Active Assistive Design and Multiaxis Self-Tuning Control of a Novel Lower Limb Rehabilitation Exoskeleton

: This paper presented the mechanical design and control of a lower limb rehabilitation exoskeleton named “the second lower limb rehabilitation exoskeleton (LLRE-II)”. The exoskeleton with a lightweight mechanism comprises a 16-cm stepless adjustable thigh and calf rod. The LLRE-II weighs less than 16 kg and has four degrees of freedom on each leg, including the waist, hip, knee, and ankle, which ensures ﬁtted wear and comfort. Motors and harmonic drives were installed on the joints of the hip and knee to operate the exoskeleton. Meanwhile, master and slave motor controllers were programmed using a Texas Instruments microcontroller (TMS320F28069) for the walking gait commands and evaluation boards (TMS320F28069/DRV8301) of the joints. A self-tuning multiaxis control system was developed, and the performance of the controller was investigated through experiments. The experimental results showed that the mechanical design and control system exhibit adequate performance. Trajectory tracking errors were eliminated, and the root mean square errors reduced from 6.45 to 1.22 and from 4.15 to 3.09 for the hip and knee, respectively.


Introduction
The mobility of the aging population is restricted owing to sarcopenia or physical disabilities. An exoskeleton is a wearable orthosis that provides human body assistance via integrated robotic mechanisms. Exoskeletons started being investigated many decades ago and have garnered significant interest owing to the current development of the aging society [1][2][3][4][5].
In the 1960s, the exoskeleton "Hardiman", which is powered by electrical motors and a master-slave control system, was the first exoskeleton to be developed by General Electric Company; however, it failed to operate as intended owing to its complex and heavy structure [6]. Recently, researchers at Tsukuba University developed a hybrid assistive limb (HAL) for patients with lower-limb illnesses. The HAL comprises posture and powerassist control and is powered by motors and a hybrid controller. Electromyography (EMG) sensors were installed on the HAL to capture foot reaction forces and detect the walking intention of the wearer [7]. Meanwhile, the Berkeley lower-extremity exoskeleton is an anthropomorphic model comprising seven degrees of freedom (DOFs) per leg, four of which are powered by linear hydraulic actuators. The exoskeleton enables the wearer to carry significant loads with minimal effort over different terrains. Furthermore, it allows various payloads to be mounted on a backpack-like frame [8,9].

1.
A mechanical design involving a stepless (continuous variable lengths) adjustable length was adopted in the novel exoskeleton. To ensure the fit and comfort of the wearer, the axes of rotation were designed on the waist and ankle joints. The entire LLRE-II system weighed 16 kg.

2.
A multiaxis (multiple motor control) system was established. Planar motors were installed at the hips and knees of the LLRE-II. Harmonic drives (HDs) were fixed using a connecting plate to the motors to enhance the torque of each joint. The motor drive strategy was based on field-oriented control, including Clarke and Park transformations. 3.
The performance of the control system was evaluated. The trajectory tracking of the exoskeleton hip joint and knee during movement was achieved via a designed self-tuning controller. The responses of the exoskeleton system were analyzed.
Machines 2022, 10, x FOR PEER REVIEW 3 of 22 a connecting plate to the motors to enhance the torque of each joint. The motor drive strategy was based on field-oriented control, including Clarke and Park transformations. 3. The performance of the control system was evaluated. The trajectory tracking of the exoskeleton hip joint and knee during movement was achieved via a designed selftuning controller. The responses of the exoskeleton system were analyzed.

DOF and Range of Motions
The design of the exoskeleton should be determined based on human motion because it is designed for human use. An analytical DOF method is clinical gait analysis, which is used to determine the joint motions of LLEs. In this study, gait patterns were obtained using infrared cameras and a motion capture system (Qualisys Oqus 100, Qualisys Oqus-CMOS, Qualisys AB, Göteborg, Sweden). The captured data were used for mechanical designand control systems. The lower leg of humans can be modeled with seven DOFs, including three DOFs at the waist and hip, one DOF at the knee, and three DOFs at the ankle based on anatomical planes.

Sagittal Plane
The motions of the sagittal plane, also known as the longitudinal plane, allow humans to move ahead. In one gait phase, the knee joint flexes, and the hip joint extends to support the body when the heel is in contact with the ground. This implies that the stance phase begins, and the ankle rocks with the leg rod to move the center of pressure from the heel to the hallux. When the toes are off the ground, the gait phase becomes the swing phase. At this moment, the hip joint flexes until the next heel is in contact with the ground, and the knee joint flexes to maintain the foot in the air.

DOF and Range of Motions
The design of the exoskeleton should be determined based on human motion because it is designed for human use. An analytical DOF method is clinical gait analysis, which is used to determine the joint motions of LLEs. In this study, gait patterns were obtained using infrared cameras and a motion capture system (Qualisys Oqus 100, Qualisys Oqus-CMOS, Qualisys AB, Göteborg, Sweden). The captured data were used for mechanical designand control systems. The lower leg of humans can be modeled with seven DOFs, including three DOFs at the waist and hip, one DOF at the knee, and three DOFs at the ankle based on anatomical planes.

Sagittal Plane
The motions of the sagittal plane, also known as the longitudinal plane, allow humans to move ahead. In one gait phase, the knee joint flexes, and the hip joint extends to support the body when the heel is in contact with the ground. This implies that the stance phase begins, and the ankle rocks with the leg rod to move the center of pressure from the heel to the hallux. When the toes are off the ground, the gait phase becomes the swing phase. At this moment, the hip joint flexes until the next heel is in contact with the ground, and the knee joint flexes to maintain the foot in the air.

Coronal Plane
The coronal plane (frontal plane) performs the basic function of balancing the human body. The center of gravity should be within the range of human body projection for a normal walking gait. In the lateral direction, the DOFs of the waist and hip rotate to maintain body balance.

Transverse Plane
Transverse plane motions are along the horizontal axis, which ensures body stability. The foot on the ground rotates around a foot pressure point to maintain the stance phase as another foot swings in the air during the walking cycle. Therefore, the rotation of the hip and ankle joints in the transverse plane ensures that the human walks in a straight line. Furthermore, exoskeletons designed for rehabilitation should restrict the DOFs resulting from unintended motions of wearers with functional limitations. Considering the actual assembly, the impact space of an exoskeleton joint cannot accommodate more than one motor. Therefore, only the required and essential DOFs are prioritized for rehabilitation exoskeletons. Although these restrictions reduce human comfort, the stability and safety of exoskeleton wearers must be ensured.

Mechanical Design and Simulation
The essential design standards for the LLRE-II are as follows.
(1) Simple and impactful design for ergonomics (2) Flexibility for wearers (3) Wearer safety (4) High strength and lightweight (5) Economical and easy component renewal We used SolidWorks software to sketch the preliminary design of the LLRE-II. In terms of ergonomics, the mechanism affords DOFs on the waist, and the mechanical design is symmetrical. The lengths of the leg rods can be adjusted up to 16 mm using stepless length adjustment mechanisms for different wearer heights. To ensure safety, the limits of the joint angles were specified using rotation stoppers to prevent the wearers from being injured. Straps were installed on the leg rods of the exoskeleton to be fixed on the wearer. Furthermore, components such as the leg rods and connectors of the exoskeleton exhibit the same geometry, rendering component renewal easy and economical. The final design of the LLRE-II is shown in Figure 2; it comprises the waist, hip, knee, leg, motor, and foot joints. A stress analysis simulation of the LLRE-II for yield strength and the close-up view of the areas with material tensions, as shown in Figure 3a,b, was performed based on some significant criteria to ensure that the exoskeleton worn by the participants satisfied the theory of failure during walking. The simulation parameters were as follows: (1) material: 6061 aluminum; (2) grid size: 3 mm; (3) nominal torque on the hip and knee joints: 1.21 Nm; (4) weight of wear: 100 kg; and (5) theory of failure: the von Mises yield criterion. The result of the simulation indicated that the critical stress at the leg rod was under the maximum stress and the exoskeleton met the safety criteria. The leg rods were hollowed to be assembled, lightweight, symmetrical for standardization, and easy to manufacture. The hip and knee joints were powered by motors. The components were fabricated using 6061 aluminum to achieve a lightweight but strong structure. The total weight of the LLRE-II, including the motors, was approximately 16 kg. Machines 2022, 10, x FOR PEER REVIEW 5 of 22

Waist Design
The waist of the LLRE-II primarily comprises back support, rotary adjustment mechanisms, and waist-hip connectors, as shown in Figure 4. The rotary angles of the back support can be adjusted based on the wearer and walking gait. This adaptive design can maintain the stability of the wearer when yaws occur or disturbances cause lateral external rotations. The back support was 374 mm long and 80 mm wide. The waist-hip connector linked to the hip motor plate was hollow.

Leg Rod, Motor Plate, and Foot Designs
The leg rod and motor plate design are shown in Figure 5. The lower and upper leg rods, motor plate, and other connections of the LLRE-II exhibit the same geometry, affording an economical design and ease of component renewal. As shown in Figure 6, the lengths of the upper and lower leg rods can be adjusted up to 8 mm using stepless length adjustment mechanisms to accommodate different wearer heights. The external and internal diameters of the hollowed-leg rod were 20 and 12 mm, respectively. The hollow-rod design can increase torsional strength and reduce material weight. No actuator was installed at the ankle of the LLRE-II. In fact, the ankle of the LLRE-II comprised a screw, nylon nut, and foot pad, which allowed it to be connected conveniently to the lower leg rod and swing freely.   The waist of the LLRE-II primarily comprises back support, rotary adjustment mechanisms, and waist-hip connectors, as shown in Figure 4. The rotary angles of the back support can be adjusted based on the wearer and walking gait. This adaptive design can maintain the stability of the wearer when yaws occur or disturbances cause lateral external rotations. The back support was 374 mm long and 80 mm wide. The waist-hip connector linked to the hip motor plate was hollow.

Leg Rod, Motor Plate, and Foot Designs
The leg rod and motor plate design are shown in Figure 5. The lower and upper leg rods, motor plate, and other connections of the LLRE-II exhibit the same geometry, affording an economical design and ease of component renewal. As shown in Figure 6, the lengths of the upper and lower leg rods can be adjusted up to 8 mm using stepless length adjustment mechanisms to accommodate different wearer heights. The external and internal diameters of the hollowed-leg rod were 20 and 12 mm, respectively. The hollowrod design can increase torsional strength and reduce material weight. No actuator was installed at the ankle of the LLRE-II. In fact, the ankle of the LLRE-II comprised a screw, nylon nut, and foot pad, which allowed it to be connected conveniently to the lower leg rod and swing freely.     The hip and knee joints were the motive sources with flat motors (EC 90 flat 400W, Maxon, Switzerland) and were designed to satisfy the required DOFs. The hip and knee joint designs are shown in Figures 7 and 8, respectively. The hip and knee joints are not only connected mechanisms but also coupled with motors and HDs. The motor plate comprises a symmetrical hollow cylinder; one side of the motor plate is embedded with the motor, while the other side is installed with an HD to smoothly uprate and transfer torques. We selected an HD with speed reduction ratios of 1:50 and 1:30 for the hip and knee joints, respectively. To ensure safety, we set the limits of the joint angles using rotation stoppers to prevent the wearers from being injured.

Hip Joint and Knee Joint Designs
The hip and knee joints were the motive sources with flat motors (EC 90 flat 400W, Maxon, Switzerland) and were designed to satisfy the required DOFs. The hip and knee joint designs are shown in Figures 7 and 8, respectively. The hip and knee joints are not only connected mechanisms but also coupled with motors and HDs. The motor plate comprises a symmetrical hollow cylinder; one side of the motor plate is embedded with the motor, while the other side is installed with an HD to smoothly uprate and transfer torques. We selected an HD with speed reduction ratios of 1:50 and 1:30 for the hip and knee joints, respectively. To ensure safety, we set the limits of the joint angles using rotation stoppers to prevent the wearers from being injured.  The LLRE-II, which is based on a 16-cm stepless length-adjustment mechanism, is designed for humans with heights between 1.64 and 1.80 m. The joint angle ranges of the LLRE-II should be sufficiently large to allow the wearers to completely move their lower limbs. In addition, the LLRE-II joints should limit the wearer from performing unexpected movements to prevent them from moving beyond the range of their joints. Otherwise, the wearer may be injured. The angle range for walking, angle range of humans, and joint angle range of the LLRE-II wearer are listed in Table 1; to achieve comfortable walking, the hip and knee angles of the LLRE-II should be greater than the values shown in the first column (human joint angles when walking) and smaller than those shown in the second column (the angle range of humans) [4,5]. The legs of the LLRE-II are similar to those of human lower limbs in terms of their kinematics and motions.

Hip Joint and Knee Joint Designs
The hip and knee joints were the motive sources with flat motors (EC 90 flat 400W, Maxon, Switzerland) and were designed to satisfy the required DOFs. The hip and knee joint designs are shown in Figures 7 and 8, respectively. The hip and knee joints are not only connected mechanisms but also coupled with motors and HDs. The motor plate comprises a symmetrical hollow cylinder; one side of the motor plate is embedded with the motor, while the other side is installed with an HD to smoothly uprate and transfer torques. We selected an HD with speed reduction ratios of 1:50 and 1:30 for the hip and knee joints, respectively. To ensure safety, we set the limits of the joint angles using rotation stoppers to prevent the wearers from being injured.  The LLRE-II, which is based on a 16-cm stepless length-adjustment mechanism, is designed for humans with heights between 1.64 and 1.80 m. The joint angle ranges of the LLRE-II should be sufficiently large to allow the wearers to completely move their lower limbs. In addition, the LLRE-II joints should limit the wearer from performing unexpected movements to prevent them from moving beyond the range of their joints. Otherwise, the wearer may be injured. The angle range for walking, angle range of humans, and joint angle range of the LLRE-II wearer are listed in Table 1; to achieve comfortable walking, the hip and knee angles of the LLRE-II should be greater than the values shown in the first column (human joint angles when walking) and smaller than those shown in the second column (the angle range of humans) [4,5]. The legs of the LLRE-II are similar to those of human lower limbs in terms of their kinematics and motions. The LLRE-II, which is based on a 16-cm stepless length-adjustment mechanism, is designed for humans with heights between 1.64 and 1.80 m. The joint angle ranges of the LLRE-II should be sufficiently large to allow the wearers to completely move their lower limbs. In addition, the LLRE-II joints should limit the wearer from performing unexpected movements to prevent them from moving beyond the range of their joints. Otherwise, the wearer may be injured. The angle range for walking, angle range of humans, and joint angle range of the LLRE-II wearer are listed in Table 1; to achieve comfortable walking, the hip and knee angles of the LLRE-II should be greater than the values shown in the first column (human joint angles when walking) and smaller than those shown in the second column (the angle range of humans) [4,5]. The legs of the LLRE-II are similar to those of human lower limbs in terms of their kinematics and motions. The master and slave motor-driven system of the LLRE-II is shown in Figure 9. An embedded microcontroller from TI (TMS320F28069) was used as the master controller, and four TI evaluation boards (TMS320F28069/DRV8301) were used as the slave motor controllers. The master controller provided gait commands to accomplish gait patterns. For improved efficiency, the master controller processed the gait commands only, i.e., it did not perform any other complex calculations, such as tracking errors. By contrast, complex algorithms for feedback control and tracking errors were calculated by the four slave motor controllers. The controller area network bus protocol was used to deliver commands to the slave motor controllers. The obtained gait patterns of comfortable and normal walking gait were used for the gait commands. Thus, the hip and knee joint angles during gait were obtained. These joint angles were used as position commands to control the hip and knee. Additionally, although the healthy gait phases were captured and stored in the master controller, other specific or abnormal gaits were able to be captured and installed in the master controller for unique rehabilitations. The control performance of the position loop is important in LLRE-II controllers. In this study, position control was used to control the motion and trajectory of the LLRE-II. The developed control strategy was applied to the slave controllers for further control applications. The motors on the hips and knees of the LLRE-II were controlled to perform a normal walking gait. The experimental results verified the proposed system design. A block diagram of the developed motor-driven system of the LLRE-II, including the controllers, Park and Clarke transformations, space vector pulse width modulation (SVPWM), three-phase inverter, and motor, is shown in Figure 10. Here, I * q and I * d are the q-and d-axis current commands, respectively; I q and I d are the q-and d-axis currents, respectively; V q and V d are the q-and d-axis voltages, respectively; I α and I β are the αand β-axis currents, respectively; V α and V β are the αand β-axis voltages, respectively; I u , I v , and I w and V u , V u , and V w are the three-phase currents and voltages of the motor, respectively.

Control System Design
A robust and adaptive control system for the exoskeleton allows the latter to be adapted to various walking conditions. The proposed control method includes bandwidth selection and controller gain self-tuning. The parameter tuning method used in this study allows the gain of the controller to be adjusted directly using the current signals of the motor. This results in a simple method that allows the system to provide a fast response and converge to a stable state.

Control System Design
A robust and adaptive control system for the exoskeleton allows the latter to be adapted to various walking conditions. The proposed control method includes bandwidth selection and controller gain self-tuning. The parameter tuning method used in this study allows the gain of the controller to be adjusted directly using the current signals of the motor. This results in a simple method that allows the system to provide a fast response and converge to a stable state.
First, the most critical aspect is bandwidth selection. In a motor control system, both Clarke and Park transformations are used to transform operations that convert a threephase current configuration to the de-referenced direct (D) and quadrature (Q) reference

Control System Design
A robust and adaptive control system for the exoskeleton allows the latter to be adapted to various walking conditions. The proposed control method includes bandwidth selection and controller gain self-tuning. The parameter tuning method used in this study allows the gain of the controller to be adjusted directly using the current signals of the motor. This results in a simple method that allows the system to provide a fast response and converge to a stable state.
First, the most critical aspect is bandwidth selection. In a motor control system, both Clarke and Park transformations are used to transform operations that convert a threephase current configuration to the de-referenced direct (D) and quadrature (Q) reference First, the most critical aspect is bandwidth selection. In a motor control system, both Clarke and Park transformations are used to transform operations that convert a threephase current configuration to the de-referenced direct (D) and quadrature (Q) reference frames as currents i d and i q , respectively. The currents of the motor are captured and returned for bandwidth selection. The slope of the current variations (m c ) reflects the stability of the motor drive system, as shown in Equation (1).
The system bandwidth increases with the proportional gain of the controllers and can improve the relative stability and steady-state error. Although an increase in the proportional gain reduces the steady-state error, it affects the relative stability. Therefore, we considered the stability of the controller gain in the motor drive system (s c ), as shown in Equation (2).
After m c and s c are calculated, the mean values of (m c ) and (∆m c ), i.e., Mm c and Ms c , respectively, are calculated using Equations (3) and (4), respectively. Instead of conventional fixed-window methods, the sliding window method was used in this study as it can perform a faster calculation for Ms c .
As shown in Figure 11a, if Mm c is greater than the maximum mean value of m c , then the controller gain should increase. This step determines whether the system bandwidth increases. As shown in Figure 11b, we classified Ms c into unstable, stable, and critical areas using the lower and upper boundaries. When Ms c is between the lower and upper boundaries, it is stable. If Ms c decreases from the stable area, then the system is unstable. Hence, the controller gain should decrease to allow the system to return to the stable area. However, if Ms c is greater than the upper boundary, then the system is in the critical area, and the gain will increase.
The system bandwidth increases with the proportional gain of the controllers and can improve the relative stability and steady-state error. Although an increase in the proportional gain reduces the steady-state error, it affects the relative stability. Therefore, we considered the stability of the controller gain in the motor drive system ( ), as shown in Equation (2).
After and are calculated, the mean values of (mc) and (Δmc), i.e., and , respectively, are calculated using Equations (3) and (4), respectively. Instead of conventional fixed-window methods, the sliding window method was used in this study as it can perform a faster calculation for .
As shown in Figure 11a, if is greater than the maximum mean value of mc, then the controller gain should increase. This step determines whether the system bandwidth increases. As shown in Figure 11b, we classified into unstable, stable, and critical areas using the lower and upper boundaries. When is between the lower and upper boundaries, it is stable. If decreases from the stable area, then the system is unstable. Hence, the controller gain should decrease to allow the system to return to the stable area. However, if is greater than the upper boundary, then the system is in the critical area, and the gain will increase.
(a) (b) Figure 11. Relationship between (a) and gain and (b) and gain. Figure 11. Relationship between (a) Mm c and gain and (b) Ms c and gain.
Using these criteria, the controller gains can be easily obtained and the system optimized using the feedback values of currents. A flowchart of the proposed strategy is presented in Figure 12. Using these criteria, the controller gains can be easily obtained and the system optimized using the feedback values of currents. A flowchart of the proposed strategy is presented in Figure 12. Second, controller gain self-tuning was developed. We propose a self-tuning method to adjust the control gains of the motor control system, including the current, speed, and position loops. The architecture of the control system of the LLRE-II is shown schematically in Figure 13, where * , * , and * are the position, voltage, and current commands, respectively, and , , and are the position, voltage, and current feedback values, respectively.  Second, controller gain self-tuning was developed. We propose a self-tuning method to adjust the control gains of the motor control system, including the current, speed, and position loops. The architecture of the control system of the LLRE-II is shown schematically in Figure 13, where θ*, ω*, and i* are the position, voltage, and current commands, respectively, and θ, ω, and i are the position, voltage, and current feedback values, respectively. Using these criteria, the controller gains can be easily obtained and the system optimized using the feedback values of currents. A flowchart of the proposed strategy is presented in Figure 12. Second, controller gain self-tuning was developed. We propose a self-tuning method to adjust the control gains of the motor control system, including the current, speed, and position loops. The architecture of the control system of the LLRE-II is shown schematically in Figure 13, where * , * , and * are the position, voltage, and current commands, respectively, and , , and are the position, voltage, and current feedback values, respectively.   (5). It primarily comprises a PI controller and a motor electrical model.
where k pc and T ic are the PI controller gain and time constant, respectively; T Σ is the delay time; I* and I are the command and feedback of the current, respectively; and L m and R m are the inductance and resistance of the motor, respectively. The open-loop transfer function can be rewritten based on pole-zero elimination, as shown in Equation (6).
where w c is the searched bandwidth gain. Subsequently, k pc is expressed as The phase margin of the current loop (PM c ) is derived using Equation (8).
Hence, the relationship between the phase margin and controller parameters is obtained. Once the optimal bandwidth of the current controller is selected using the proposed method, the controller gains are adjusted automatically. Based on Equation (8), the current loop is regarded as stable when PM c is between 30 • and 60 • . Typically, phase margins between 30 • and 60 • result in reasonable tradeoffs between the bandwidth and stability.
Next, the speed control loop is modeled, and the open-loop transfer function is represented by Equation (9). The speed loop comprises a PI controller and a motor mechanical model. All the dead and delay times of the speed control loop (T Σs ) are merged into a single delay time. The controller gain (k ps ) is expressed as shown in Equation (10).
where J and B are the inertia and friction coefficient of the system, respectively. The phase margin of the speed loop (PM s ) is derived using Equation (11).
where w s is defined as 1/(w c k r ), and k r is the ratio of k ps to k pc . The position closed-loop transfer function is derived, and the position control gain is determined using Equations (12) and (13).
Hence, the system is evaluated using the bandwidth selection and controller gain self-tuning methods. After the system bandwidth is obtained, the system stability is verified based on the phase margins of the current and speed loops. The controller gains are calculated synchronously when the phase margins are not between 30 • and 60 • . In summary, the proposed self-tuning method yields faster responses and better tracking errors compared with other methods.

Test of the Exoskeleton Worn by the Participant
The DOFs of the LLE were designed to model those of the lower extremity of humans. Based on the design concept, the hip and knee joints of the LLRE-II are driven by motors with safety limits in the sagittal plane for the requirement of walking. In the coronal plane, motion is required to maintain balance. The walking direction and comfort of the wearer are considered for the waist, hip, and knee joints. Meanwhile, the rotations of the ankle joints are restricted.
The exoskeleton was manufactured via computerized numerical control machining to achieve improved machining accuracy. Aluminum 6061 was used as the material for the components owing to its high fatigue strength and machinability. The structure of the exoskeleton was designed to achieve easy disassembly, fast component replacement, and cost reduction. The LLRE-II was developed to support the walking motion of individuals, as shown in Figure 14. The limb rods were hollow and adjustable for various heights of the wearer, as shown in Figure 15. A front view of the waist of the LLRE-II is shown in Figure 16, where the two axes of rotation allow the wearer to be fitted well and comfortably. The exoskeleton was evaluated while being worn by a walking participant, as shown in Figure 17. The height and weight of the wearer were 173 cm and 65 kg, respectively. Straps were installed on the thighs and calves of the exoskeleton to be fixed on the wearer. The wearer was able to adjust the length of the LLRE-II before walking. For the preliminary test, walking data without the exoskeleton were obtained using infrared cameras and a motioncapture system. Those data can be used to establish the basic concept for determining the rotation angles of the LLRE-II joints, motor output power, and corresponding control strategy. The gait data for normal walking motion are shown in Figure 18. calculated synchronously when the phase margins are not between 30° and 60°. In summary, the proposed self-tuning method yields faster responses and better tracking errors compared with other methods.

Test of the Exoskeleton Worn by the Participant
The DOFs of the LLE were designed to model those of the lower extremity of humans. Based on the design concept, the hip and knee joints of the LLRE-II are driven by motors with safety limits in the sagittal plane for the requirement of walking. In the coronal plane, motion is required to maintain balance. The walking direction and comfort of the wearer are considered for the waist, hip, and knee joints. Meanwhile, the rotations of the ankle joints are restricted.
The exoskeleton was manufactured via computerized numerical control machining to achieve improved machining accuracy. Aluminum 6061 was used as the material for the components owing to its high fatigue strength and machinability. The structure of the exoskeleton was designed to achieve easy disassembly, fast component replacement, and cost reduction. The LLRE-II was developed to support the walking motion of individuals, as shown in Figure 14. The limb rods were hollow and adjustable for various heights of the wearer, as shown in Figure 15. A front view of the waist of the LLRE-II is shown in Figure 16, where the two axes of rotation allow the wearer to be fitted well and comfortably. The exoskeleton was evaluated while being worn by a walking participant, as shown in Figure 17. The height and weight of the wearer were 173 cm and 65 kg, respectively. Straps were installed on the thighs and calves of the exoskeleton to be fixed on the wearer. The wearer was able to adjust the length of the LLRE-II before walking. For the preliminary test, walking data without the exoskeleton were obtained using infrared cameras and a motion-capture system. Those data can be used to establish the basic concept for determining the rotation angles of the LLRE-II joints, motor output power, and corresponding control strategy. The gait data for normal walking motion are shown in Figure 18.        Figure 19a,b show the tracking performances of a conventional PI controller for the gait of the hip and knee motors. The phase margins of the current and speed loops were set at 45°, and the gaits were evaluated. The results showed that the response of the hip was relatively good, and the average tracking error was approximately 1.37°, as shown in Figure 20a. However, the response of the knee was unsatisfactory as compared with that of the hip, and the average tracking error was 3.14°, as shown in Figure 20b.   Figure 19a,b show the tracking performances of a conventional PI controller for the gait of the hip and knee motors. The phase margins of the current and speed loops were set at 45°, and the gaits were evaluated. The results showed that the response of the hip was relatively good, and the average tracking error was approximately 1.37°, as shown in Figure 20a. However, the response of the knee was unsatisfactory as compared with that of the hip, and the average tracking error was 3.14°, as shown in Figure 20b.  Figure 19a,b show the tracking performances of a conventional PI controller for the gait of the hip and knee motors. The phase margins of the current and speed loops were set at 45 • , and the gaits were evaluated. The results showed that the response of the hip was relatively good, and the average tracking error was approximately 1.37 • , as shown in Figure 20a. However, the response of the knee was unsatisfactory as compared with that of the hip, and the average tracking error was 3.14 • , as shown in Figure 20b.

Self-Tuning Controller
The proposed self-tuning method can synchronously adjust the controller gains based on the system conditions. In addition, the stability of the system can be ensured via the phase-margin design of the system. Figure 21a,b and Figure 22a,b show the results of hip and knee responses obtained by modulating the gains of the control loops using the proposed self-tuning control strategy, respectively, where the controller gains are obtained from 7 to 20 for the hip responses and from 3 to 14 for the knee responses. The responses and stability of the system improved, and the average tracking errors were 0.96 • and 2.35 • for the hip and knee, respectively, as shown in Figure 23a,b, respectively. This is because the variations in the controller gains were adjusted based on the slopes of the system currents.
Because the boundaries of the controller gains can be appropriately controlled by the phase margins, system instability was avoided.

Self-Tuning Controller
The proposed self-tuning method can synchronously adjust the controller gains based on the system conditions. In addition, the stability of the system can be ensured via the phase-margin design of the system. Figures 21a,b and 22a,b show the results of hip and knee responses obtained by modulating the gains of the control loops using the proposed self-tuning control strategy, respectively, where the controller gains are obtained from 7 to 20 for the hip responses and from 3 to 14 for the knee responses. The responses and stability of the system improved, and the average tracking errors were 0.96° and 2.35° for the hip and knee, respectively, as shown in Figure 23a,b, respectively. This is because the variations in the controller gains were adjusted based on the slopes of the system currents. Because the boundaries of the controller gains can be appropriately controlled by the phase margins, system instability was avoided.

Self-Tuning Controller
The proposed self-tuning method can synchronously adjust the controller gains based on the system conditions. In addition, the stability of the system can be ensured via the phase-margin design of the system. Figures 21a,b and 22a,b show the results of hip and knee responses obtained by modulating the gains of the control loops using the proposed self-tuning control strategy, respectively, where the controller gains are obtained from 7 to 20 for the hip responses and from 3 to 14 for the knee responses. The responses and stability of the system improved, and the average tracking errors were 0.96° and 2.35° for the hip and knee, respectively, as shown in Figure 23a,b, respectively. This is because the variations in the controller gains were adjusted based on the slopes of the system currents. Because the boundaries of the controller gains can be appropriately controlled by the phase margins, system instability was avoided.

Discussion and Related Studies
To compare the performances of the abovementioned methods, the root mean square error (RMSE) was defined to analyze the experimental results as follows: where e(n) is the tracking error, and N r is the tracking error size. Figure 24 shows the RMSE results for the conventional and self-tuning controllers, where the self-tuning controller indicates lower RMSEs, i.e., 1.22 and 3.09 for the hip and knee, respectively. In general, the RMSE reduced from 6.45 to 1.22 for the hip joint and from 4.15 to 3.09 for the knee joint.
where is the tracking error, and is the tracking error size. Figure 24 shows the RMSE results for the conventional and self-tuning controllers, where the self-tuning controller indicates lower RMSEs, i.e., 1.22 and 3.09 for the hip and knee, respectively. In general, the RMSE reduced from 6.45 to 1.22 for the hip joint and from 4.15 to 3.09 for the knee joint. Challenges pertaining to the development of the exoskeleton system have been reported in previous studies. One of the challenges is the development of the exoskeleton mechanism and control algorithm for addressing human-machine movements and facilitating rehabilitation. Another challenge is the optimization of the exoskeleton system to enable its adaptation to different individuals and tasks. In this study, a novel mechanism for an LLE with a lightweight but strong structure was developed. The hip and knee joints are powered by motors and HDs, respectively. Furthermore, a self-tuning controller was developed to optimize the control structure. The experimental results showed improved system performance. Table 2 presents the differences between a few relevant previous studies and our study. In future, the exoskeleton will remain indispensable in the rehabilitation field for aiding people with disabilities. Exoskeleton systems with high efficiency and flexibility are expected to be manufactured at a large scale prior to their deployment to users in daily life. Challenges pertaining to the development of the exoskeleton system have been reported in previous studies. One of the challenges is the development of the exoskeleton mechanism and control algorithm for addressing human-machine movements and facilitating rehabilitation. Another challenge is the optimization of the exoskeleton system to enable its adaptation to different individuals and tasks. In this study, a novel mechanism for an LLE with a lightweight but strong structure was developed. The hip and knee joints are powered by motors and HDs, respectively. Furthermore, a self-tuning controller was developed to optimize the control structure. The experimental results showed improved system performance. Table 2 presents the differences between a few relevant previous studies and our study. In future, the exoskeleton will remain indispensable in the rehabilitation field for aiding people with disabilities. Exoskeleton systems with high efficiency and flexibility are expected to be manufactured at a large scale prior to their deployment to users in daily life.

Conclusions
A lower-limb rehabilitation exoskeleton named LLRE-II was developed to assist people with walking disabilities. The mechanical design of the LLRE-II allowed the length to be adjusted to fit wearers of different heights. A lightweight but strong structure was designed using a hollow rod fabricated using aluminum 6061 material with high strength and ductility. The total weight of the LLRE-II, including the motors, was 16 kg. The design of the LLRE-II was based on the DOFs of human lower legs. Therefore, four DOFs for one leg were considered for the rehabilitation exoskeletons. In addition to joint movements at the hip and knee joints, the two axes of rotation at the waist allowed the wearer to be fitted well and comfortably. Computer-aided designs and simulations were performed to satisfy these requirements. The LLRE-II was manufactured using computerized numerical control machining to ensure adequate machining accuracy. Furthermore, the LLRE-II was integrated with a multiaxis motor control system. The joints of the hip and knee were operated by motors and HDs, respectively. A TI microcontroller was used as the master controller, and four TI evaluation boards were used as the slave motor controllers. The conventional controller design and self-tuning controller were compared in the gait experiment of the LLRE-II. The self-tuning controller yielded better responses and eliminated oscillations. The RMSE of the hip decreased significantly by 81% (from 6.45 to 1.22). The performance of the LLRE-II was evaluated, and the experimental results showed that the designed controllers and mechanical design exhibited satisfactory performance in terms of motion control. The LLRE-II developed based on a master-slave controller strategy demonstrated potential for further applications, such as for training muscles and assisting injury recovery.

Conflicts of Interest:
The authors declare no conflict of interest.