Effects of the degree of freedom and assistance characteristics of powered ankle-foot orthoses on gait stability

We studied the use of powered ankle-foot orthoses (PAFOs) and walking stability of the wearers, focusing on the ankle joint, which is known to play a critical role in gait stability. Recognizing that the subtalar joint is an important modulator of walking stability, we conducted the walking experiment on a treadmill by applying varying assistance techniques to the 2-degree-of-freedom (DOF) PAFO, which has the subtalar joint as the rotating axis, and the commonly used 1-DOF PAFO. The participants were 8 healthy men (mean±SD: height, 174.8±7.1 cm; weight, 69.8±6.5 kg; and age, 29.1±4.8 years) with no history of gait abnormality. Center of pressure (COP) was measured with an in-shoe pressure sensor, and stability was estimated on the basis of the angular acceleration measured with the inertial measurement unit attached to the trunk. The experimental results of the 2-DOF PAFO, with or without assistance, showed a significantly higher stability than those of the 1-DOF PAFO (up to 23.78%, p<0.0326). With the 1-DOF PAFO, the stability deteriorated with the increase in the degree of assistance provided. With the 2-DOF PAFO, this tendency was not observed. Thus, the importance of the subtalar joint was proven using PAFOs. The mean position analysis of the COP during the stance phase confirmed that the COP highly correlated with stability (Pearson correlation coefficient: −0.6607). Thus, we conclude that only the 2-DOF PAFO can maintain walking stability, regardless of the assistance characteristics, by preserving the COP in the medial position through eversion. Awareness regarding the role of the subtalar joint is necessary during the manufacture or use of PAFOs, as lack of awareness could lead to the degradation of the wearer’s gait stability, regardless of effective assistance, and deteriorate the fundamental functionality of PAFO.


Introduction
Exoskeletons, also called wearable suits, are a type of robot designed to be worn by a person to provide functions that assist in human movement [1]. These robots are being actively developed in the field of rehabilitation engineering and are usually used for elderly people or patients who have lost their gait ability. They can be used as rehabilitation exercise devices to improve or relearn walking skills and have been developed and utilized for various other PLOS ONE PLOS ONE | https://doi.org/10.1371/journal.pone.0242000 November 10, 2020 1 / 19 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 [19]. The fall-prone elderly people had significantly greater COP speed, mediolateral and anteroposterior accelerations of the trunk, and maximum Lyapunov exponent. In addition, Howcroft et al. also proved the difference in stability between fall-prone and healthy elderly people during dual-task walking by using a triaxial accelerometer and pressure-sensing insole [20]. These situations show the reason why the subtalar joints should not be excluded from the development of exoskeletons. However, the existing PAFOs have 1 degree of freedom (DOF) with a talocrural joint. This means that they only have a fixed point of action and a constant force direction regardless of the type of actuator, which cannot help wearers keep their balance from external perturbations. Nevertheless, they are still useful because their focus was on the effective assistance for reducing metabolic rate to the maximum. However, if subjects with low stability due to the absence of a subtalar joint are given a certain direction of assistance limited to that subtalar joint, as discussed by Anam and Al-Jumaily, this can be perceived as a perturbation by the robot-human interface [28]. The muscle activity of the ankle might be reduced, and the overall stability is deteriorated, which affects other joints and elements. Therefore, these assistive techniques is unlikely easy to use owing to these shortcomings, as safety is the most important factor considering the characteristics of the subjects.
Therefore, we hypothesized that the presence of a subtalar joint in the PAFO design would improve the wearer's stability. As the DOF increases, the wearer can achieve the FTS with assistance; through this, direction can be controlled. Thus, we expected that effective force transmission in the optimal direction with high stability is possible. Currently, 2-DOF PAFOs with actuatable talocrural and subtalar joints with pneumatic artificial muscles (PAMs) are available. In this study, by using the existing 2-DOF PAFOs and the additionally manufactured 1-DOF PAFOs, the effect of the subtalar joint in the PAFO and the change in the wearer's gait stability resulting from various assistance techniques were analyzed to prove our hypothesis using the COP and stabilogram data.

Materials and methods
This study compared the wearer's stability, measured in unpowered and powered conditions, with the changes in the size and direction of assistance during walking with the 1-and 2-DOF PAFOs. The 2-DOF PAFO used for the experiments was developed by Choi et al. [29], and an additional 1-DOF PAFO lacking a subtalar joint was developed for this study.

The 2-DOF powered ankle-foot orthosis
The 2-DOF PAFO used in this study divides the ankle joint into 2 axes of rotation, as shown in Fig 1A and explained by Choi et al [29]. Spatial formulas for the talocrural and subtalar joints were calculated using the mean of the individual values based on the anthropometric data of Isman and Inman [10]. The robot is interfaced with humans at the feet, calves, and thighs as shown in Fig 1C. Force sensitive resistors (FSRs) are located under the foot to determine the heel strike, and each joint is equipped with an encoder to measure the angle of rotation. Two PAMs are used as the actuator, one acting as the soleus to aid plantar flexion and the other acting as the peroneus longus to assist eversion with plantar flexion as shown in Fig 2. Both PAMs are connected to the solenoid valves, which are controlled by pulse width modulation (PWM) signals and supplied with air pressure, maintained at 6 bar, from the air compressor and regulator. The PAMs and frame are connected by wires, and in the middle of the wires, tensile loadcells are attached to measure the force transmitted. All sensing values are measured on the STMicroelectronics (STM) Nucleo board and transmitted to the STM Discovery board via controller area network (CAN) communication. The discovery board determines the stage of the gait cycle based on the acquired values and sends the certain duty ratio calculated for the contraction of the PAMs to the solenoid valve to implement PAFO assistance. A more detailed explanation is given in the paper by Choi et al. The 1-DOF PAFO was manufactured by simply removing the subtalar joint, as shown in Fig 1B.

Assistance techniques
Various assistance techniques were developed and applied to compare the stability between wearing the 1-and 2-DOF PAFOs. The types of assistance techniques are listed in Table 1.  For the reference data, the experiments were conducted in the unpowered state without assistance.
The 1-DOF powered ankle-foot orthosis. We used a commonly used phase-based controller (P-bc), known as an ankle positive power inspired technique for a 1-DOF PAFO [8]. The P-bc is an assistance technique commonly used with PAFOs that have a PAM as an actuator to maximize the duty ratio of the solenoid valve at a certain timing to provide intensive assistance in the period when the ankle power is positive during the gait cycle [30][31][32][33]. The period with positive values occurs when the ankle joint performs plantar flexion. We used the FSR sensor to determine the time point. Among experiments of PAFOs with PAMs, the onset timing of positive power was between 13% and 54% of the gait cycle [33], but high effectiveness of assistance was most frequently achieved between 40% and 50% [32,34,35]. We used the stage of the gait cycle, detected by the FSR sensor, to provide 3 duty ratios (30%, 60%, and 90%) at the heel strike and then stopped the pulse at the toe-off time. This results in an onset timing of positive power between 40% and 50% for all the cases are shown in Table 1, which also contains the magnitudes of peak force and assistance timing for each duty ratio, which is explained in detail in Fig 3. The 2-DOF powered ankle-foot orthosis. The same P-bc was used for comparison with the 1-DOF PAFO. However, in addition to PAM1, the 2-DOF PAFO has PAM2, which acts as the peroneus longus, allowing for a wider variety of controls. As shown in Table 1, the control methods of the P-bcs for the 2 PAMs are classified. The duty ratio of PAM2 does not exceed the size of PAM1, and in both cases, 3 duty ratios were used, and a total of 8 P-bcs were applied.

Experimental protocol
The number of subjects was determined by referring to the number of previously conducted PAFO experiments [33][34][35][36]. A total of 8 healthy men (mean ± SD: height, 174.8 ± 7.1 cm; weight, 69.8 ± 6.5 kg; and age, 29.1 ± 4.8 years) with no history of gait abnormality participated in the experiment, which was approved by the institutional review board of Yonsei University (7001988-202003-HR-833-03). Proper written consents were obtained from the participants before the experiment. They were recruited on the campus of Yonsei University regardless of gender. The participants wore a pressure-sensing insole to measure the COP and an IMU to measure the postural sway of the trunk, in addition to the PAFO, as shown in Fig 1C. The subjects walked on the treadmill at a speed of 1.2 m/s, and various assistance techniques were applied. The assistance techniques were applied to the left foot only, and the right PAFO was used without actuation. As with other exoskeleton experiments, we gave the wearer some time to get used to the robot to allow for reliable experimental data measurements and gave the wearers enough rest time between experiments to avoid fatigue. Specifically, before the experiments, they performed treadmill walking two times within 30 minutes to get used to each robot with assistance [35,37], and 3 minutes was provided between each set of 50 steps. When the experiments with 1-DOF PAFO was finished and before entering the second experiment with 2-DOF PAFO, they took a 10-minute rest to prevent fatigue. The total walking time was around 2 hours, and all the assistance techniques were evaluated thrice over 50 steps each.

Measurements
Center of pressure. We measured the COP using a pressure-sensing insole (MP2512PLUS; Kitronyx Inc, Seoul, Korea) that can be worn inside the shoe and obtained the data at a frequency of 50 Hz. The data were normalized by the gait cycle using the FSR foot sensor, and the average was calculated and represented as a single trajectory. After this, we calculated the average COP position (COP Avg ), which is the average of its medial-lateral displacement values as in  Eversion angle. After measuring the angle change during the gait cycle from the rotary encoder attached to the subtalar joint of the PAFO, the average (θ Avg ) was calculated to determine the degree of quantitative eversion.
Positive power of the PAM. By substituting the rotation angle of the 2 joints into the Rodrigues' rotation formula used by Choi et al., the change in the length of the PAM can be calculated. The Rodrigues' rotation formula determines the location at which a point is rotated at an angle with respect to an arbitrary straight line in space [38]. The contraction rate of the PAM can be calculated from the change in length, and the power can be obtained by multiplying the magnitude of the force obtained from the load cell. Normally, the average value of positive power applied to the human body during the gait cycle is proportional to the decrease in electromyography (EMG) activity or metabolic cost [39]. The average positive power is the same as the work applied to the human body. Thus, to compare the difference in the work applied to the human body, we also calculated and showed the average value of the positive area (P Avg ) in the power curve for each experiment.
Stabilograms. The stabilograms obtained in this study consisted of the angular acceleration values of the IMU attached to the trunk. According to Kang et al. [17], maintaining the balance of the upper body is important to avoid falling during any form of movement, including walking, and this balance is determined by the movement of the lower limb. Therefore, as in other studies, because the trunk has the smallest change in external perturbation and represents the COM of the whole body, the IMU was attached to it, and stability was judged on the basis of the detected movement [17,19]. The values obtained from the IMU were converted into Euler angles using a low-pass filter and a complementary filter. We used the Newton difference quotient with backward differences to convert the angles of the roll (medial/lateral) and pitch (anterior/posterior) to angular accelerations. These were represented as a stabilogram on a two-dimensional (2-D) plot, as shown by Seimetz et al. So far, studies have used the maximum radius to compare these stabilograms [40]. However, this comparison is not reliable, and we need stochastic values. Therefore, we applied the Gaussian ellipsoid [41]. As shown in Fig 5, we can calculate the covariance of 2-D angular acceleration data and draw an ellipsoid with vertices of eigenvalue, which means 2 standard deviations. Usually, 1δ, 2δ, and 3δ are used to represent 3 Gaussian ellipsoids containing 39%, 68%, and 99% of the data, respectively. This enables a quantitative and reliable comparison of stabilograms. We compared the overall stability by calculating the root mean square values (δ RMS ) with two 1δs representing the roll and pitch directions, respectively. So, if stability deteriorated, then the δ RMS will be bigger than before.

Statistical analyses
We compared the average COP position (COP Avg ), average eversion angle (θ Avg ), stabilogram (δ RMS ), and average positive power (P Avg ), and calculated the average and standard deviation for each experimental parameter in Table 2. In the case of COP Avg , the data were expanded by interpolating 100 data recorded during the stance phase to increase reliability. The rest of the data were also normalized to the 100 data for the entire gait cycle and compared. To compare the above-mentioned results according to the DOF and assistance techniques, the homogeneity and heteroscedasticity of variance were judged using the f-test between a total of 12 test results, and the difference between the data was verified using a t test for each case. The p value, the result of the t test, is shown for easy comparison between the experiments through the p-table. For comparison between the 12 cases, δ RMS was converted to the rate with respect to the unpowered condition with the 2-DOF PAFO, and the average positive power was divided by the participant's weight. The average eversion angle and COP position were used as they were and included in the S1 Dataset. The level of significance was determined on the basis of the false discovery rate (FDR) [42]. In addition, Pearson correlation coefficients (PCCs) were calculated between P Avg −θ Avg , θ Avg −COP Avg , COP Avg −δ RMS , and P Avg −COP Avg .

Center of pressure
The results of the experiments with the 1-DOF PAFO show that the COP trajectories were generally more localized in the lateral direction than those in the experiments with the 2-DOF PAFOs ( Table 2). This difference was statistically significant, as shown in Fig 6. Regarding the COP Avg , we found different trends between the 1-and 2-DOF PAFOs. In the 1-DOF PAFO experiment, the larger the duty ratio applied, the more the COP tended to move toward the lateral direction (1-DOF UNP: 51.433, 1-DOF A: 50.688, 1-DOF B: 49.172, 1-DOF C: 48.731). In the case of the 2-DOF PAFO, no significant difference was found between the experiment results, as shown in Table 2   The bigger the magnitude of δ RMS , the much worse the stability is. And the direction of COP Avg is that when its magnitude increase, it goes toward medial direction. Likewise, for θ Avg , the bigger value means that eversion was enhanced. https://doi.org/10.1371/journal.pone.0242000.t002

Eversion angle
As eversion is a motion only available in the 2-DOF PAFO, we could only obtain data from experiments using the 2-DOF PAFO. We found that the eversion angle was larger in the experiments with the duty ratio of PAM2 (2-DOF A2, 2-DOF B2, 2-DOF C2, and 2-DOF C3) than in the other experiments (eversion angle sheet of the S1 Dataset).

Positive power of PAM
The duty ratio and applied P Avg showed a proportional relationship in PAM1, regardless of the DOF of PAFO. However, in the case of PAM2, the P Avg was determined by the presence or absence of the duty ratio; however, no correlation was observed. For the 2-DOF PAFO, as PAM2 generates the force together with PAM1, PAM1 has a lower power than for the 1-DOF PAFO, even if the duty ratios are the same (average positive power sheet of the S1 Dataset).

Stabilogram
The 1-DOF PAFO experiment results showed that the stability in the roll and pitch directions was lower when assistance was generated by applying the duty ratio than that in the unpow-

Correlation coefficients
Between the experimental results, the Pearson correlation coefficients (PCCs) are calculated and shown in Table 3. They are interpreted by following a guide for use in medical research [43]. COP Avg −δ RMS , P Avg −θ Avg (2-DOF PAFO) and P Avg −COP Avg (1-DOF PAFO) have a moderate to high relationship with −0.66 ± 0.15, 0.74 ± 0.10 and −0.71 ± 0.16, respectively. However, θ Avg −COP Avg (2-DOF PAFO) has a negligible to low correlation of 0.25 ± 0.20, and P Avg −COP Avg (2-DOF PAFO) has no significant relationship between them.

Discussion
In this study, we applied various assistance techniques for PAFOs with 1-and 2-DOF and compared their stabilities when the direction and magnitude of force applied to the wearer was changed. As a result, we found that 2-DOF PAFOs capable of eversion motion with a subtalar joint ensure high stability. Examination of the stabilogram revealed that most experiments performed with 1-DOF PAFOs demonstrated lower stability (δ RMS ) than those with 2-DOF PAFOs, as shown in Table 2 Table 2). This comparison is not accurate without taking into account the applied P Avg ; however, the difference in δ RMS between the experiments with the highest stability among the 2-DOF PAFO experiments (2-DOF A2) and those with the highest stability among the 1-DOF PAFO experiments was 23.78%. As in Fig 7, the comparison of the data between the 1-and 2-DOF PAFO experiments could be achieved on the basis of data with pink shadow, which are significantly different. Notable results were obtained when each DOF was considered separately. In the case of the 1-DOF PAFO experiments, shown in Table 2, the stability worsened when a larger P Avg was applied to the wearer using a larger duty ratio for PAM1. The data with yellow shadow in Fig 7, which represents comparisons between the 1-DOF PAFO experiments, showed a significant difference in 1-DOF B and C as compared with those in the unpowered condition. We used P-bcs as in the other PAFO experiments, and the P Avg applied to the wearer resulted in a reduction in metabolic cost and EMG activity of the muscles Interpretation of correlation was based on the guide for use in medical research [43].
https://doi.org/10.1371/journal.pone.0242000.t003 involved in ankle movement. Therefore, wearing a 1-DOF PAFO may have some advantages; however, the negative correlation implies that it does not improve stability. Therefore, a stable assistance for balanced walking, which prevent wearers from falls because of the absence of a subtalar joint, could be difficult to achieve. By contrast, in the case of 2-DOF PAFO, a high P Avg does not cause deterioration of stability and shows no obvious tendencies. Notably, the unpowered condition is also worse than the other cases, as shown in Table 2, and when PAM2 generated force together with PAM1 (2-DOF A1, 2-DOF B1, and 2-DOF C1), the stability was higher in both the roll and pitch directions, regardless of the magnitude of P Avg when compared with the situations in which only PAM1 was actuated. Therefore, applying a high P Avg to the wearer, regardless of DOF, does not reduce the stability; however, other confounding factors may exist.
We analyzed the COP Avg for this purpose. Previous studies showed that indexes based on the COP trajectory play significant roles in the assessment of gait stability, such as the distance between the anteroposterior and mediolateral displacements of the COP, velocity, frequency, or other dimensionless values [44][45][46]. These values help interpret the balance during gait because the location of the COP under each foot represent the neural control of the muscles related to the ankle joint [47], status of the postural sway during one-leg stance [22], and adjustment of ankle joint moments to change the COM position of the whole body [48]. Among them, the mediolateral movement of COP in the frontal plane can help predict the postural sway in one-leg stance during the stance phase and the risk of injurious falls [44,[49][50][51]. Thus, we converted the COP trajectory within a sole into the mean value of the mediolateral position during the stance phase, as shown in Table 2.
The result of the experiment conducted with 1-DOF PAFO shows that the greater the P Avg applied, the more the COP Avg was located in the lateral position as compared with that in the unpowered condition. In general, when the trajectory of the COP is located in the lateral direction, the extrapolated COP also increases, which reduces the walking stability [25,52]. Therefore, increasing the duty ratio at 1-DOF PAFO lowers the stability because the COP Avg is located in a more lateral position. The COP Avg for the 2-DOF PAFO experiments was small but showed a similar trend as those in the 1-DOF PAFO experiments. When actuating PAM2 with PAM1 as mentioned earlier, the stability was higher. The COP Avg was located in a more medial direction. Therefore, we conclude that even when wearing PAFOs, keeping the COP in the medial position can help maintain high stability of the individual. The PCC of COP Avg and  Table 1 with 1-and 2-DOF PAFOs, respectively. (C) The stabilogram of the unpowered and maximum output states of 1-and 2-DOF PAFO experiments for comparison. The circles represent 1δ of covariance, which comprised 39% of the data. 2δ (68%) and 3δ (99%) are not shown for clarity of comparison, as they are simple magnifications.
https://doi.org/10.1371/journal.pone.0242000.g008 δ Euclid were −0.6607, supporting our conclusion with strong negative correlations, as shown in Table 3. In addition, the blue and gray dots in Fig 9A represent  This raises the question of how P Avg affects stability. We conclude that this effect is caused by the determination of the location of the COP. We calculated the PCC between the P Avg and COP Avg by using the results of the 1-DOF PAFO experiments and demonstrated a strong negative correlation of −0.7149. Therefore, the greater the force, the lower the COP will be in the lateral direction. However, the result differed when the 2-DOF PAFO was used.
The difference between the 1-and 2-DOF PAFOs is the presence of a subtalar joint. Therefore, the eversion angle must be evaluated. We added and actuated PAM2 to enhance the eversion motion and found that when a higher duty ratio was applied to PAM2, its size increased (2-DOF A2, 2-DOF B2, 2-DOF C2, and 2-DOF C3), and the eversion motion became stronger, as shown in Table 2. Moreover, the higher the duty ratio applied, the larger is the P Avg applied by PAM2 to the wearer. We can therefore infer that the greater power PAM2 exerts, the more the eversion can be pulled outward. The PCC between P Avg and θ Avg was 0.7441, demonstrating a strong positive correlation (Table 3). Generally, the greater the eversion, the more the COP enters the medial direction. We also calculated the correlation between the two (θ Avg −-COP Avg ), with a value of 0.2480 showing no significant relationship. However, as shown in Table 2, the COP of 2-DOF A2, 2-DOF B2, 2-DOF C2, and 2-DOF C3, in which PAM2 was actuated, moved more in the lateral direction than those of 2-DOF A1, 2-DOF B1, and 2-DOF C1, in which PAM2 was not actuated. From this, we can predict that the COP were not related to each other. However, in Fig 7, we can observe significantly reduced δ RMS values between 2-DOF A1-2-DOF A2 (p = 1.37e-5) and 2-DOF B1-2-DOF B2 (p = 2.90e-2), which suggest that PAM2 affects stability. Therefore, as PAM2 was actuated, the eversion motion was stronger, which means that the COP did not move out in the lateral direction and, as a result, did not lead to the deterioration of stability, even though the wearer received assistance.
While PAM2 plays a key role in preserving COP in a stable state through eversion, the primary role of PAM1 is to assist plantar flexion. Unlike in the case of 1-DOF PAFO, the stability did not deteriorate despite the increase in the amount of work that the PAM1 of the 2-DOF PAFO exerted on the wearer. This proves that a high stability can be maintained even if the assistance of the wearer is increased by the addition of DOF and change in the direction of the resultant force to the foot, which is our assumption. However, other existing studies have used 1-DOF PAFO, and in this case, as our study revealed that the greater P Avg applied to the wearer resulted in lower stability of the wearer. Our experiments were conducted in the same environment, and even in this situation, if the differences in DOF and force direction cause such a large change in stability, they are expected to have greater effects in situations involving rough terrains, slopes, and stairs, which require walking outside the laboratory.
The experiments and results of this study have some limitations. First is that we did not measure EMG activity and metabolic cost. These parameters have primarily been analyzed for experimental validation in previous studies that used 1-DOF PAFOs, whose research focus was the effectiveness of assistance. However, in the field of rehabilitation, those values are not important. As rehabilitation involves training to return to a normal state, subjects who use PAFOs for rehabilitation are patients who wanted to walk normally. These would include patients who have to relearn their walking skills and proprioception, which were lost or deteriorated by accidents, diseases, or aging. As mentioned in the Introduction section, the stabilizing moment is essential in the elderly for training their gait skills so as not to lose their stability [53]. Many exercises can aid in balance training, including the one-leg stance, walking on a narrow path, or weight shifting. In these exercises, PAFOs can help subjects train their evertors and increase the range of motion of eversion by controlling the magnitude and direction of the stabilizing moment in stages [54][55][56]. After repetition of training with PAFO, subjects can achieve proprioception of their foot during various motions. Hence, the results of this study can be considered meaningful as they show that a 2-DOF PAFO is more suitable for stable assistance.
The second limitation is that we did not measure the temporal parameters during experiments such as step width, stride length, and time. These parameters can affect postural sway, balance, and gait stability, so previous studies used them to evaluate gait quality. For example, the margin of stability (MOS) and extrapolated COM, which are related to balance, require the step width to be calculated [57]. However, an in-shoe pressure sensor was used in this paper, so those parameters cannot be determined. Although the COP trajectory in the foot, which was used in this study, is an important factor for attaining gait stability during one-leg stance, the effect of the parameter is as significant as that of gait stability itself, so an accurate analysis is not possible without it. In the Results section, θ Avg and COP Avg have a negligible or low positive relationship (0.25 ± 0.20), which cannot be easily explained because when the eversion motion was enhanced, the COP should be in a more medial position normally. This situation can be interpreted when temporal parameters are measured. We can expect some possible answers for the weak relationship similar to when the eversion motion was enhanced; if the step width is wider than before, then the COP Avg cannot be in a medial position as much as expected. Thus, these can help us analyze the series of processes in the function of the PAFO in maintaining the wearer's stability in more detail.
The third limitation is that all the participants were healthy and had no need for rehabilitation. Elderly people and patients with abnormalities in their walking skills or body elements are the potential wearers of 2-DOF PAFOs when these are applied in rehabilitation. Thus, experiments in these people should be conducted following this research to validate the functions of the 2-DOF PAFO because they may respond differently with 2-DOF PAFOs, although the presence of a subtalar joint and its actuation were proven to be useful with healthy people. For the rehabilitation of people in weakened and unstable states, the optimal design and controller of the assistive device for each participant will be needed, which were not realized in this paper. Two axes of the 2-DOF PAFO were calculated on the basis of the average values of the anatomical data from cadavers [10], so they are not perfect for various sizes of participants. Of course, the existence of a subtalar joint was proved, and its actuation can provide the wearer more effective assistance in terms of stability than the existing 1-DOF PAFO, but the outcome can be improved with adjustment of the misalignment achieved. Solving a misalignment between the joints of the wearable robots and the wearers is difficult, but many research studies have attempted to find solutions. A 4-bar linkage for the knee joint is a representative example. We are now considering this mechanism and the Schmidt coupling joint or something else to solve the problem. This might be the focus of our future work. For the controller, we used P-bc for the PAM actuation, but it is not a notable and adjustable method because it does not conduct a tracking control of the predefined or real-time force profile. It induces the maximum contraction of the PAM with given pressure, generating a force that varies with the circumstances at that time. Although a certain duty ratio can generate similar magnitudes of force during experiments, it cannot be adjustable for various sizes and characteristics of wearers and circumstances. The benefit of PAM2 was proved by experiments, but the existence of PAM2 was newly introduced in this paper, so its optimal controller or force profile has not been developed yet, which can be also a direction for our future work. To develop a controller for PAM2, the relationship of the 2 PAMs should be determined because their effects on the moment and rotation of 2 joints are coupled as shown in Fig 2. However, this is not easily solved because the free body diagram of the ankle joints is too complex owing to their structure, stiffness, and force translation model. Thus, some solutions for the free body diagram can be used regardless of difficulty and obtain the exact effect of the portions of the 2 PAMs on each joint or develop a new controller without them. New methods can be created by locating the COP in the medial position as much as possible or using the chaos theory and maximum Lyapunov exponents as objective variables for optimization such as human-in-the-loop [58][59][60]. In addition, our results can be used for assistive PAFOs to identify the optimal torque profile to reduce the metabolic cost or EMG, which were not measured in this study, and simultaneously secure the gait stability. This indicates that assistance effectiveness can be obtained and PAFOs can also achieve its fundamental purpose.

Conclusion
We measured the stability of the wearer by applying assistance techniques with various characteristics to 1-and 2-DOF PAFOs and found that the presence of an additional DOF and the direction of force affected stability, regardless of assistance efficiency. Unlike the 1-DOF PAFO, the 2-DOF PAFO has a subtalar joint as the axis of rotation, which enables the eversion motion to preserve COP Avg in the medial position without being affected by the amount of assistance. The location of the COP Avg was directly related to the stability of the trunk, the most inferior segment; thus, stability was also preserved. By contrast, the 1-DOF PAFO, which only has the talocrural joint as the axis of rotation, was unable to alter the eversion. As the applied P Avg increased, the COP moved out in the lateral direction. Consequently, the stability of the trunk deteriorated. This demonstrates the importance of subtalar joints in the use of PAFOs. Further studies are required to prove their importance as indicators of stability and efficiency of assistance.
Supporting information S1 Dataset. Experimental results of all the participants. This file contains all relative result data during experiments with the participants, which consists of sheets named "Stabilogram," "Eversion angle," "Average positive power," "Average center of pressure," and "Correlation coefficient.". Mean and standard deviation of Table 2 was calculated based on the data of this file and graph data of Figs 4 and 6-8 is also included. (ZIP) S1  Table 3