3.1. System overview

A schematic diagram of the proposed teaching system for elbow flexion motion is shown in Figure 3. The system assumes that time-series data of the instructor’s arm joint angle $ {\theta}_{\mathrm{I}} $ are recorded in advance. As shown in Figure 3, the learner imitates the instructor’s motion while simultaneously receiving torque feedback from the assistive suit and visual feedback from the CG model on display. The CG model shows the motion of the instructor’s joint angle $ {\theta}_{\mathrm{I}} $ and the learner’s current joint angle $ {\theta}_{\mathrm{L}} $ overlapped on it. The motion of the learner’s arm is measured in real-time using motion capture system, and the marker coordinate information is sent to the PC that controls the PAM via virtual-reality peripheral network (VRPN). We use the Miqus M3 camera system from Qualisys Inc. for motion capture, and the learner’s motion is monitored at a sampling rate of 500 Hz. The load cell’s measured voltage (means the measured force $ {F}_{\mathrm{true}} $ ) is also monitored simultaneously. Upon receiving the information, the PAM control PC controls the internal pressure of the PAM by adjusting the servo valve openings to provide force feedback according to the difference between the learner’s joint angle $ {\theta}_{\mathrm{L}} $ and the instructor’s joint angle $ {\theta}_{\mathrm{I}} $ . The control program was written using ROS (Robot Operating System).

Figure 3.

Schematic diagram of the proposed teaching system for elbow flexion motion.

3.2. Control method

We set the assist torque $ T $ generated around the elbow joint in response to the magnitude of the deviation in elbow joint angles ( $ {\theta}_{\mathrm{I}} $ for the instructor and $ {\theta}_{\mathrm{L}} $ for the learner) as

(3.1) $$ T=\left\{\begin{array}{cc}0& \left({\theta}_{\mathrm{I}}\le {\theta}_{\mathrm{L}}\right)\\ {}K\left({\theta}_{\mathrm{I}}-{\theta}_{\mathrm{L}}\right)& \left({\theta}_{\mathrm{I}}>{\theta}_{\mathrm{L}}\right)\end{array},\right. $$

where $ K $ is a proportional gain to compensate for angular misalignment. This controller generates the torque $ T $ only in case of $ {\theta}_{\mathrm{I}}>{\theta}_{\mathrm{L}} $ . We provide the learner with feedback torque to correct the deviation in motion proportionally.

To achieve the torque feedback, the target driving force $ {F}_{\mathrm{ref}} $ of the PAM is determined by the following equation:

(3.2) $$ {F}_{\mathrm{ref}}=\frac{T}{h}=\left\{\begin{array}{cc}0& \left({\theta}_{\mathrm{I}}\le {\theta}_{\mathrm{L}}\right)\\ {}\frac{K\left({\theta}_{\mathrm{I}}-{\theta}_{\mathrm{L}}\right)}{h}& \left({\theta}_{\mathrm{I}}>{\theta}_{\mathrm{L}}\right)\end{array}.\right. $$

Here, $ K $ means the torque per unit deviation in joint angle, which is the torque stiffness. $ h $ is the distance between the elbow joint and the cable, as shown in Figure 2, and it is a variable expressed as a function of the learner’s joint angle $ {\theta}_{\mathrm{L}} $ . The detail of calculating $ h $ is described in (Tomita et al., Reference Tomita, Miyazaki and Sogabe2023).

We implement force-tracking control to align the actual driving force ( $ {F}_{\mathrm{true}} $ ) of the PAM with the target driving force $ {F}_{\mathrm{ref}} $ . Using a method that controls the PAM’s internal pressure by adjusting the opening and closing of the servo valve through force feedback control, as indicated by the black lines in the block diagram of Figure 4, there was a problem of reduced accuracy in tracking control, due to the impact of the time delay from the change in internal pressure to the change in driving force.

Figure 4.

Block diagram of force control using the load cell.

Therefore, in this study, to compensate for this driving delay, we propose a 2-DOF control approach that combines feedback and feedforward. As shown in the red lines in Figure 4, we compensate for the driving delay of the PAM by adding the differential value of the target force to the control voltage of the servo valve through feedforward control, thereby improving the accuracy of force-tracking control. In Figure 4, $ z $ is the $ z $ -transformation operator. This article represents the control systems and variables in discrete time form.

Finally, feedforward controller and PI controller give control voltage $ u $ of the servo valve so that the measured force $ {F}_{\mathrm{true}} $ follows the reference force $ {F}_{\mathrm{ref}} $ as

(3.3) $$ u\left[k\right]={K}_{\mathrm{ff}}{\dot{F}}_{\mathrm{ref}}\left[k\right]+{K}_{\mathrm{P}}\left({F}_{\mathrm{ref}}\left[k\right]-{F}_{\mathrm{true}}\left[k\right]\right)+{K}_{\mathrm{I}}\Delta t\sum \limits_{j=0}^k\left({F}_{\mathrm{ref}}[\hskip0.3em j]-{F}_{\mathrm{true}}[\hskip0.3em j]\right), $$

where $ k $ and $ j $ are current and past time steps, and $ \Delta t $ is sampling time. The feedforward gain $ {K}_{\mathrm{ff}} $ and PI gains $ {K}_{\mathrm{P}} $ and $ {K}_{\mathrm{I}} $ are set as follows:

(3.4) $$ {K}_{\mathrm{ff}}=0.035\;\left(\mathrm{V}\cdot \mathrm{s}\right)/\mathrm{kPa},{K}_{\mathrm{P}}=0.2\;\mathrm{V}/\mathrm{kPa},{K}_{\mathrm{I}}=0.003\;\mathrm{V}/\left(\mathrm{kPa}\cdot \mathrm{s}\right). $$

4.1. Force estimation

The previous section proposed the force-tracking control method for PAM using the load cell. However, using electrical sensors such as the load cell can make the suit more complicated and increase the risk of malfunctions, making it challenging to build a lightweight, low-cost, and highly usable system that allows intuitive teaching.

To solve the above issue, this study proposes a method to estimate the driving force from the internal pressure value of a small sealed PAM connected in series to the driving PAM, as shown in Figure 5. The small PAM is initially pressurized and sealed, and its internal pressure changes along with the tension force of the Bowden cable pulled by the driving PAM.

Figure 5.

Force estimation using the inner pressure of the serial-connected small PAM.

The reason for using the sealed small PAM is described as follows. If the PAM for estimating force deforms significantly, its expansion may unintentionally absorb the length change of the driving PAM, which may hinder the desired driving. To address the above concern, reducing the deformation of the PAM to estimate force is effective. In this study, we used the smallest size PAM currently available. The small PAMs shown in Figure 6, manufactured by Bridgestone Corporation, had a total length of 65 mm, a contraction section of 30 mm, a diameter of 7 mm, and a braiding angle of 25 deg. The PAM used to estimate the force in the elbow flexion direction is referred to as the small PAM1, and the PAM used to estimate the extension direction is referred to as the small PAM2. The sealed small PAM used in this study had an initial length of 0.030 m, a length of 0.029 m when 90 kPa was applied and unloaded, and a length of 0.030 m when 90 kPa was applied and a load of 80 N was applied. The driving PAM had an initial length of 0.35 m and a length of 0.24 m when 600 kPa was applied and unloaded. From the above, the deformation of the sealed small PAM is sufficiently small compared to the deformation of the driving PAM and will not be a problem in practical use. By replacing the load cell with a sealed small PAM, it is possible to eliminate electric sensors from the suit attachment part, which is expected to improve the usability of the suit. The limitation of the sealed small PAM is that the range of load that can be measured is limited within the deformation range. For example, when 90 kPa is applied to the sealed small PAM used in this study, the upper limit of the load that can be measured is 80 N, which stretches the PAM to its initial length. If there is a desired measurement range, designing a sealed small PAM to satisfy this is one of our future works.

Figure 6.

Small PAMs for force estimation.

The proposed system uses a pressure sensor to measure the internal pressure of the sealed small PAM. The pressure sensor is installed away from the wearing part of the suit via an air tube. This configuration eliminates electrical sensors from the vicinity of the wearing part, improving the suit’s environmental resistance and usability. However, when measuring the pressure inside the PAM via an air tube, using a tube that is too long can cause a delay in the pressure response. For this reason, in this study, to prevent excessive delays in the pressure response, we connected the sealed small PAM and pressure sensor with an air tube 120 mm long and with an inner diameter of 4 mm, as shown in Figure 7.

Figure 7.

The connection between the pressure sensor and the sealed small PAM.

Several force estimation methods were verified, including the Prandtl–Ishlinskii model (Mayergoyz, Reference Mayergoyz1986) and the neural network (NN) model. These models take into account characteristics such as the PAM’s hysteresis. In this study, a small-scale NN shown in Figure 8 was adopted for force estimation. In Figure 8, $ p\left[k\right] $ and $ \dot{p}\left[k\right] $ are measured pressure and its time derivative in the small sealed PAM at time step $ k $ . w_ih and w_ho are weight variables that are optimized as design parameters in the learning process. Considering the real-time performance of estimation and control, NN architecture is designed to be as minimal as possible to reduce the amount of calculation. The used NN has a structure of three fully connected layers: two input, four hidden, and one output. The activation function for all layers is the ReLU function. A force estimation method is adopted using the small sealed PAM and NN, realizing a force-controlled motion teaching system without the load cell.

Figure 8.

Simple neural network for force estimation from pressure information.

4.2. Parameter learning of neural network for force estimation

Preliminary experiments were conducted for each small PAM to learn the NN parameters for force estimation. The experimental setup is shown in Figure 9. The small PAM was sealed by applying an initial pressure of 90 kPa without any external force, and the driving PAM was driven so that the contraction force changed from 0 to 60 N repeatedly. Data were measured for 120 s, which contains the inner pressure of the small sealed PAM and the force measured by the load cell. The former 60 s of the measured data shown in Figure 10 were used for learning, and the remaining 60 s of the data were used for testing.

Figure 9.

Experimental setup for learning NN parameters.

Figure 10.

The measured data for learning of the small PAM’s NN.

During the learning and estimation process, the small PAM internal pressure $ p\left[k\right] $ and its differential value $ \dot{p}\left[k\right] $ were used as the input values for the NN after the standardizing processing as follows:

(4.1) $$ \hat{p}\left[k\right]=\frac{p\left[k\right]-{\overline{p}}_{\mathrm{train}}}{\sigma_{p_{\mathrm{train}}}},\hat{\dot{p}}\left[k\right]=\frac{\dot{p}\left[k\right]}{\sigma_{p_{\mathrm{train}}}}. $$

where $ {p}_{\mathrm{train}} $ is the training data of $ p $ . $ {\overline{p}}_{\mathrm{train}} $ is the $ {p}_{\mathrm{train}} $ ‘s average, and $ {\sigma}_{p_{\mathrm{train}}} $ is the $ {p}_{\mathrm{train}} $ ‘s standard deviation.

The normalized root mean square error (NRMSE) was used to evaluate force estimation performance. The NRMSE [%] is calculated as follows:

(4.2) $$ \mathrm{NRMS}{\mathrm{E}}_{\mathrm{esti}}=\frac{\sqrt{\frac{1}{N}{\sum}_{i=1}^N{\left({F}_{\mathrm{true}}\left[i\right]-{F}_{\mathrm{esti}}\left[i\right]\right)}^2}}{\max\;{F}_{\mathrm{true}}}\ast 100. $$

$ i $ is the index of the sample data, and $ N $ is a total data number for calculation. The force estimation results using the NN trained based on the input data are shown in Figure 11. The estimated and measured values’ NRMSEs were 1.8% for the PAM1 and 1.8% for the PAM2, respectively, sufficient estimation accuracy for the motion teaching task.

Figure 11.

The force estimation result of the small PAMs.

This study used a simple NN for force estimation using a sealed small PAM. The calculation accuracy obtained was sufficient for applying human motion assistance, and it is desirable to have low calculation costs for real-time estimation. Therefore, we did not adopt a complex NN architecture for this force estimation application; instead, we adopted a simple NN, which we thought was best. However, when performing more complex state estimation using the dynamics of a pneumatic pipeline system, including PAM, the calculation performance of a simple NN will likely be insufficient. We plan to test more advanced NN structures in our future work for such cases.

4.3. Force control method combined with force estimation

The force control method combined with the force estimation using the small PAMs is shown in Figure 12. In Figure 12, the back and ventral side PAMs are defined as the driving PAM1 and PAM2. The small PAM1 and PAM2 are connected to the driving PAM1 and PAM2. The load cell of the force-tracking control method proposed in the previous section is replaced with the sealed small PAM. The estimated force $ {F}_{\mathrm{esti}} $ is obtained using the NN, and the data stream is smoothed by applying a low-pass filter.

Figure 12.

Block diagram of force control combined with force estimation.

The assist torque $ {T}_1 $ and $ {T}_2 $ of the driving PAM1 and PAM2 generated around the elbow joint in response to the magnitude of the deviation in elbow joint angles:

(4.3) $$ {\mathrm{T}}_1\left[k\right]=\left\{\begin{array}{cc}\tau & \left({\theta}_{\mathrm{I}}\left[k\right]\le {\theta}_{\mathrm{L}}\left[k\right]\right)\\ {}K\left({\theta}_{\mathrm{I}}\left[k\right]-{\theta}_{\mathrm{L}}\left[k\right]\right)+\tau & \left({\theta}_{\mathrm{I}}\left[k\right]>{\theta}_{\mathrm{L}}\left[k\right]\right)\end{array},\right. $$

(4.4) $$ {\mathrm{T}}_2\left[k\right]=\left\{\begin{array}{cc}K\left({\theta}_{\mathrm{I}}\left[k\right]-{\theta}_{\mathrm{L}}\left[k\right]\right)-\tau & \left({\theta}_{\mathrm{I}}\left[k\right]\le {\theta}_{\mathrm{L}}\left[k\right]\right)\\ {}-\tau & \left({\theta}_{\mathrm{I}}\left[k\right]>{\theta}_{\mathrm{L}}\left[k\right]\right)\end{array},\right. $$

where $ \tau $ is the canceling torque to reduce the wire slack. This controller generates the torque $ T={T}_1+{T}_2 $ both in cases of $ {\theta}_{\mathrm{I}}>{\theta}_{\mathrm{L}} $ and $ {\theta}_{\mathrm{I}}\le {\theta}_{\mathrm{L}} $ thanks to the antagonistic drive mechanism of the suit.

To achieve the torque feedback, the target force $ {F}_{i,\mathrm{ref}} $ of the driving PAM $ i $ is determined by the following equation:

(4.5) $$ {F}_{1,\mathrm{ref}}\left[k\right]={T}_1\left[k\right]/{h}_1\left[k\right]=\left\{\begin{array}{cc}\tau /{h}_1\left[k\right]& \left({\theta}_{\mathrm{I}}\left[k\right]\le {\theta}_{\mathrm{L}}\left[k\right]\right)\\ {}\left(K\left({\theta}_{\mathrm{I}}\left[k\right]-{\theta}_{\mathrm{L}}\left[k\right]\right)+\tau \right)/{h}_1\left[k\right]& \left({\theta}_{\mathrm{I}}\left[k\right]>{\theta}_{\mathrm{L}}\left[k\right]\right)\end{array}\right., $$

(4.6) $$ {F}_{2,\mathrm{ref}}\left[k\right]={T}_2\left[k\right]/{h}_2=\left\{\begin{array}{cc}\left(K\left({\theta}_{\mathrm{I}}\left[k\right]-{\theta}_{\mathrm{L}}\left[k\right]\right)-\tau \right)/{h}_2& \left({\theta}_{\mathrm{I}}\left[k\right]\le {\theta}_{\mathrm{L}}\left[k\right]\right)\\ {}-\tau /{h}_2& \left({\theta}_{\mathrm{I}}\left[k\right]>{\theta}_{\mathrm{L}}\left[k\right]\right)\end{array}\right., $$

where $ {h}_1\;\left[k\right] $ is the distance between the elbow joint and the cable connected to the flexor carpi radialis, and it is a variable expressed as a function of the learner’s joint angle $ {\theta}_{\mathrm{L}} $ . The moment arm length $ {h}_2 $ of the driving PAM2 was set to half the measured thickness of the learner’s arm because the PAM2’s cable is always in close contact with the arm surface and can be considered constant.

The control voltages $ {u}_1 $ and $ {u}_2 $ of the servo valves that control the driving PAM1 and 2 can be calculated according to the following equations:

(4.7) $$ {u}_i\left[k\right]={K}_{\mathrm{ff}}{\dot{F}}_{\mathrm{i},\hskip0.48em \mathrm{ref}}\left[k\right]+{K}_{\mathrm{P}}\left({F}_{i,\mathrm{ref}}\left[k\right]-{F}_{i,\mathrm{esti}}\left[k\right]\right)+{K}_{\mathrm{I}}\Delta t\sum \limits_{j=0}^k\left({F}_{i,\mathrm{ref}}[\hskip0.3em j]-{F}_{i,\mathrm{esti}}[\hskip0.3em j]\right)\;\left(i=1,2\right). $$

5.1. Force-tracking experiments using force measurement type suit

To demonstrate the effectiveness of the proposed control method using the force measurement type suit in Figure 1(b), we conducted force-tracking experiments. In this experiment, we measured five healthy adult male subjects aged 21–38. The experiments in this study were reviewed and approved by the ethical review board of The University of Tokyo under Application No. UT-IST-RE-230809-2. Written informed consent was obtained from the subject, including its consent to participate and for the findings to be published. Table 1 shows the subjects’ arm parameters defined in Figure 2.

Table 1.

Subjects’ arm parameters

The instructor’s joint angle was set to a periodic flexion movement with a motion frequency of 0.25 Hz, a motion range of approximately 1.0 to 1.8 rad, and the subject was instructed to maintain a joint angle of about 0.8 rad. Note that the condition described above is a specific case. The subject will be instructed to follow the presented motions in the general motor learning experiment. Thanks to the above specific condition, the deviation between the target angle and the measured angle increases or decreases without changing its sign, allowing for a clear comparison and evaluation of the force-tracking performance of the proposed method and the standard feedback control method. The reason the subject consistently maintained its joint angle smaller than the target joint angle is that the prototype suit was capable of generating torque only in the elbow flexion direction.

We performed force-tracking control using two methods: (i) the proposed 2-DOF control method and (ii) a method utilizing only feedback. After gathering data for five cycles utilizing two distinct control methods, we calculated performance indices encompassing NRMSE and phase delay between the measured force ( $ {F}_{\mathrm{true}} $ ) and the reference force ( $ {F}_{\mathrm{ref}} $ ). The NRMSE [%] is represented by equation (5.1), and the phase delay [deg] is defined by the cross-correlation of the signals and is defined by equation (5.2).

(5.1) $$ \mathrm{NRMSE}=\frac{\sqrt{\frac{1}{N}{\sum}_{i=1}^N{\left({F}_{\mathrm{ref}}\left[i\right]-{F}_{\mathrm{true}}\left[i\right]\right)}^2}}{\max\;{F}_{\mathrm{ref}}}\ast 100, $$

(5.2) $$ \mathrm{delay}=\frac{\underset{k}{\mathrm{argmax}}{\sum}_{i=1}^N{F}_{\mathrm{true}}\left[i\right]\;{F}_{\mathrm{ref}}\left[i-k\right]}{f_{\mathrm{s}}T}\ast 360. $$

i is the index of the sample data, and $ N $ is a total data number for calculation. $ {f}_s $ is the sampling rate of 500 Hz. $ T $ is the motion cycle time of 4 s. In the experiments, the torque stiffness $ K $ was set to $ 2\mathrm{N}\cdot \mathrm{m}/\mathrm{rad} $ .

All subjects’ force NRMSE and phase delay calculated in (5.1) and (5.2) for both control methods are shown in Table 2. For example, Figure 13 presents the experimental results of subject 2 of the proposed 2-DOF control method and the feedback-only experiment for five cycles. The solid line shows the data of the proposed 2-DOF control, and the broken line shows the data of the conventional feedback control. We set $ {K}_{\mathrm{ff}} $ as 0 in the conventional feedback control. The upper figure represents the transition of the elbow joint angle, where the green line denotes the instructor’s angle serving as the reference, and the red line indicates the learner’s angle. The middle figure depicts the measured force ( $ {F}_{\mathrm{true}} $ ) with a blue line and the reference force ( $ {F}_{\mathrm{ref}} $ ) with an orange line. The bottom figure illustrates the internal pressure of the PAM. According to the error between the instructor’s and learner’s joint angles, the force reference value in the middle figure varies, leading to fluctuations in the pressure of the PAM by using each control method. The subject 2’s NRMSE was 4.4% for the proposed method and 8.2% for the feedback-only method. The subject2’s phase delay for both methods was 0.0 deg for the proposed method and 13.9 deg for the feedback-only method.

Table 2.

Force’s NRMSE and time delay of the proposed and conventional control

Figure 13.

Subject 2’s experimental results of the proposed 2-DOF control (solid line) and the conventional feedback control (broken line).

These results indicate a quantitative improvement in accuracy with the proposed approach. The introduction of the proposed method improved the responsiveness of the measured force $ {F}_{\mathrm{true}} $ to the rise of the force target $ {F}_{\mathrm{ref}} $ , leading to an enhancement in tracking accuracy.

In the experiment mentioned above, the focus was on evaluating the performance of force-tracking control. To ensure uniform experimental conditions, the subject was instructed not to move during the experiment; however, subjects generally will move their arms to mimic the instructor’s motion in an actual motor learning scene. Therefore, we evaluated the data collected while the subject tracked the instructor’s motion to verify whether the proposed method could achieve the desired control even when the subject moved. All subjects’ force NRMSE and phase delay using the proposed control method during tracking motion are shown in Table 3. For example, the subject 2’s measured data is presented in Figure 14. When the subject moved, the measured force fluctuated due to its motion, resulting in behavior different from that of the subject when stationary. For instance, during arm extension, where the elbow joint angle decreased, the PAM was pulled by the subject’s arm, causing the measured force to increase. Consequently, alternating pressure reduction due to PAM pressure control and pulling the PAM by the arm resulted in oscillatory behavior. The tracking error of the driving force, NRMSE, increased to 39.8% compared to when stationary. However, the measured force could still follow the general shape of the reference force, and the time delay was still low (delay = 3.4 deg). Therefore, we confirmed that even in situations where subjects move, it is possible to teach deviations in motion to the subjects through the proposed method.

Table 3.

Force’s NRMSE and time delay of the proposed control during the learner tracking the instructor’s motion

Figure 14.

Subject 2’s experimental result of the proposed 2-DOF control during the learner tracking the instructor’s motion.

5.2. Force-tracking experiments using force estimation type suit

An experiment was conducted to confirm that the novel motion teaching suit of force estimation type can achieve the desired control. Three subjects (Subjects 1 to 3 in Table 1) were fitted with this motion teaching suit and went through an exercise of elbow flexion, using a reference motion of 4 s cycles. The gain values of the PI controller and feedforward controller in the control method were set as follows:

(5.3) $$ {K}_{\mathrm{P}}=0.2\;\mathrm{V}/\mathrm{kPa},{K}_{\mathrm{I}}=0.003\;\mathrm{V}/\left(\mathrm{kPa}\cdot \mathrm{s}\right),{K}_{\mathrm{ff}}=0.005\;\left(\mathrm{V}\cdot \mathrm{s}\right)/\mathrm{kPa}. $$

The proportional constant $ K $ between the joint angle error and the target torque was set to $ 2\mathrm{N}\cdot \mathrm{m}/\mathrm{rad} $ . The canceling torque was set to $ \tau =0.05\mathrm{N}\cdot \mathrm{m} $ .

All subjects’ force NRMSE and phase delay between the estimated and reference values are shown in Table 4. For example, Figure 15 presents the subject 1’s experimental results of the joint angle transitions of the instructor and learner and the reference and estimated force of the driving PAM1 and PAM2. The Subject 1’s NRMSE was 14.7% and 14.0% for PAM1 and PAM2, respectively. The Subject 1’s phase delay was 1.8 deg and 0.0 deg for PAM1 and PAM2, respectively.

Table 4.

Force’s NRMSE and time delay of the proposed control with force estimation

Figure 15.

Experimental results of force control combined with force estimation: Joint angle trajectories of the teacher and learner, and reference and estimated force of the PAM1 and PAM2.

To compare the proposed system with a sensor-based system, we can compare the results of the force control experiment using a load cell (Table 3) and the force control experiment based on force estimation (Table 4). Both of these results achieved rough force tracking of the target value with a small time delay. As a result, the estimated driving force roughly tracked the reference force, and the intended force control was generally achieved.