Improving Passive Ankle Foot Orthosis System Using Estimated Ankle Velocity Reference

This study aims to investigate an appropriate ankle velocity reference (<inline-formula> <tex-math notation="LaTeX">$\omega _{\mathrm {ref}}$ </tex-math></inline-formula>), which is the average ankle velocity of a certain healthy subject when walking with a certain walking speed. The goal is to improve a Passive Controllable Ankle Foot Orthosis (PICAFO) by implementing the ankle velocity reference. Firstly, the function to estimate <inline-formula> <tex-math notation="LaTeX">$\omega _{\mathrm {ref,}}$ </tex-math></inline-formula> based on walking speed and body mass index (BMI), is obtained from 16 able-bodied subjects walking gait data. The effect of controlled stiffness (based on <inline-formula> <tex-math notation="LaTeX">$\omega _{\mathrm {ref}}$ </tex-math></inline-formula>) to the user’s ankle kinematics and muscle activity was evaluated by comparing it to other settings, such as walking barefooted and various constant damping stiffness (0%, 30%, 60%, and 100% of the maximum damping stiffness). Two able-bodied subjects (normal and overweight) participated in the evaluation, where they had to walk at two different walking speeds (1 and 2 km/h). The result showed that ankle kinematics and muscle activity were improved when <inline-formula> <tex-math notation="LaTeX">$\omega $ </tex-math></inline-formula> was controlled during walking speed of 1 km/h for both subjects. In terms of ankle kinematics, the toe clearance occurred, and walking stability increased. In terms of muscle activity, the average muscle activity had reduced by ~29% for the normal subject and by ~57% for an overweight subject, which shows that PICAFO provides necessary damping stiffness to replace the muscle works partially. In the future, by using the <inline-formula> <tex-math notation="LaTeX">$\omega _{\mathrm {ref}}$ </tex-math></inline-formula> based on walking speed and BMI, the therapists can skip the trial and error process of finding an appropriate PICAFO prescription for a post-stroke patient.


I. INTRODUCTION
A recently developed Ankle Foot Orthosis (AFO) by researchers had an articulated ankle joint with the addition of a mechanical actuator or electrical actuator to control the walking gait [1]. Researchers established control systems for automatic post-stroke rehabilitation using AFO. There are two approaches to controlling the AFO, such as active control and passive control. The actively controlled AFO can generate the walking posture [2], [3], and keeping the body balance [4], which is more suitable for amputee patients. Meanwhile, the passively controlled AFO controls the walking gait by restricting the foot movement to maintain the correct gait [5]. Despite the less functionality of The associate editor coordinating the review of this manuscript and approving it for publication was Jesus Felez . passively controlled AFO compared to actively controlled AFO, patients with less gait impairment are suggested to have passively controlled AFO due to its simplicity and low cost.
A control reference is mandatory, which serves as a guide for the controller to control the gait properly. The control reference must suit the AFO user's needs to optimize the training benefits [6]. For instance, an active AFO tracks the predicted motion path, which suits the user's intention measured by EMG [7]. Another example is a passive AFO that maintains the correct walking gait by controlling the joint stiffness. Too much joint stiffness means high walking energy recruitment during push-off, but a slight joint stiffness means less gait assistance from the passive AFO is required [8].
The control reference is related to the mechanical properties of an AFO that can be controlled. In passive AFO, the mechanical properties, such as ankle velocity [9], [10], and damping stiffness [11], [12] are controlled to maintain the correct walking gait. The adjustment of mechanical properties of passive AFO to suit the user's need can be accomplished before the usage using mechanical actuators (i.e., spring [13] and oil-damper [14]) or during the usage using electrical actuators, such as Magnetorheological (MR) devices (i.e., damper [15] and brake [16]). Damping stiffness is generated directly by the actuator. Meanwhile, the ankle velocity is controlled by applying appropriate damping stiffness. For instance, if the ankle velocity exceeds the reference, then the controller generates damping stiffness to reduce the ankle velocity.
Previous works had demonstrated damping stiffness control according to the gait phases [17]- [19]. For example, when the foot is on the ground, the stiffness is less generated, but the stiffness is more generated when the foot is in the air. However, there is no clear report on estimating the degree of damping stiffness to suits the user's needs. Instead, a trial and error attempt was executed to find the optimum damping stiffness [20]. The estimation of the damping stiffness reference is found to be challenging because it requires the Ground Reaction Force (GRF) information during walking performance [3], [21]. GRF is a force that resulted from the foot's contact on the ground. A multi-axis force transducer can be used to obtain the GRF information, but the sensor's bulky dimension may obstruct the AFO's sole surface.
Meanwhile, ankle velocity reference estimation is more practical than the damping stiffness reference estimation, which does not require the GRF information [22]. Kikuchi et al. [10] demonstrated an estimation of ankle velocity reference in the Initial Contact (IC) to the Foot Flat (FF) period only, which is associated with the users walking speed, such as slow, normal, and fast. Using the estimated ankle velocity reference, the passive AFO can adapt to different gait phases and different walking styles, such as the walking speed. Meanwhile, the subject's anthropometric, such as the Body Mass Index (BMI), has also been reported to contribute to a better estimation of ankle velocity reference, but it has yet to be implemented in a passive AFO system [22].
Therefore, there are two contributions to this study. The first contribution is to investigate ankle velocity reference function based on walking speed and BMI in four distinct gait phases [22]. Phase 1 is from IC to FF, Phase 2 is from FF to Heel Off (HO), Phase 3 is from HO to Toe Off (TO), and Phase 4 is the swing phase. The second contribution is to improve a passive AFO equipped with an MR brake, called PICAFO (Passive Controllable AFO), by implementing the ankle velocity reference. By doing so, the previous version of PICAFO [16] can be improved in terms of appropriate control reference that can be straightforwardly estimated. Because of this, the PICAFO's user is expected to get benefits using the PICAFO for walking, such as better ankle kinematics with less muscle activity [8] and less energy [3].
Section II describes the PICAFO system. Section III discusses the estimation of the ankle velocity reference based on the walking speed and BMI. Statistic parameters are used to observe the strength of including BMI as the estimator instead of the walking speed only. Section IV presents the implementation of the ankle velocity reference on the PICAFO system. Implementation results are also discussed in terms of ankle kinematics and muscle activity when the user walks using PICAFO with the ankle velocity reference compared to several constant damping stiffness references, such as zero (0%), low (30%), medium (60%, and high (100%) damping stiffness. Lastly, Section V concludes the study.
For your information, the orthopedic doctor's committee, Institutional Review Board of Education Hospital of Universitas Sebelas Maret, Indonesia, in an approval letter no. 893/UN27.49/TU/2018 declared that the walking experiment in this study is safe for the category of work involving human subjects. The subjects also gave their written consent before the experiment was executed.

II. PASSIVE CONTROLLABLE AFO (PICAFO) A. PICAFO TEST RIG
Overall, PICAFO's architecture is shown in Fig. 1. The prototype structure was made by modifying a commercial Air Ankle Boot produced by China OEM, which initially had an articulated ankle joint and adjustable ankle ROM (maximum -45 to 45 degree). An MR brake at the ankle joint generates controllable damping stiffness [23], [24]. The MR brake is a T-shape brake [25], where the gap is filled with MR fluid LORD-132DG. The MR brake is powered using an external power supply. At 0% damping stiffness state or when the current is equal to zero, the damping stiffness is 0.34 Nm. Meanwhile, the 100% damping stiffness is 2.05 Nm when the maximum current of 1 A is applied.
There are rotary encoders at the ankle joint and footswitches inside the foot insole as the sensing unit.   P3: HO to Toe Off (TO), and P4: swing. For data monitoring and logging, all the sensors and actuators are connected to LabVIEW on the computer through a USB-6211 Data Acquisition from National Instrument. An external circuit is available to bridge the electronic components.

B. CONTROLLER
In general, the PICAFO prototype controls the walking gait based on the ankle velocity reference (ω ref ), which is estimated based on walking speed and BMI, as shown in Fig. 2. There are four ankle velocity references (ω 1 , ω 2 , ω 3 , ω 4 ) for each of the four gait phases (P1 -P4) detected by the footswitches. The PID controller controls the ankle velocity (ω) according to ω ref by calculating I est for the MR brake to generate appropriate stiffness. If the ankle velocity exceeds the control reference in the same direction, then the MR brake would apply appropriate stiffness to reduce the ankle velocity. On the other hand, the MR brake will do nothing if the activation condition is not fulfilled. The activation condition of P1 and P3 is when ω is less than zero. When ω is more than zero, the activation condition of P2 is fulfilled. Meanwhile, the activation condition during P4 is when θ is more than zero.

III. ANKLE VELOCITY REFERENCE ESTIMATION A. DATA COLLECTION
The purpose of controlling the ankle velocity using PICAFO is to maintain the correct walking gait; in other words, a healthy walking gait. Therefore, ω ref estimation function was established by utilizing ω data of able-bodied subjects with different BMI walking at different walking speeds. A total of 16 young (24 -29 years old) male able-bodied subjects who participated in the walking experiment (n = 16) participated in this study. The subject's BMI varied in 3 categories: underweight (n = 4), normal (n = 6), overweight (n = 6). The subject was required to walk on a treadmill with constant walking speed and variations of 1, 3, and 5 Km/h, which represented slow, decent, and fast walking speed. The walking gait data was measured using lower limb plug-in gait in the VICON motion capture system [26]. Each step data consisted of approximately 60 to 260 data points, depending on the step period (sampling frequency was 100 Hz). In one session, there were 30 steps of captured walking data being selected for further processing. There was a total of 48 sessions (16 subjects x 3 walking speed). Therefore, there were 1440 sets of walking data that were used for establishing ω ref estimation function.

B. DATA PROCESSING
The measured walking gait data involved in the ankle position. The difference between the initial ankle position and the final ankle position in one phase was divided by the time-lapse, which defined the average ω, as presented in previous work [10], [22]. Further analysis involved regression analysis with statistic parameters, such as R-value, standard of error, and t-test. As mentioned earlier, the previous work by Kikuchi et al. [10], [27] only showed ankle velocity reference estimation based on the walking speed. The statistic parameters of 9 different cases were compared to observe BMI's strength as an additional estimator in ω ref function, as shown in Table 1. The ω ref estimation was investigated for P1 until P3. Meanwhile, on P4, the ω ref estimation was not investigated. The PICAFO could straightforwardly apply maximum stiffness to lock the ankle joint (ω = 0), which ensured toe clearance on P4 regardless of the subject's walking speed and BMI [17], [28], [29].
There are two critical parameters to build ω ref function, such as the walking speed X1 and BMI X2. The statistic parameters of the regression analysis explain the relationship between the critical parameter and control reference. The R-value describes the correlation score of critical parameters to the ankle velocity, where n is the sample-numbers, E i is the residual between the estimated ω ref and the actual ω, ω i is the i-th actual ω data, and ω mean is the average ω. The absolute R-value showed the correlation. If the R-value is positive, it means a positive correlation, and if the R-value is negative, then it means a negative correlation. The absolute R-value that approaches one means a better correlation. Meanwhile, the standard of error (Se) Then, the probability of the critical parameter coefficients, b 1 and b 2, being zero is explained by performing a t-test where b j is critical parameter coefficients (j = 1, 2), c jj is variances of b j , and s is the residual (E i ) mean square. Based on the t statistics, the p-value can be found. If the coefficient is zero (p-value > 0.05), then it means that the critical parameter is insignificant for estimating the control reference.

C. RESULT OF ANKLE VELOCITY REFERENCE ESTIMATION
The correlation of critical parameters (X1, X2, and X1&X2) with ω is negative during P1 and P3, while the correlation is positive during P2, as shown by R-value in Table 2. A negative correlation means that the higher the critical parameter, the higher the ankle velocity in the negative direction (plantarflexion), and a positive correlation means the opposite (dorsiflexion). Here, the foot movement is plantarflexion in P1 and P3, and dorsiflexion in P2. For an illustration of the regression analysis result, readers can refer to Appendix A. The estimation based on X1&X2 produces the highest correlation score for all phases. The standard error result also agrees, where X1&X2 estimation produces the least standard error compared to other estimation. Meanwhile, Table 3 shows the critical parameter coefficient analysis. Both b 1 and b 2 have a similar coefficient sign, as shown in Table 3. The walking speed is the more significant critical parameter than BMI, as reflected by a higher b1 compared to b 2 . Despite the less significant of b 2 than b 1 , the probability of the b 2 to be zero is very unlikely, as shown by the p-value < 0.05. The only thing that might be zero is the intercept c, of estimation on P1 (p-value = 0.924), which does not affect the contribution of the critical parameters to ω ref estimation in general.
In summary, the result implies that the addition of BMI improves ω ref estimation. Compared to a previous study conducted by Kikuchi et al. [10], where the ankle velocity has a clear proportional relationship with walking speed, the relationship between ankle velocity and BMI needs further explanation. The total torque around the ankle joint affects the joint's angular acceleration [30]. The higher the ankle torque, the higher the angular acceleration, which also means higher ankle velocity. Several forces contribute to the total torque around the ankle joint during walking, such as ankle force, foot weight, and GRF. The body mass affects the force amount, as observed in higher BMI persons with higher GRF [31], [32]. The foot torque's length depends on the foot length. A taller person is most likely to have a longer foot length compared to a shorter person. Thus, a taller person is most likely to have a higher ankle torque [33]. Other research also reports that a higher BMI person has shorter strides [34]; thus, if that person walks at the same walking speed as another person with lower BMI, the shorter stride length will result in higher ankle velocity. Compromise all this information leads to the possibility of a relationship between ankle velocity and BMI. The regression analysis result has confirmed that ω ref has a proportional relationship with walking speed and BMI, fulfilling the first contribution. Table 4 shows the ω ref function for the PICAFO system in radians unit, where c, b 1 , and b 2 are obtained from Table 3  only represents a small population of samples (n = 16). Thus, the implementation of this control reference was focused on the small population in this research first. The purpose is to demonstrate the strength of estimating the control reference rather than trial and error to find the appropriate damping stiffness. Afterward, the ω ref function should be improved by inviting a large sample population for more generalization.
The pre-clinical evaluation can also be considered by creating a machine that simulates the variables' incremental variation and wears the PICAFO system to the extreme.

IV. IMPLEMENTATION OF THE ANKLE VELOCITY REFERENCE
The implementation has been conducted to achieve the second contribution of this research, improving the previous version of PICAFO by implementing the ankle velocity reference. It is expected that the users can benefit when using PICAFO with the controlled stiffness based on the ω ref , in terms of ankle kinematics and muscle activity.

A. DATA COLLECTION
Two subjects from the previous 16 subjects were invited back for the implementation of ω ref using the PICAFO system. Subject 1 (S1) has a normal BMI of 22.2, while Subject 2 (S2) has an overweight BMI of 28.7. The subjects also had to walk on a treadmill with constant walking speed, WS1 (1 km/h), and WS2 (2 km/h), and different joint stiffness conditions instead of being barefooted. Walking speed of 1 and 2 km/h was chosen to replicate post-stroke condition who cannot perform fast walking [35], [36] whom PICAFO is intended for. There are 6 PICAFO stiffness conditions, which are zero stiffness, low stiffness (30%), medium stiffness (60%), high stiffness (100%), and controlled stiffness (the damping stiffness is based on ω ref estimation in Table 4). There are four cases (2 BMI x 2 walking speed) and six stiffness conditions. Therefore, there are a total of 24 data collection sessions, where 30 walking gait data are selected in each session.
The walking gait data are ankle kinematics and muscle activity. The ankle kinematics data, during PICAFO assistance, such as ankle position (θ) and ankle velocity (ω), were collected using a rotary encoder in the PICAFO prototype. Meanwhile, the ankle kinematics data taken during barefooted walking were collected using the VICON motion capture system. As for the muscle activity, the RMS electromyography (EMG) of Tibialis Anterior (TA) and Gastrocnemius (G) muscles were collected using a Biopac instrument and Acqknowledge software. Firstly, the raw EMG data were gathered with a sampling frequency of 1000 Hz [37]- [40]. Then, the raw EMG is filtered using a low pass filtered (cutoff frequency of 6 Hz) and rectified before the RMS EMG is calculated [8].
B. DATA PROCESSING AND ANALYSIS Fig. 3 displays an overview of the data processing. First, the walking gait data (θ, ω, and RMS EMG) are divided using the gait events. These divided data are called step data. The step data began from the IC, which ended on the next IC of the same leg. Next, the data is normalized based on the gait completion or gait cycle percentage. IC is 0%, and the next IC is 100% of the gait cycle. After normalizing the time domain data to the gait cycle percentage data, the average of step data in one case is calculated by averaging the data point of the step data to build a whole average step data. Data analysis is accomplished by comparing the average steps of data according to different joint stiffness. For θ comparison, the ankle Range of Motion (ROM), ankle pushoff, and toe clearance are the observation highlights, as shown in Fig. 4. Meanwhile, the ω is compared with ω ref to see the effect of applying different ankle joints' stiffness. For statistics comparison, the variances of θ and ω describe the walking stability. Lower variance means a more stable walking gait parameter [41]. The t-test was also performed to see the significance of the PICAFO stiffness compared to barefooted walking and zero stiffness.
The average step data of RMS EMG compare the muscle activity between different PICAFO joint stiffness for each case. The average muscle activity (AMA) in one gait cycle AMA = 100 0 NRE d% 100 (7) of the TA and G compares the muscle activity between different PICAFO joint stiffness for each case, where NRE is the normalized RMS EMG, and % is the gait percentage. The RMS EMG data were normalized first to the maximum average RMS EMG of walking barefooted in one case for comparison purposes. The RMS EMG is normalized per case because the MA of walking barefooted is different for each case [8].
Replacing the muscle's work using an actuator that works in unison will decrease the muscle activity [42], [43]. TA works in dorsiflexion, where it keeps ω during P1 [44], and ensures toe clearance during P4 [37]. Meanwhile, G is responsible for plantarflexion, where it maintains the forward force during P2 to avoid over-extending [45]. In this case, the reduction of TA and G muscle activity is expected when assisted by the MR brake with appropriate stiffness because it has the same working principle, which restricts the foot movement. Fig. 5 shows the average ankle kinematics in the different ankle joint stiffness for case S1-WS1. Please refer to Appendix B for ankle kinematics results of other cases. Walking with a variable stiffness of PICAFO significantly affects the ankle's ROM, push-off ability, and toe clearance compared to walking barefoot and walking with zero stiffness PICAFO (p-value < 0.05). Refer to Fig. 5 (a), the ankle ROM (1) is more restricted upon using PICAFO. However, the higher the stiffness does not necessarily be felt in the lowest ankle ROM. On P1, the angular distance between the lowest ankle position and initial ankle position (2) and duration to reach it (3) are affected by ankle joint stiffness. The angular distance on P1 during barefooted walking is longer, and the duration to reach the lowest ankle position is shorter compare to walking with PICAFO. When the subject walks using PICAFO, the ankle angular distance becomes smaller, but the duration is longer.

C. ANKLE KINEMATICS RESULT
Meanwhile, the toe clearance (4) from P3 to the mid of P4 still appears in all the cases. Toe clearance appearance is natural since the subjects are healthy. However, the able-bodied subjects do not require much ankle position recovery after the push-off when walking with the assistance of PICAFO (5), which can be seen from the ankle position that does not drop much. The PICAFO maintains the ankle position by retaining the ankle position above the neutral position, ensuring clearance without ankle position recovery.
Although the ankle position is significantly different due to different ankle joint stiffness, the ankle velocity, ω, does not change much before and after the use of PICAFO with different stiffness (p-value > 0.05). The similarity is especially apparent for P2 and P3, but not for P1 and P4 because the foot moves when walking barefooted. Refer to Fig. 5 (b), ω approaches the ω ref (shown in a straight line) better when the stiffness is controlled. For example, at the end of P3, the ω of zero, low, and medium stiffness exceeds the ω ref, but ω resulted from controlled and high stiffness does not exceed ω ref. This result indicates that the use of PICAFO with controlled and high stiffness can help maintain the ankle VOLUME 8, 2020
Meanwhile, in S2 (see Appendix B), the ω never approaches the reference during P1, P2, and P3, except during P4, where the controller controls the ω to reach 0 rad/s. Even when walking barefooted, the ω also does not approach ω ref despite the functions derived from ankle velocity data of healthy subjects that walked barefooted. This result shows that the ω ref function is more accurate for S1 compared to S2 to estimate the control reference. In this scenario, the PICAFO will not make any attempt to correct the ankle velocity since it never exceeds the ω ref . Improvement of the estimation should be done in future work, such as by increasing the sample sizes. Fig. 6, 7, and 8 show the variance of step period, ankle position, and ankle velocity, respectively, in all cases as an effect of different joint stiffness. All the variances are small in general (less than 0.05), which demonstrates PICAFO reliability for collecting the data. The variance value varies due to different joint stiffness. When the subject walked with zero stiffness PICAFO, the ankle position variance, and step period increase, while the variance of ankle velocity decreases. If joint stiffness is applied, then all the variance is smaller compare to variance resulted from zero stiffness. Using the controlled stiffness resulted in the lowest variance of gait parameters. The result is similar across the two subjects but not similar to different walking speeds. In the WS1 case (a and c in Fig. 6, 7, and 8), the lowest gait parameter variance occurs due to applied control stiffness. However, in the WS2 case (b and d in Fig. 6, 7, and 8), the control stiffness is inferior in maintaining the gait variance, while high stiffness is more superior.
Controlling the gait in faster walking speed requires more stiffness because the ankle torque is higher, which explains the superiority of the constant high stiffness compared to the controlled stiffness in the case of WS2. The MR brake capacity should be improved to cope with this situation. However, in rehabilitation, the post-stroke patient usually ambles (walking speed ≤ 2 Km/h) [35], [36]. Thus, it is suitable for him/her to be assisted using the PICAFO in this study. Therefore, the modification on the MR brake capacity is only necessary if the PICAFO is used outside of rehabilitation.

D. MUSCLE ACTIVITY RESULT
PICAFO decreases the walking muscle activity in P1 and P2 but not in P3 and P4, as shown in the case sample S1-WS1 in Fig. 9. Please refer to Appendix C to see the muscle activity result of the other case.
In P1, when the subjects use the PICAFO, the TA activity decreases, but the G activity gets higher instead (except for S2-WS2's case where both TA and G activities decrease). At this phase, the main movement is plantarflexion as the foot moves to reach the foot flat from the initial contact position. The G generates the movement, while TA provides braking torque at the same time. As a result of using PICAFO, the G activity increases because the PICAFO restricts the plantarflexion. In contrast, the TA activity decreases because the PICAFO joint stiffness replaces the work. However, more stiffness does not always mean more G increment or TA reduction for both subjects. For the S1-WS1 case, the lowest TA activity occurs when the stiffness is high. Nevertheless, in the case of S2-WS1, the lowest TA activity belongs to PICAFO with controlled stiffness.  On P2, the TA and G activities decrease with a significant reduction in the G activity, and the result is similar for all cases involving the subjects and the walking speed. In this phase, the main ankle movement is dorsiflexion, with the body weight shifted to the direction of walking. The TA muscle activity, which is responsible for dorsiflexion, can be seen in the barefoot walking data for case S1-WS2 and S2-WS1.  Theoretically, if the ankle joint is restricted, the TA should exert more force. However, the result shows a decrement instead of an increment. One possible explanation is that the subjects feel restricted when walking on the treadmill using the PICAFO. They let the treadmill move the leg backward during the stance (P2), resulting in ankle dorsiflexion without the TA muscle's need to work. Meanwhile, the G muscles maintain the forward force, where the PICAFO assistance naturally replaces the G muscle's work. Because of this, G activity was reduced significantly.
Meanwhile, the TA and G activities generally increase from P3 until the middle of P4. The push-off and toe clearance happen during this period. During P3, the G muscle generates a plantarflexion to push the foot off the ground so the body forward propulsion can happen. During the initial swing or P4, the TA dorsiflexes the foot to ensure toe clearance for the next walking step. These movements require minimum restriction; thus, the additional restriction will increase the muscle activity to perform the same movement. For example, the high stiffness resulted in the highest TA activity, as shown in cases involving S1-WS1 in Fig. 9. However, after achieving toe clearance, the TA needs to hold the foot position only. The need aligns with PICAFO's stiffness restriction. Thus, the TA activity was reduced during the middle to late swing or P4 due to PICAFO's stiffness restriction.
The PICAFO restricts the ankle movement, especially when stiffness is applied. The restriction affects the TA and G activity augmentation or reduction, as shown in Fig. 9. At some point, the TA activity may decrease, but at the same time, the G activity may increase due to the PICAFO ankle joint stiffness. A suitable amount of stiffness can minimize this kind of drawback by compromising the augmentation and reduction of TA and G muscle activity. However, a suitable amount of stiffness is different from person to person due to anthropometric differences, such as BMI or different walking speed preferences. Therefore, the ω ref function developed in this study is essential, which enables PICAFO to control the walking gait with suitable joint stiffness. The average muscle activity provides an understanding of joint stiffness that compromises muscle activity augmentation and reduction. Fig. 10 and Table 5 show the effect of different ankle joint stiffness on the average muscle activity of both S1 and S2 at different walking speeds (WS1 and WS2). The percentage number in Table 5 is calculated by comparing the muscle activity of PICAFO aided walking with muscle activity of walking barefooted. For instance, controlled stiffness in the S1-WS1 case resulted in overall muscle activity reduction by 29% compared to walking barefooted in the S1-WS1 case.
Refer to Table 5, S1 favors PICAFO with medium stiffness to reduce the TA activity by ∼39% and low stiffness to reduce the G activity by ∼32% in WS 1. The combined results of both muscle activities indicate that the medium stiffness PICAFO is the most suitable ankle stiffness for S1 in the case of WS1 compared to the low and high stiffness, which reduces the overall muscle activity by ∼34%. In the same WS1 case, the S2 favors different ankle joint stiffness, such as low stiffness to reduce the TA activity by ∼67%, high stiffness to reduce G activity by ∼58%, and high stiffness to compensate for both muscle activity reduction by ∼62%. In the case of WS2, both subjects also exhibit different muscle activity results. Low stiffness is more suitable for S1 compared to other forms of stiffness (muscle activity reduction of ∼3%), while zero stiffness is suitable for S2 (muscle activity reduction of ∼58%). These results prove that different walking speed people require unique ankle joint stiffness that needs to be supported by the PICAFO system. Fig. 10, Fig. 11, and Fig. 12 also illustrate the effect of applying controlled stiffness to TA activity, G activity, and both muscle activities, respectively. The graph shows the average muscle activity, which is normalized to the highest barefooted muscle activity in that case. There are four graphs in each Fig. 10, Fig. 11, and Fig. 12, such as S1-WS1 (a), S1-WS2 (b), S2-WS1 (c), and S2-WS2 (d).
If the most suitable PICAFO stiffness is responsible for significantly reducing muscle activity, then the developed control stiffness will never be the most suitable PICAFO stiffness for both subjects. Except for the S1-WS2 case, the TA activity has resulted in the most muscle activity reduction by ∼25% when the controlled stiffness is applied. Despite that, the controlled stiffness is not the all-loser compared to the other ankle stiffness. For instance, the controlled stiffness is better (overall muscle activity reduced by ∼29%) than the high stiffness (overall muscle activity reduced by ∼8%) in the case of S1-WS1. Therefore, the use of the estimated ω ref can decrease the trial and error process of prescribing a suitable ankle joint stiffness. Suppose the overall muscle activity can be further reduced compared to walking barefooted or with zero stiffness, as shown in the case of WS1 for both subjects. In that case, that stiffness is assumed to give positive assistance, which is achieved using the estimated ω ref as the control reference. However, the result of overall muscle activity reduction (TA+G) from PICAFO stiffness does not appear in both S1-WS2 and S2-WS2 cases. Although the TA activity reduces, the G activity does not decrease. This study's participating subject is the able-bodied subject who can do push-off, which requires plantarflexion with less restriction. Naturally, the push-off will get faster following the increase in the walking speed. More muscle force is required to achieve a higher speed, push-off under the restriction of PICAFO stiffness. Since the G is the muscle responsible for plantarflexion, it explains the high G activity in S1-WS2 and S2-WS2 case, as shown in Fig. 11.
The PICAFO controllers have initiated the foot push-off during P3 by having high plantarflexion ω ref . In case of inaccurate detection, for example, when the PICAFO detects P4 instead of P3, the controller will instruct the MR brake to generate stiffness since it should lock the ankle position during P4. As a result, the muscle activity increases when performing the push-off. Meanwhile, if the PICAFO detects the gait correctly, then the MR brake will generate stiffness to sufficiently control the ω. Walking gait control using PICAFO allows muscle activity reduction. For example, TA activity reduction on P4 and G activity reduction on P2 are observed in Fig. 9.
The conventional rigid AFO by Delafontaine et al. [46] was reported to reduce TA activity. The unpowered AFO with spring [8] and the unpowered AFO with oil-damper [14] were reported to reduce G activity, especially on P2. However, PICAFO control stiffness reduced both TA and G activity by applying sufficient damping stiffness whenever necessary, based on the ω ref . The TA was notably reduced in P1, P2, and the end of P4, unlike the results of the gait assistance using constant stiffness MR-Link by Hassan et al. [15] and Oba et al. [17] and soft actuator by Thalman et al. [47], where the TA reduced in P4 only. Even though the PICAFO only generates stiffness accordingly, the muscle activity reduction result is not inferior compared to the active powered AFO by Mazumder et al. [48]. S1 TA was reduced by ∼26%, and G was reduced by ∼31%, while Mazumder reported that the TA and G reductions were ∼26% and ∼29%, respectively. The comparison may not be fair because each work invites different subjects, uses various methods of controlling the ankle movement, and uses different test rigs or prototypes [49]. Therefore, further study should focus on increasing the subject numbers to evaluate the walking gait control performance using PICAFO with the improved estimated ω ref based on walking speed and BMI.

V. CONCLUSION
This research has focused on improving passive AFO equipped with MR brake, called PICAFO by implementing ankle velocity as the control reference, based on walking speed and BMI. The control reference, which acts as the guidance of a control system, is crucial because it determines PICAFO's action to control the user's walking gait. A useful control reference should be able to adapt to different gait phases, walking modes, and even subjects while at the same time not producing bulky devices due to over-specified actuators and sensors. Therefore, this study chooses the ankle velocity as the control reference (ω ref ) because it can be passively controlled using the MR brake and measured using a rotary encoder only (non-bulky sensor).
The investigation of ω ref function shows that ω ref for P1, P2, and P3 can be estimated based on walking speed and BMI, where both the independent variable's coefficient is significantly not to be zero (p-value < 0.05). The implementation result shows a positive effect (i.e., more energy-efficient walking [3]) of PICAFO's controlled stiffness to the able-bodied subject, who does not need any assistance. Therefore, PICAFO is also expected to give positive aid to people in need, such as post-stroke patients with foot drop. Primarily ankle kinematics and muscle activity result in P4 show that PICAFO achieves the toe clearance by locking the foot position (ankle velocity equals zero rad/s). Thus, it reduces muscle activity because the MR brake partially replaces the muscle work. This function is necessary for a post-stroke patient with foot drop who cannot lock the foot position by himself. Also, the controlled stiffness on P1, P2, and P3 makes the patient walks with less walking energy, as suggested by muscle activity reduction on P2.
This study's results serve as the groundwork for further developing a sophisticated PICAFO system, which can be adaptable to different gait phases, walking modes and can also be subjected to intensive and autonomous gait rehabil- itation. Using the controlled stiffness, which is based on ω ref , the therapist or doctor can do intensive, collaborative, and personalized AFO prescription [50]. They can skip the trial and error process of finding an appropriate control reference using the ω ref function based on walking speed and BMI. Future works and recommendations for the PICAFO system, such as improving the ankle velocity reference estimation by increasing the sample sizes and ankle velocity-based gait phase detection to optimize sensor numbers, are demanded. Meanwhile, functionality validation of PICAFO with controlled stiffness for assisting the post-stroke patient should also be carried out.

ACKNOWLEDGMENT
The authors would like to express their gratitude to Universitas Sebelas Maret for supporting some of the hardware and the APC through Hibah Kolaborasi Internasional 2020 and the Institut Teknologi Telkom Surabaya for their partial support on APC.