpowered⁴². Future studies will incorporate detailed joint kinematic analysis to better characterize these adaptations and their relationship to stability outcomes. Therefore, the exoskeleton’s physical design, added weight, and modifications in joint kinematics and kinetics could be potential factors influencing MoS in the ML direction.

The observed adaptations likely arise from how hip exoskeleton assistance alters whole-body balance demands. Assistance applied at the hip can modify lower body coordination and walking stability requirements, prompting users to regulate balance through foot placement adjustments, which is the primary mechanism for controlling mediolateral stability during steady walking. Rather than attempting to minimize center-of-mass motion, participants appear to adopt a wider base of support to maintain robustness against small perturbations under altered mechanical conditions. This distinction is critical for advancing exoskeleton design, as controllers intended to enhance balance may need to explicitly target foot placement or frontal-plane dynamics rather than focusing solely on sagittal-plane propulsion or energetic efficiency. Additionally, the passive flexion assistance provided by the spring elements on the anterior side of the device may have contributed to step-to-step consistency by facilitating limb advancement during swing, potentially influencing foot placement and, in turn, MoS ML. Future controlled studies isolating the flexion component are needed to clarify its independent contribution to stability outcomes. Consistent with this interpretation, the frontal-plane hip kinematics in Fig. 1D-E showed a peak in hip abduction during the late-stance-to-swing transition that was descriptively larger in the assisted conditions than in the No-Exo condition, coinciding with the gait phase associated with limb unloading and contralateral foot placement. This pattern is consistent with a mechanistic link between hip ab/adduction motion and the mediolateral foot-placement adaptations underlying the observed ML MoS increases, although the present descriptive comparison does not establish a direct causal or statistical relationship.

Step width increased in four out of ten assisted conditions compared to the No-Exo condition, though these changes were not consistent across all conditions. A wider step width is associated with an increased base of support, which can directly impact MoS in the ML direction and aligns with the observed stability changes in this study. Previous research shows that walking with the passive-elastic knee-ankle exoskeleton led to an approximately 21% increase in step width compared to walking without an exoskeleton⁴⁴. The bulk of the orthosis in the groin/medial thigh region may have contributed to this increase in step width. The changes in step width might indicate a compensatory mechanism in response to the additional mass and the exoskeleton’s position on the leg. Although a slightly wider step width can improve mediolateral MoS by expanding the base of support, this adaptation may increase lateral leg motion and energy expenditure. In this pilot study, the modest step-width changes were unlikely to significantly affect metabolic cost; however, future studies integrating metabolic measurements will help determine the stability–energy trade-off associated with hip-exoskeleton assistance.

Step variability was significantly increased in only one of ten torque assistance conditions (Low Torque at 28% stride) compared to the No-Exo condition, specifically for step time variability. In contrast, other conditions showed no significant differences (Fig. 3). Mean step time increased under Low Torque at 28% stride, though other conditions did not exhibit consistent or statistically significant changes compared to the No-Exo condition (Fig. 2). Step time variability is a strong indicator for predicting fall occurrences in older adults^45,46, with greater variability being linked to an increased risk of falling. The increase in step-time variability at 28% Low Torque does not directly correspond to the MoS changes in the ML direction, which were observed at 35% High Torque and 42% Low Torque. However, changes in step-time variability may still reflect an adaptive strategy to maintain stability during assisted walking. Although a significant increase in step time variability was observed in one of ten conditions, other conditions showed non-significant trends. These variations may reflect early adaptation to the new device, with potential learning effects occurring over time. Extensive training is necessary for users to benefit fully from exoskeleton assistance. Although walking performance improves quickly with initial use, it is further enhanced as individuals become more adept at using the device^15,17,17. In the early stages of learning, movement variability increases as the nervous system explores potential control strategies. This variability decreases exponentially with experience as the nervous system refines and adopts an optimal control strategy. Previous research showed that healthy younger adults typically needed about three hours of training to adapt to ankle exoskeleton use completely.

The LyE and SampEn of the center of mass exhibited direction-dependent changes during assisted walking. In the AP direction, both LyE and SampEn increased, indicating greater nonlinear variability and irregularity²⁴. However, in the ML and Ver directions, LyE primarily decreased across conditions, whereas SampEn increased in most comparisons, suggesting distinct adaptations in dynamic stability mechanisms across movement planes²⁴. The exoskeleton assistance may introduce a new walking pattern that requires mastering practice. This aligns with discussions on the adaptive capacity of the human movement system, highlighting the role of interactivity in motor control and exploration in participants^47,48. However, movement variability is critical for novice and skilled behavior performance⁴⁹, as it reflects the availability of multiple movement options, allowing for flexible and adaptive strategies instead of relying on rigid movements during walking. Using the LyE, Yamada reported that body sway in healthy adults during standing resembles mathematical chaos, revealing inherent complexity and irregularity⁵⁰. From an information-processing perspective, this chaotic nature benefits the body’s posture-regulating system.

This pilot study involved a small sample size of ten participants across multiple assistance conditions, which limits statistical power and increases the likelihood of Type II errors. These results should therefore be interpreted as exploratory trends to inform larger follow-up studies. Although MoS ML increased significantly while step width did not, these metrics capture different aspects of mediolateral control: MoS reflects the dynamic interaction between center-of-mass motion and foot placement, whereas step width represents static spatial positioning. The observed difference may therefore indicate subtle dynamic adaptations in stability control that are not evident from step width alone. The present study does not include joint-level biomechanical analyses that would allow causal attribution of these adaptations to the exoskeleton itself. Without direct measures of hip joint moments, frontal-plane kinetics, or muscle activation, it is not possible to determine whether the observed compensatory strategies were mechanically induced by the device or voluntarily adopted by participants in response to altered walking conditions. Therefore, these findings should be interpreted as adaptive gait responses associated with exoskeleton use rather than direct evidence of joint-level modulation. Future studies integrating joint kinetics, electromyography, and frontal-plane assistance paradigms will be essential for clarifying the mechanistic pathways through which hip exoskeletons influence foot placement and mediolateral stability. As this study is a secondary analysis of a dataset collected under the original hip exoskeleton device-validation protocol³⁷, several methodological elements were inherited from that protocol. Markers used to estimate hip kinematics included a combination of skin-mounted anatomical landmarks and markers affixed to rigid exoskeleton components (waist belt and thigh braces); motion of the device relative to the underlying anatomical segments may have introduced soft-tissue or device-interface artifact into the estimated hip angles, consistent with limitations previously noted for this device³⁷. Frontal-plane hip kinematics (Fig. 1D-E) were derived from the same marker set used for the sagittal-plane analysis, which included markers affixed to rigid exoskeleton components; the absolute magnitude of the hip ab/adduction estimates may therefore be subject to similar soft-tissue and device-interface artifact as the sagittal-plane angles, and a formal statistical comparison of frontal-plane kinematics across conditions was beyond the scope of this analysis. Transverse-plane hip rotation was not analyzed in this dataset and remains a direction for future work.

Other limitations of this study include fixed walking speed, use of a relatively young population compared to the most likely target population, and impacts on device structure, which has the most potential impact between conditions. Adapting to a new assistive device requires significant time and cannot be achieved quickly. In future studies, we plan to incorporate variable walking speeds to reflect real-world conditions better and explore iterative design improvements to the device structure. Future studies should incorporate complementary measures such as whole-body angular momentum to better characterize sagittal-plane stability beyond MoS AP alone. Recent perturbation-based work demonstrates that mediolateral foot placement is primarily governed by linear CoM momentum, while deviations in whole-body angular momentum are largely corrected during stance and contribute only minimally and time-specifically to subsequent step placement⁵¹. These findings suggest that stability control is distributed across multiple mechanisms and phases of the gait cycle. Therefore, combining MoS AP with momentum-based measures may provide a more comprehensive mechanistic interpretation of stability adaptations under hip exoskeleton assistance.

Conclusions and future study

This study demonstrated that hip exoskeleton assistance timing and torque magnitude influenced walking stability adaptations differently across gait phases. Earlier assistance timings were associated primarily with AP stability adaptations, whereas later timing conditions demonstrated greater ML stability changes linked to foot-placement regulation. Although nonlinear COM measures suggested increased gait irregularity during assisted walking, the findings overall indicate that assistance timing may play an important role in modulating specific stability-control strategies during exoskeleton-assisted gait. Even in the powered-off condition, wearing the exoskeleton was associated with changes in MoS values compared to walking without the device, though the direction of this difference differed from the powered conditions. However, several factors may have influenced these outcomes, including the short training duration, the device’s mass and shape, and the extension-dominant torque profiles and the passive flexion spring elements (described in the Methods). These factors — the limited familiarization period, the device’s added mass and structural shape, and the nature of the assistance profiles — may have introduced mechanical or phase imbalances that partially limited improvements in foot placement control. Increased step variability and width magnitude indicate the need for extensive training before the exoskeleton can be completely beneficial.

MoS in the anterior–posterior direction primarily reflects the natural forward-fall condition that enables continuous walking, and its interpretation should therefore be made with caution. Although a larger negative MoS value indicates the center of mass moves farther beyond the base of support, this does not necessarily signify instability during locomotion but rather the mechanics of forward progression. Our stability analysis also focused primarily on MoS at heel contact, which may not capture continuous control throughout the gait cycle. Future work will therefore incorporate additional metrics, such as whole-body angular momentum, and foot-placement control gains, to better evaluate stability responses. While the participants in our study were young, this work is widely applicable to older adults with muscle weakness. Future exoskeleton studies should examine long-term use to better understand the device’s impact on variability and stability. Additionally, further research should include larger sample sizes and relevant clinical populations to understand the full implications of exoskeleton-assisted walking.

Methods

• i.Hip exoskeleton device

This study represents a secondary analysis of kinematic, kinetic, and gait-stability data collected using the hip exoskeleton device and experimental protocol previously described and validated by our group³⁷; several methodological aspects (e.g., marker placement, device design, and the planes of motion recorded) were therefore inherited from that original protocol rather than newly designed for the present stability analysis. We developed a semi-rigid hip exoskeleton end-effector designed to increase freedom of movement and improve anchoring to body segments³⁷. The waist belt and thigh segments are rigid but hinge-free. The hip exoskeleton is integrated with a commercially available high-powered off-board actuation system (HuMoTech, Pittsburgh, PA, USA), which applies force to the dorsal side of the hip to assist with extension. Additionally, a set of springs on the hip’s frontal side provides passive flexion assistance. The exoskeleton provides bilateral hip extension assistance through a dorsal cable actuation system linked to an off-board HuMoTech actuator. The rigid waist and thigh segments are connected by flexible interfaces without hinges, allowing greater freedom of motion while improving anchoring stability. Passive elastic elements on the anterior side supply mild flexion support during swing. These passive springs applied a flexion-directional force that varied with the degree of hip extension achieved during stance; as the hip extended, the springs stored elastic energy that was released during the transition to swing to assist limb advancement. The magnitude of this passive flexion torque was not independently controlled and remained modest relative to the active extension profiles. Its primary purpose was to facilitate a smooth transition between the extension-assistance and swing phases and to support natural limb advancement without introducing additional active control signals.

The controller applies sinusoidal torque profiles that deliver extension-dominant assistance during early stance (approximately 21–49% of the gait cycle). Two torque magnitudes (0.06 and 0.12 Nm/kg) were tested, and assistance timing was varied across five end-timing conditions. The control scheme uses a temporal force-tracking PID algorithm operating at 1 kHz to match desired and measured torque in real time, as described in Mohammadzadeh Gonabadi et al. (2024)³⁷. These assistance timings were implemented symmetrically for both legs, ensuring identical torque profiles bilaterally. The assistance region was selected to coincide with the late stance and early swing phases, periods corresponding to active hip extension, followed by initiation of flexion. Prior findings from our previous study, which used the same device³⁷, demonstrated that this interval effectively supports propulsion and reduces hip extensor effort while maintaining a natural gait rhythm. The torque magnitudes and timing combinations used in this work replicate those validated conditions, ensuring consistency and comparability across studies.

Figure 5 shows the bilateral semi-rigid hip exoskeleton (adapted from Mohammadzadeh Gonabadi et al., 2024) and the representative torque-time assistance profiles. The system provides active hip extension torque through dorsal cable actuation, controlled by a temporal PID-based force-tracking controller synchronized to stride timing. Assistance occurred primarily during early stance (21–49% of the gait cycle) with two torque magnitudes (0.06 and 0.12 Nm/kg). Passive springs on the anterior side provided minor hip flexion support during swing.

• ii.Participants

Ten healthy young adults (four males, six females; age: 27.6 ± 5.9 years, body mass: 65.3 ± 13.1 kg, height: 1.66 ± 0.08 m). All participants were physically active and free from neurological or musculoskeletal impairments. Subjects provided written informed consent before participation. The study adhered to the Declaration of Helsinki and was approved by the Ethics Committee (0101-19-FB). Additionally, the University’s Institutional Review Board reviewed and approved all procedures.

• iii.Data collection

The session began with a 20-minute warm-up with all assisted conditions and individual gain-tuning adjustments as needed. During all trials, participants were instructed to walk naturally at the fixed treadmill speed (1.25 m/s), look straight ahead, avoid holding the handrails, and maintain a consistent, comfortable gait pattern across conditions. Participants were not instructed to intentionally modify their step width or gait strategy in response to the device. Participants did not use handrails during walking trials. For safety, all participants wore a fall-arresting harness throughout the session. No weight was supported by the harness, and none of the participants experienced a trip or needed to rely on the harness during the activities. The testing protocol varied assistance-timing and peak magnitude across 10 conditions, combining five assistance-timings (21% to 49% of the gait cycle) and two peak torque magnitudes (0.06 to 0.12 Nm kg − 1). Additionally, participants walked in two reference conditions: without assistance (Powered-Off) and without the exoskeleton (No-Exo). The protocol was divided into three blocks, each with low and high magnitudes and different timings in random order. Each block started and ended with a five-minute condition, with other trials lasting two minutes. Participants rested for at least 10 min between blocks. Three-dimensional kinematics were recorded using motion capture (VICON Vero, Oxford Metrics, Yarnton, UK; 2000 Hz) with 23 reflective markers placed on anatomical landmarks³⁷. In addition to markers placed on standard anatomical landmarks, a subset of markers was affixed to rigid components of the exoskeleton (the waist belt and thigh braces) to track segment motion relative to the device, consistent with the marker placement protocol used in the original device-validation study³⁷.

A schematic of the full protocol has been added (Fig. 6). Each block began and ended with a 5-minute walking condition, while all intermediate conditions were 2-minute trials. The 5-minute bouts allowed participants to reach stable gait patterns and to acclimate to the device at the beginning and end of each block. The 2-minute trials were selected based on prior exoskeleton studies using randomized assistance profiles^37,52, which show that gait kinematics, MoS, and nonlinear COM metrics stabilize within short durations and do not require steady-state metabolic adaptation.

Fig. 6.

Overview of the experimental walking protocol. Participants first completed a 20-minute warm-up and familiarization period, during which they experienced all 10 assisted conditions and adjusted controller gains as needed. The main experiment consisted of three blocks, each beginning and ending with a 5-minute walking trial (either No-Exo or Powered-Off), with two randomized 2-minute assisted conditions in between. Assistance conditions combined five timing intervals (21–49% of the gait cycle) and two torque magnitudes (0.06 and 0.12 Nm·kg⁻¹). A 10-minute seated rest was provided between blocks. All strides from each trial were analyzed except outliers identified using a median ± 1.5×IQR criterion.

Before formal data collection, each participant completed a 20-minute warm-up session during which all assistance timings and magnitudes were experienced at least once. This ensured sufficient familiarization with the device and minimized learning effects during the randomized testing blocks.

Data included for analysis

All strides within each 5-minute and 2-minute trial were processed, except for strides removed as outliers using a median ± 1.5×IQR criterion. Thus, the entire usable duration of each trial contributed to the analysis.

• iv.Data analysis

The processed data was analyzed in MATLAB (MathWorks) to extract various biomechanical measures, including the MoS in both the anterior-posterior (AP) and medial-lateral (ML) directions, step time, step length, step speed, step width, step variation, the largest Lyapunov exponent (LyE)^53,56,55, and sample entropy⁵⁵. Based on foot contact detection from ground reaction force data, we segmented all data into strides, starting at the ipsilateral heel strike and ending at the subsequent ipsilateral heel strike. Outliers were identified by checking if signals stayed within a band defined by the median ± 1.5 times the interquartile range, and any outlying strides were removed.

MoS was quantified at the heel contact event. The details of the MoS calculation have been previously published³⁸. In summary, the extrapolated COM was calculated using the following equation:

• The velocity of the center of mass (V_COM) and the velocity of the base of support (V_BOS) were determined. Due to the moving treadmill belt, the anterior velocity of the base of support was added to the velocity of the center of mass.

• The position of the center of mass (COM) was calculated based on the average position of markers on the pelvis⁵⁶.

• The pendulum’s natural frequency (ω₀) was defined as the square root of the acceleration due to gravity divided by the length from the COM to the lateral heel marker at heel contact⁵⁷.

The MoS was calculated as the base of support (BOS) minus the extrapolated COM. The BOS was defined using the posterior heel marker position coordinates in AP and ML directions, representing the projection of the distal foot contact with the ground at heel contact. The MoS was calculated in the AP and ML directions at heel contact. The mean and variability (standard deviation) of the MoS for each overground condition were calculated.

Step Characteristics (Linear Measures). Step time was calculated as the interval between two contralateral heel contacts, and step length was obtained from the anterior–posterior distance between the heel markers. During treadmill walking, the distance traveled by the belt between heel contacts was added to the anterior–posterior distance to obtain total step length. Step speed was determined by dividing step length by step time for each step. Step width was measured as the mediolateral distance between heel markers at consecutive heel contacts. Only linear measures of step performance were analyzed. The mean values of each variable were computed to describe average gait patterns, and the standard deviation of each time series was calculated to represent step-to-step variability (i.e., linear variability). Nonlinear methods, such as Lyapunov exponent and sample entropy, were applied separately to center-of-mass motion and not to step parameters.

The largest Lyapunov exponent (LyE) was calculated as the local divergence from an attractor (i.e., a steady-state condition), quantifying the motor system’s ability to mitigate small perturbations⁵⁸. The largest LyE estimated an individual’s capacity to respond to movement disturbances or perturbations. A LyE value near zero indicates minimal divergence and a steady system (e.g., a sine wave), while higher values indicate greater local divergence and sensitivity to small perturbations in the movement trajectory. Sample entropy was used to assess the regularity of gait signals^59,60. Understanding the regularity of gait data using sample entropy is important because it provides information about the condition and operation of neuromuscular control systems⁶¹. Values closer to zero indicate a more regular pattern, while values farther from zero are interpreted as greater irregularity in the gait signal.

This study utilized a customized MATLAB script to compute the largest Lyapunov exponent using the Wolf algorithm⁶² and to calculate sample entropy⁶³ for the COM position in three directional motions.

• v.Statistics

The percentage changes in outcome variables between each assistance condition and the no assistance and no exoskeleton conditions were calculated using descriptive statistics, with the data averaged across all subjects.

A linear mixed-model ANOVA (random effect: subject; fixed effect: average torque or timing) was used to test for trend significance across experimental conditions in the measured outcomes. The Jarque–Bera test was applied to ensure the normality of the sample distributions being compared. For experimental conditions with assisted exoskeleton torque, pairwise statistical comparisons were made concerning the conditions of no assistance and no exoskeleton. After performing pairwise comparisons, the Holm–Sidak step-down correction for multiple comparisons was applied using a significance level of α = 0.05.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Conceptualization, A.M.G.; methodology, A.M.G. and F.F.; software, A.M.G.; validation, A.M.G.; formal analysis, A.M.G.; investigation, A.M.G., F.F.; resources, A.M.G., F.F., S.A.M.; data curation, A.M.G. and F.F.; writing—original draft preparation, A.M.G. and F.F.; writing—review and editing, A.M.G., F.F., S.A.M., and J.M.B; visualization, A.M.G. and F.F.; supervision, A.M.G.; project administration, A.M.G.; funding acquisition, S.A.M. All authors reviewed the manuscript.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.