Previous studies have introduced BWS robots with different mechanical design concepts. Many BWS robots actuate the suspension mechanism and allow users to move around a floor, lifting both sides of the body using a solo actuator (Hidler et al., 2011; Vallery et al., 2013; Mignardot et al., 2017; Plooij et al., 2018). These robots provide overground walking rehabilitation, which is fundamentally different from treadmill walking; however, they have not been developed for modulating impaired body orientation. Fewer BWS robots provide dynamic and asymmetric support for each side of the body using more than two actuators. Kwak et al. (2017) developed a robot with a pair of compact series elastic actuators (SEA) that assist the left and right sides of the body to provide vertical forces while freeing the user’s natural medial-lateral movement. Van Thuc and Yamamoto (2016) designed a BWS robot with four pneumatic actuators arranged at the corners of the walking space to follow the displacement of the user’s CoP and adopt the virtual application point of support. Dong et al. (2021) developed a mobile-type BWS walker with two variable stiffness actuators on both sides of the lower limbs to relieve part of the body weight. Meanwhile, robots intended to actuate the pelvis have also been investigated. Pietrusinski et al. (2010) developed a robot that generates a force field around the pelvis using linear electromagnetic actuators placed on the left and right sides of the user’s body to guide pelvic obliquity. Aoyagi et al. (2007) designed a pelvis assist manipulator with pneumatic cylinders to assist the pelvic motion that can be used together with a separate overhead BWS system. Khan et al. (2018) designed a trainer for static and dynamic CoM stability. Patton et al. (2008) developed a mobile base system that holds the torso using a pelvic belt to provide partial BWS and postural control on the torso. Luu et al. (2014) designed a pelvic assistance mechanism holding the pelvis by a rigid frame to provide BWS and body weight shifting during gait rehabilitation. The advantages and limitations of past studies are discussed in the following section.

Even though the point of contact between a human and a BWS robot drastically affects walking patterns, it has rarely been studied (Plooij et al., 2021). Most BWS robots use a harness that shares points of pressure with the lumbar-thoracic harness and thigh straps (Hidler et al., 2011; Kwak et al., 2017; Mignardot et al., 2017). While conventional harnesses wrap around the upper torso and connect double shoulder points to a spreader bar, Van Thuc and Yamamoto (2016) designed an original lumbar-thoracic harness with four shoulder point connections to four PAMs. The trunk is stabilized if the attachment points are as high as those at the shoulder or trunk level (Plooij et al., 2021). Meanwhile, a pelvic brace (Aoyagi et al., 2007; Pietrusinski et al., 2010), pelvic belt (Patton et al., 2008; Khan et al., 2018), and pelvic frame (Luu et al., 2014) are selectively used to apply the desired force around the pelvis. Attachments on the sides of the pelvis are beneficial in that they do not impede the forward-leaning of the upper body to take a step, compared to assists at a higher position (Plooij et al., 2021). However, Plooij et al. (2021) argued that the mechanical structure inhibits pelvic rotations along the vertical axis. Responding to these suggestions, we aim to design a harness and attachments to intervene in the pelvic obliquity, but not to impede natural walking movement, introduced in Section “3. Mechanical design” and evaluated in Sections “5.1. Mechanical design evaluation and 6.1. Mechanical design evaluation.”

Previous studies have demonstrated that the support force of the existing BWS systems is weak in modulating spatiotemporal walking patterns. For example, Dragunas and Gordon (2016) reported that the step width and step length were not significantly modulated by BWS devices with less than 60% of the participant weight in their experiment with healthy participants. Similarly, Tran et al. (2020) reported that abnormal stride length was not corrected by counterweight supports with less than 70% of the weight of healthy participants who reproduced the gait pattern of hemiplegia. From this perspective, the range of force control of Pietrusinski’s robot (Pietrusinski et al., 2010), which is less than 10 N, is insufficient for modulation. Other BWS robots can provide large forces but have evaluated the force tracking performance in a relatively smaller range. For example, a robot by Dong et al. (2021) can provide more than 100% of body weight but test with less than 20%. A robot by Kwak et al. (2017) can provide 300 N at maximum but evaluate the robot with a small range using a 40–80 N sinusoidal force reference. Only Van Thuc and Yamamoto (2016) showed their robot capability with 500 N at maximum and a 100–500 N sinusoidal reference tracking performance at various frequencies. We refer to this study to conduct a force-tracking task in Sections “5.2. Force tracking task with mass and 6.2. Force tracking task with mass.”

Conventional BWS devices relieve the load on therapists to support and provide stability to the patients performing gait training. However, many manual assists are still required, such as encouraging weight shift with pelvic motion (Aoyagi et al., 2007). Thus, pelvic actuation and unconstrained natural movements have been investigated. Ichinose et al. (2003) recorded and replayed a pelvic motion and showed pelvic position tracking performance of position/force control during unimpaired human walking. Aoyagi et al. (2007) further developed synchronization control for the robot and demonstrated its position-tracking performance with individuals with spinal cord injury. Pietrusinski et al. (2014) showed pelvic obliquity tracking performance with healthy participants where the reference was measured from a healthy participant. Vashista et al. (2016) showed pelvic anterior-posterior and vertical motion-tracking performance. Dong et al. (2021) demonstrated mediolateral pelvic trajectory tracking performance. Therefore, although previous robots have the ability to control the CoM/CoP through pelvic control, the actual position controllability of the CoM/CoP has not been well discussed. To date, only two studies have investigated weight-shifting performance. Kwak et al. (2022) have shown tracking performance in the vertical displacement of a hanged mass CoM. Van Thuc and Yamamoto (2016) showed CoP tracking performance with three healthy participants. Moreover, they were designed to track the CoP measured with load cells so that the right-side actuator increases the force when the CoP moves to the right foot. However, when a robot refers to the abnormal pattern of a patient’s gait, it is impossible to modulate their impaired gait. In the clinical setting, a therapist gently pushes the patient’s pelvis and transfers the body weight to the stance leg (Yagura et al., 2006). Thus, in this study, the robot aimed to lead the users in shifting their body weight. To prove the concept of this function, we evaluate the robot control performance in a split-force control task using a test bench in Sections “5.3. Split-force control task with test bench and 6.3. Split-force control task with test bench.”

The upper body motions were compared during natural and laterally identical force-controlled 30% BWS walking. Three healthy participants (Participant A: 71-year-old male, Participant B: 71-year-old female, and Participant C: 32-year-old female) wore a motion capture suit (Prime 17W OptiTrack, NaturalPoint Inc.) and walked on a treadmill at their preferred speed for 1 min (Figure 4A). Eight cameras were arranged surrounding the SF-BWS, all at 2.5 m high from the ground. Reflection markers were attached just above the left and right acromie on the motion capture suit. For the left and right posterior superior iliac spine (PSIS), markers were attached to the pant-type harness. We compared the orientation of the upper body using the angle between the vectors passing through these four points (Figure 4B). We designed an analog low-pass filter with a passband within 3 dB from 20/250/2 rad/s while rejecting at least −40 dB below 100/250/2 rad/s (sampling frequency was 250 Hz). The order was 2. Marker positions were passed through the filter before calculating the following.

The three-dimensional angle between the two vectors that connect the left and right acromie a→=(ax,ay,az) and PSISs b→=(bx,by,bz) was obtained using the following equations:

Here, the straight-line vectors are a→=PL⁢A⁢PR⁢A→ and b→=PL⁢P⁢PR⁢P→, where P_LA = [x_LA, y_LA, z_LA], P_RA = [x_RA, y_RA, z_RA], P_LP = [x_LP, y_LP, z_LP], and P_RP = [x_RP, y_RP, z_RP]. The angle time history was separated based on the gait cycles. The step was detected using the foot load cells in Figure 4A built into the pair of shoes (weight: 1.2 kg). Each heel strike was detected if the load cell force exceeded the threshold. In this experiment, the age of the two participants was high, and they had no previous experience with BWS; therefore, safety was prioritized and 30% BWS was set. This is because Hesse (2008) reported that unloading more than 30% BW is not recommended due to decreased muscle activity in the lower extremities. The reference force F_r = [F_rL, F_rR]^T in Figure 3 is as follows:

where a partial body weight support rate is β, the participant’s weight is M, and the gravity acceleration is g. All participants provided written informed consent before participation, and the local ethical committee approved the study protocol.

To evaluate the force controller consisting of the feedback PAM model and PID feedback, we demonstrated the control performance of the wide range of force tracking using the SF-BWS. Figure 4C shows the experimental setup. At this point, the mass and the Bowden cables of the PAM were connected by a string. Since this string was elastic, the PAM contracted even when the mass did not change its height; the nonlinearity of the PAM increases most when it is elastic. Therefore, this task allowed us to evaluate the control performance of the proposed method in a system with PAM nonlinearities.

As it is required to have a large enough force to modulate spatiotemporal walking patterns by previous studies (Dragunas and Gordon, 2016; Tran et al., 2020), we used a mass assuming the human body and hooked it at the end of the inner Bowden cable, as shown in Figure 4C. It can be stabilized by support at one point; thus, the mass is hooked directly without the proposed harness. For assisting patients, the weight of the mass was 60 kg. We set the force tracking task with the reference force with a sinusoidal wave to show that SF-BWS can dynamically change the amount of support in real time based on measured interaction forces. Since the possible amplitude of partial BWS is approximately 30–70% of the body weight according to previous studies (Hesse, 2008; Dragunas and Gordon, 2016; Tran et al., 2020), we set the minimum support at 176.4 N (60 kg × 9.8 m/s² × 30 %). The range of the reference is up to 600 N per PAM to fully compensate for the mass weight; thus, SF-BWS totally supports 1,200 N. Note that we limited the maximum force reference up to 600 N for safety. The PAM itself can generate a much larger force (1,500 N). In this experiment, the right PAM is not used. Thus, the reference force F_r = [F_rL, 0]^T in Figure 3 at time step t is as follows:

where the amplitude A of the sinusoidal reference is 211.8 N, the bias B is 388.2 N, and the frequency f is 0.5 Hz [referred to Van Thuc and Yamamoto’s (2016) study].

In addition, we performed a force-tracking task using different simulated load weight setups (40, 50, and 60 kg masses). The smallest weight was selected because the 2.5 percentile of elderly Japanese people’s body weight is 40 kg according to a database (Kouchi and Mochimaru, 2005). To examine the 30–70% weight support, the reference force was set as A=12⁢(0.7-0.3)⁢M, B = A + 0.3M, and f = 0.5 in Eq. (9). The mass was in contact with the ground, while the air pressure was zero; that is, PAM was at its natural length and the length of the string connecting PAM and the mass was adjusted to be tightened. The string was released and retightened each time we changed the mass. Again, the right PAM was not used in this experiment, so F_rR was set to zero.

We derived that the coefficients a_u, b_u, c_u, a_l, b_l, and c_l are 0.00013, −0.00361, 336.6179, 0.00017, 519.0473, and 38.66615 for left PAM in Eqs. (2) and (3). We set K_p, K_i, and K_d as 6.0 × 10⁻², 7.0 × 10⁻⁴, and 6.0 × 10⁻⁵ in Eq. (5).

This section illustrates the force control strategy for the proposed SF-BWS robot in a split-force control task. We use a test bench to demonstrate that SF-BWS can precisely track arbitral desired force. To test the functionality indicated in contribution 3 mentioned in the introduction, the test bench on a reaction force plate (AMTI Inc., BP400600-1000) mimicked the human body. We hooked the bench at the end of the inner Bowden cable via load cells. Figure 5A shows the configuration of the test bench model. Figure 5B shows the bench used in this task. The weight of the mass is 60 kg. The size of the test bench made of aluminum frames is 530 × 300 × 120 (width × depth × height). The masses are threaded through a screw shaft (M24, 606 mm) and screwed to the top of the bench with holders. M8 eyebolts are also screwed on the top of the bench to hook carabiners. A string is tied to the carabiner, and its length is adjustable by the rope ratchet at the other end. The string goes through the M8 eyebolt screwed to the load cell.

The equations for the equilibrium of force and moment around the origin O can be described with the following equations:

where the reaction force measured on the reaction force plate is F_Z. The 60 kg mass is located in the middle of the bench, where the height difference between the mass CoM and the positions where inner Bowden cables are attached to the test bench (weight: 7.55 kg) is negligible. Thus, M in Eqs. (10) and (11) is the sum of the weight of the mass and the bench. PAMs are attached in the distance y_l from the bench center. The distance from the origin to the attachment location of the left PAM is defined as y_L, and that of the right PAM is y_R. The physical parameters of the test bench are provided in Table 1. When a partial body weight support rate is β, the partial BWS force of PAMs F_rL and F_rR are

If we give SF-BWS a desired trajectory of the CoP, the forces are determined geometrically to accomplish the target CoP position. Thus, the pelvic rotational force of PAMs F_rL and F_rR at time step t will be

where the CoP reference is

Since the amplitude of the natural human CoP trajectory is assumed within stride width, which is the distance between the two heels during the double stance, and the normal stride width of adults is between 3 to 8 cm (Wellmon, 2007), the CoP reference was set as a sinusoidal wave with A = 0.050 m, B = 0.300 m where the center of the reaction force plate locates and f = 1.0 Hz for Eq. (15), which was set by referring to the cadence reported in previous studies [52.5 ± 17.0 steps/min by Tudor-Locke et al. (2020) at 0.8 km/h treadmill speed where the upper range walking speed of most stroke patients (Capó-Lugo et al., 2012)]. Then, the required forces for two PAMs were obtained from Eq. (13) and Eq. (14). The left PAM’s coefficients are the same as the force-tracking task (explained above). We derived that the coefficients a_u, b_u, c_u, a_l, b_l, and c_l are −0.00059, −0.00021, −0.00117, −0.00035, −0.00016, and −0.00186 for right PAM in Eqs. (2) and (3). We set the proportional gain K_p, integral gain K_i and derivative gain K_d as 8.0 × 10⁻², 2.0 × 10⁻³, and 5.0 × 10⁻³ for the right-side PAM. For the left-side PAM, K_p, K_i, and K_d are 3.0 × 10⁻², 1.5 × 10⁻³, and 5.0 × 10⁻³, respectively, in Eq. (5). We conducted experiments in two conditions: (1) First condition: 1-second single-wave reference for the reproductivity check, and (2) Second condition: 20 s block-designed reference.

We used load cells for feedback control. Thus, the measured forces F_m = [F_mL, F_mR]^T in Figure 3.

The reaction force F_Z is not always measurable at clinical sites; thus, we did not use it for feedback control. We used the reaction force plate to evaluate the CoP displacement in the Y-direction as follows:

M_x and F_y are the measured moment and force on the force plate. z₀ is the distance between the top plate surface and the true origin of the force plate.

Figure 6A shows the three-dimensional displacement of vectors connecting the left and right acromie and PSIS of Participant B (71-year-old female) in two conditions; natural walking or walking under laterally identical force-controlled 30% BWS condition wearing the proposed harness. The minimum detected number of gait cycles across conditions was 29. The origin of the mediolateral (Y) direction is at the center of the left and right PSIS positions of the participant. Figures 6B, C show the angle θ and the lateral displacement of the center position of the left and right PSIS of Participant B in two conditions. The trend within each gait cycle is qualitatively similar between the conditions. The root mean square error (RMSE) between the reference and measured forces, the average θs between natural and 30% BWS walking, and the average yL⁢P-yR⁢P2 were evaluated (Table 2). While Plooij et al. (2021) argued that a higher support point impedes the forward-leaning of the upper body to take a step, and the mechanical structure inhibits the pelvis motion, the proposed harness poses negligible influence.

The above results suggest that the proposed harness has no significant effect on walking motion, and the trend of upper body motion is qualitatively equivalent to that of natural walking among three participants in the experimental setup of the current study. However, Plooij et al. (2021) compared propelling velocity difference; thus, additional evaluation may be needed in our study because the velocity could not be measured in the current experimental setup. Moreover, Van Thuc and Yamamoto (2016) and Tran et al. (2020) identified the difference in CoM/CoP displacement between the different amounts of unloading conditions due to the pendulum effect (the trunk of participants swung) at higher level BWS. Thus, the current evaluation is limited, and verifying the motion restriction due to the proposed harness with different BWS levels is necessary. In addition, Kwak et al. (2022) confirmed that under an impedance-controlled BWS walking condition, the RMSE of pelvic roll rotational angle was smaller than the BWS walking condition without impedance control. Although it has not been confirmed in our experiments, split-force-controlled walking may alter the influence on the upper body and pelvic motion. However, these evaluations are extended focuses for the current study and must be conducted with hemiparetic patients, prioritizing their safety. Thus, hereafter, we use a mass instead of involving human participants for force control evaluation.

Split force-controlled-BWS with the force controller consisting of the feedback PAM model and PID feedback successfully tracks the reference force. Figure 7A top panel shows the force-tracking performance of SF-BWS. RMSE between the reference and measured force was 29.84 N within 20 s. Figure 7A bottom panel shows the PAM’s contraction length. The mass is in contact with the ground; thus, the change in the PAM contraction length was caused by the stretch of the string connecting the PAM and the mass. The range of operation was 6.91 cm. Note that the length is not controlled; thus, the PAM is extended when the reference force is smaller than the mass weight. In contrast, the weight is fully compensated when the PAM exerts 600 N force, and the length of the PAM becomes shorter and the contraction stops at the equilibrium point. Consequently, the length of the PAM is determined by the weight of the mass in this experiment. This experimental result shows that the force can be freely controlled in the range from 176.4 N to 600 N when the connection position of the mass is constant. This connection position can be arbitrarily changed according to the user’s waist height by adjusting the length of the climbing ropes and strings. In other words, by adjusting the length of the climbing rope and string connecting to the proposed harness, a large force can be generated, even when the PAM contraction length is short.

SF-BWS with the force controller successfully tracks the reference force with different masses (Figure 7B). RMSE between the reference and measured forces was 17.14 N at 60 kg mass, 12.88 N at 50 kg mass, and 10.69 N at 40 kg mass within 20 s.

The reliability of controlling PAMs to oscillate the CoP under 60% BWS was sufficient, as more than 60% BWS was required to modulate spatiotemporal walking patterns in previous studies (Dragunas and Gordon, 2016; Tran et al., 2020). For the first experimental condition, the SF-BWS successfully accomplished CoP oscillation in a 1-s single-wave reference. Figure 8A shows the reference and the measured CoP position in the y-direction. The mean of RMSE between the reference and measured CoPs by the reaction force plate using Eq. (16) was 0.011 m for ten trials. Figure 8B shows the force tracking results. The RMSE of reference and measured force in the right PAM was 9.7 N, and that of the left PAM was 10.3 N within ten trials. Since the test bench did not move, the SF-BWS force control performance and the resulting CoP tracking were highly reproducible in the current study. The average of the measured total body weight support force (F_L + F_R) was 399.2 N, while the total body weight support force is supposed to be 397.2 N.

The bench was never lifted off the reaction force plate or actively moved. The change in the PAM contraction length (Figure 8C) was caused by the stretch of the string connecting the PAM and the bench. The string length causes the difference between the left and right PAM contraction lengths because the string length is adjusted manually using the rope ratchets. The contraction length critically affects the force generated by the PAMs. Thus, better control of the initial setting of the string length is needed for more precise force control. In addition, the sinusoidal wave frequency is higher than that of the force-tracking task in Figure 7; thus, the delay caused by the air exhaust was more striking. Although the delay and the force errors can be compensated by adding the velocity terms of pressure and contraction rates and selecting a string that never stretches, the actual interaction with humans while walking increases the error. Moreover, PAM responsiveness for the desired force affects the user’s comfort (the time constant is added and set to 0.3 in our clinical trial for the patient’s comfort). Thus, further investigation of patient response to the intervention force with close collaboration with the clinical site is the future direction of SF-BWS development. The CoP acceptably tracked the reference in the mediolateral direction using the test bench.

For the second experimental condition, based on the successful results of tracking the COP in Figure 8, we also attempted advanced tracking under conditions closer to the clinical conditions used in our previous conference paper. SF-BWS successfully achieved CoP oscillation in a 20 s block-designed reference. Figure 9A shows the CoP displacement measured using the reaction force plate. Since SF-BWS applies the forces in the coronal plane, the CoP displacement in the X-direction is negligible (it is also obvious from Figure 9B). The reference and measured CoP positions in the Y-direction are shown in Figure 9C. The RMSE between the reference and measured CoPs obtained using the reaction force plate [Eq. (16)] was 0.014 m within 20 s. The RMSEs were below 30% compared with the amplitude (0.050 m). Thus, the residual mean displacement of the mass CoP was sufficiently small compared to the reference range. The bench never actively moved, nor was it lifted off the reaction force plate. Thus, the robot was able to lead the shift in users’ body weight.

Figure 9D shows the force tracking results. RMSE of reference and measured force in the right PAM was 8.6 N, and that of the left PAM was 9.6 N within 20 s. The total body weight support force was assumed to be 397.2 N, and the average of the measured total body weight support force (F_L + F_R) was 397.5 N. Thus, the developed SF-BWS was capable of assisting both pelvic rotations and constant body weight support.