Design and Control of a Reconfigurable Upper Limb Rehabilitation Exoskeleton with Soft Modular Joints

Upper limb rehabilitation robot can effectively help patients recover motor ability. Existing rehabilitation robots are usually driven by rigid motors and the mechanical structures cannot adapt to the different patients with the different physical parameters and different rehabilitation needs. This paper designs a reconfigurable upper limb rehabilitation exoskeleton for elbow and wrist joints driven by pneumatic muscle actuators (PMAs). The exoskeleton can assist patients to achieve elbow flexion/extension, wrist flexion/ extension and adduction/abduction by integrating soft elbow and wrist joint modules which can work separately or together. The wrist joint can realize two degrees of freedom (2-DoF) movement via adjustable modules. To conquer the dynamic model errors and load disturbances when reconstructing the modular joints, a non-singular fast terminal sliding mode control method based on nonlinear disturbance observer (NFTSMC-NDO) is proposed, and a position/force hierarchical control method is formed to ensure the controllability of the soft modular robot. Experimental results show that the proposed method can achieve high-precision motion control of soft modular joints and provide reconfigurable assistance for patients, improving the adaptability and compliance of rehabilitation training.

the compliance and the adaptability for rehabilitation.
Reasonable mechanism design can ensure the safety and comfort of patients, and appropriate control algorithm can provide accurate trajectory tracking and seamless human-robot interaction [13,14]. To address the nonlinear control challenges for exoskeleton, Zhu et al. [13] proposed a nonlinear iterative learning control algorithm by introducing nonlinear saturation functions to tackle the uncertainties in motion control. Fellag et al. [16] used sliding mode control to achieve accurate position control of a 5-DOF upper limb exoskeleton. The non-singular terminal sliding mode technique adopted by Madani et al. [17] can achieve convergence in finite time and avoid singularity. PMAs have strong coupling, nonlinearity, and time-varying characteristics, leading to difficult control. For rehabilitation robots driven by PMAs, Chang et al. [18] adopted an adaptive self-organizing fuzzy sliding mode controller to the 2-DOF upper limb rehabilitation robots, which obtained good tracking performance. Zhang et al. [19] proposed an adaptive trajectory tracking control strategy with spatial force distribution, which contains position feedback in task space and force feedback in joint space to ensure the safety of soft robot control.
The dynamic complexity of reconfigurable exoskeleton is highly related to its mechanical structure and external interference. Reconfigurable modular design and the difference of patients with the different physical parameters will increase the uncertainty of dynamic model parameters. Wu et al. [20] proposed a fuzzy adaptive controller based on radial basis function on the 7-DOF upper limb rehabilitation exoskeleton to ensure the tracking accuracy under parameter uncertainty and environmental disturbance. The composite control strategy using disturbance observers combined with nonlinear methods can resist disturbance. For multi-input and multi-output systems with unknown external disturbances and uncertainties, Wu et al. [21] combined the interference observer and the TSM scheme to form a hybrid controller with strong anti-interference and anti-uncertainty capabilities. Wei et al. [22] combined the advantages of disturbance observers and backstepping method to tackle unknown disturbances and model uncertainties.
To address the problem of insufficient compliance and adaptability, this paper will combine soft actuators and reconfigurable modular design to provide patients with comfortable and safe rehabilitation training. Aiming at the load disturbance caused by the difference of patients with different physical parameters and the nonlinear characteristics of PMAs, a non-singular fast terminal sliding mode control method based on nonlinear disturbance observer (NFTSMC-NDO) is proposed. The improved control method can not only achieve accurate motion control, but also ensure to provide appropriate assistance torque to make the rehabilitation training more comfortable and effective. The main contributions of this work include: 1) A novel reconfigurable modular exoskeleton with the modules for elbow and wrist joints is designed and implemented for upper limb rehabilitation to enhance the adaptability and compliance of rehabilitation training. 2) To conquer the dynamic model errors and load disturbances when reconstructing the modular joints, and a non-singular terminal sliding mode control method based on nonlinear disturbance observer is proposed to reduce tracking error. 3) A force/ position hierarchical control method is proposed for the reconfigurable modular exoskeleton driven by PMAs based on NFTSMC-NDO to further improve the safety and compliance of human-robot inter action.
The rest of this paper is organized as follows. Section II describes the reconfigurable modular design of upper limb exoskeleton driven by PMAs, followed by the force/position hierarchical control method for the reconfigurable modular exoskeleton in Section III. Experimental results analysis of elbow and wrist joint modules is presented in Section IV, and the discussion and conclusion are drawn in Section V.

A. PMAs-Driven Soft Modular Joints
PMAs possess the characteristics of light weight and high compliance, but it can only generate pulling forces. To realize rotational motions, existing structures of antagonistic muscle pairs are shown in Figure 1. Compared with the other two structures, the pulley structure is easier to establish and can provide large joint torque, which is mostly adopted for the elbow and wrist modules of the upper limb exoskeleton. The normal motion range of elbow (ROM) and wrist joints is shown in Table I, as the reference standard for exoskeleton design. The zero-degree position of the elbow is defined that the upper arm droops naturally, and the forearm is 90 ° to the upper arm and parallel to the horizontal plane. The flexion of elbow joint is defined as negative and the extension of elbow joint is positive. Similarly, the zero-degree position of the wrist is defined that the palm faces down and the palm is in a straight line with the forearm. Then the flexion of wrist joint is defined as negative and the extension of wrist joint is positive, and the adduction of wrist joint is defined as negative and the abduction of wrist joint is defined as positive.
The modules for elbow and wrist joints are shown in Figure 2 and Figure 3, which mainly include the antagonistic PMAs, the support plate for PMAs, the joint pulley, the angle sensor and the force sensor. Modular designs enable personalized configuration to meet different rehabilitation requirements. When the forearm connecting rod is installed on the support plate of the modules for wrist joints, cooperative rehabilitation training of elbow and wrist joint can be realized, which mainly applies to the early-stage of rehabilitation. The protective gear can be separately installed on the upper arm or forearm connecting rod to fix the equipment, and the modules for elbow and wrist joints can be used independently for late-stage rehabilitation. During ADL training exercises, there is almost no inversion/eversion movement of the wrist joint, and the inversion and eversion of the palm occur in the radioulnar joint. Combined with the actual needs, only the most practical two degrees of freedom are designed for the wrist joint module of exoskeleton. The module for wrist joint has two degrees of freedom, of which module 1 is designed for flexion/extension, and module 2 for adduction/abduction. The conversion of the modules for wrist joint can change the degree of freedom.

B. Reconfigurable Modular Design
A reconfigurable upper limb rehabilitation exoskeleton with the soft modules for elbow and wrist joints is shown in Figure 4. The reconfigurable exoskeleton includes the modules for elbow and wrist joints, the module for joint connection, and the protective gear parts. The modules for elbow and wrist joints adopt antagonistic pneumatic muscle pairs combined with pulley structure to realize upper limb rehabilitation. The reconfigurable mechanism can improve utilization and compliance of the exoskeleton. The detachable and attachable design of the module for joint connection can not only realize compound training for patients with elbow-wrist dysfunction, but also provide separate training for elbow or wrist joint, and the conversion of wrist module can realize the mutual change from flexion/extension to adduction/adduction. According to patient's physical parameters, the 3D printed lightweight protective gear is customized to fit the upper limb and reduce the weight of the exoskeleton. The installation of protective gear can be adjusted according to patient needs. The designed reconfigurable exoskeleton adopts soft PMAs as the actuator to improve the compliance and safety of the device. The angle and force sensors can collect real-time motion data of patients and provide a hardware basis for the safe control of exoskeletons. The modules for elbow and wrist joints are connected in a detachable manner, which is convenient for disassembly and assembly, increasing the practicality and compliance of the device. The reconfigurable upper limb rehabilitation exoskeleton is shown in Figure 5, in which the customized 3D printed protective gear can fit the upper limb well, and the total weight of the exoskeleton is less than 2kg. The left figure shows the coordinated movement of elbow and wrist joint when the forearm connecting rod of the elbow joint is fixedly attached to the wrist module, and the right figures show the modules for elbow and wrist joints used separately. During control, the shoulder joint and elbow-wrist joint define an initial position, and the initial position is also shown in Figure 5. Each training starts at the initial position, and the shoulder posture has little effect on the actual control. If the structural parameters of the exoskeleton cannot be adjusted, it only suits a small number of patients. To make the reconfigurable exoskeleton suitable for different patients with different physical parameters and different rehabilitation needs, the modules for elbow and wrist joints are designed adjustable: upper arm length: 250-350 mm (adjustable range: 100 mm), forearm length: 180-300 mm (adjustable range: 120 mm), wrist to handle (handle in the front of palm): 120-160 mm (adjustable range: 40 mm). Based on the above data, the parameters of the adopted PMAs and pulley are illustrated in Table II. To verify the reconfigurable modular exoskeleton's ability to help patients complete elbow flexion/extension, wrist flexion/ extension, and wrist adduction/abduction. The simulation experiment with the kinematic model is conducted to test the ROM of the reconfigurable upper limb exoskeleton. The ROM results are shown in Figure 6. Compare the normal ROM in Table I, the ROM of the reconfigurable modular exoskeleton can meet the rehabilitation needs for elbow and wrist joints when the modules for elbow and wrist joints work separately. When the modules for elbow and wrist joints is reconstructed, i.e., both modules work together, the ROM of the elbow joint is slightly reduced due to the increased load of the elbow joint and the limit of the maximum input pressure of the PMAs. However, it still meets the most rehabilitation needs of elbow joint, and the ROM of the wrist joint remains unchanged.

A. The Design of Nonlinear Disturbance Observer
The premise of effective application of the upper limb rehabilitation exoskeleton is to realize its safe and stable motion control. On the one hand, the change of parameters such as center of gravity after exoskeleton wearing will lead to measurement error. On the other hand, different patients with various physical parameters and load disturbance will bring errors to the dynamics model. To tackle the control challenges for reconfigurable structure and the nonlinear disturbance during upper limb coordinated movement, a non-singular fast terminal sliding mode control method based on nonlinear disturbance observer (NFTSMC-NDO) is proposed to estimate and compensate the nonlinear disturbance.
where ̇ ̈ represents the joint angle, angular velocity and angular acceleration vector; is joint torque; ( ) is the positive definite symmetric inertia matrix; ( ̇) is the centrifugal force and Coriolis force matrix; ( ) is the n-dimensional gravity item; is forearm and palm mass; is forearm and palm length; is moment of inertia; is distance from center of gravity to joint center.
Considering the disturbance factors, the system dynamics is: ( ) ( ̇) ( ) is the nominal matrix of the model, and ( ) ( ̇) ( ) is the uncertain matrix of the model caused by load disturbance. Eq. (6) can be rewritten as: where ( ) ̈ ( ̇) ̇ ( ) is the load disturbance.
The nonlinear disturbance observer modifies the estimation result of the observer by the difference between the actual disturbance and the estimated disturbance.

B. Non-Singular Fast Terminal Sliding Mode Control
Terminal sliding mode control methods introduce nonlinear functions into the sliding mode surfaces. To solve the singularity problem, the sliding mode surface needs to be further improved. A non-singular terminal sliding mode control method was proposed in [23], where a non-singular fast terminal sliding mode surface is designed to improve the convergence: , and the representation of ( ̇) is similar to that of ( ) .
According to the designed sliding mode surface and the dynamic models of the system, a non-singular fast terminal sliding mode control method based on nonlinear disturbance observer is proposed to estimate and compensate the nonlinear disturbance. Combined with non-singular fast terminal sliding mode control (NFTSMC) and the disturbance observer, the final control law can be obtained as: ) , are constants greater than 0; ( ) , . The robot joint output torque includes the disturbance estimator ̂, the value of which observed by the designed disturbance observer. The stability of the proposed NFTSMC needs to be analysed, and the Lyapunov function is designed as: The disturbance observer converges exponentially and the error converges to zero.
. The sliding mode surface of the system can reach in a finite time, and the trajectory tracking error converges to zero in a finite time along the sliding mode surface.

C. Force Control of Soft Modular Joints
PMAs can only generate tension force rather than thrust, and antagonistic PMAs adopt the pulley structure. The relationship between the joint output torque of exoskeleton and the output force of antagonistic PMAs is as follows: where is the radius of the pulley.
Once the joint output torque is given, the output force difference between the antagonistic PMAs is fixed, but there are multiple solutions for the specific value.
The force distribution method adopted for the antagonistic PMAs is as follows: As the characteristics of the PMAs are similar to Bowden cables, which can only provide tension force. If the minimum output force become negative, the driving ropes of the PMAs will be in a relaxed state [24], and the pulley structure may be out of control. In order to ensure that the driving ropes of the PMAs always maintains the stretched state, the appropriate solution for the output force of each PMA is obtained by setting the minimum output force , which needs to be greater than zero.
In order to achieve precise trajectory control, while ensuring that the driving ropes of the PMAs maintains a stretched state to provide appropriate assistance torque during rehabilitation, a force/position hierarchical controller based on NFTSMC-NDO is proposed to realize the position and force control of the exoskeleton. The complete force/position hierarchical control block diagram is shown in Figure 7. The outer loop is position control, and the inner loop is force control. Based on the established dynamic model, the NFTSMC-NDO method is used to obtain the expected output torque of the exoskeleton, and the expected force of each PMA is obtained through force distribution method. Finally, through the static contraction model of the PMAs, the input air pressure is determined by the contraction displacement and the output force.
The exoskeleton reaches the final air pressure by using the desired air pressure and the adjusted output of the air pressure, so as to realize the control of the antagonistic PMAs. Firstly, the desired trajectory ( ) of the exoskeleton is solved by inverse kinematics to obtain the corresponding expected joint angles ( ). The expected joint angles ( ) and the actual joint angles ( ) collected by the angle sensors are used as input to the non-singular fast terminal sliding mode controller. Next, the expected output torque ( ) corresponding to the joint is obtained through the controller, and the expected output force of each PMA is obtained through the force distribution method. Then, the expected joint angles ( ) can be converted to the expected displacement of each PMA, and the expected contraction rate and output force of the PMAs are substituted into the static contraction model of the PMAs to obtain the desired air pressures . Finally, the difference between the expected output force of the PMA and the actual output force measured by the force sensor is used as the input to the proportional integral (PI) controller, and the adjusted output of the air pressure is obtained. The letter subscripts 11, 12, 21 and 22 respectively represent the PMA on the left side of elbow joint, the PMA on the right side of elbow joint, the PMA on the left side of wrist joint, and the PMA on the right side of wrist joint.

IV. EXPERIMENT RESULTS AND DISCUSSION
To verify the feasibility and effectiveness of the designed exoskeleton and the proposed control strategy, the simulation analysis was firstly performed in Simulink. The dynamic model shown in Figure 7 is adopted, and the specific parameter settings are as follows: , , , , , . The desired angles of the elbow and wrist joint are: ( ) and ( ), and the unit is angle (°). The simulation duration is set to 20s. Experiment (1): When there is no disturbance in the system, the angle tracking results of basic sliding mode control (SMC) and non-singular fast terminal sliding mode control (NFTSMC) is compared, and the angle tracking results of the two methods under the same expected trajectory are shown in Figure 9. Both methods can achieve low tracking errors of the elbow and wrist joint with no disturbance, which verifies the feasibility of the control method. The response time of SMC before reaching stable state is 1.288s for the elbow joint and 1.044s for the wrist joint, while the response time of NFTSMC is 0.492s for the elbow joint and 0.3397s for the wrist joint, which shows that NFTSMC can respond quickly to the expected trajectory. Experiment (2): When there is system disturbance, the angle tracking results of NFTSMC and NFTSMCNDO are compared, and the angle tracking results of the two methods under the same disturbance are shown in Figure 10. To verify the control effects using a nonlinear disturbance observer, the disturbance ). It can be seen from Figure 9 and 10 that the tracking error of NFTSMC increases under disturbance. With the same initial state and disturbance, the average error of the elbow and wrist joint using NFTSMC are 0.1288° and 0.0245°, respectively. In comparison, the average error of the elbow and wrist joint of NFTSMCNDO are 0.0607° and 0.0088°, respectively, which is significantly reduced compared to NFTSMC. The simulation analysis verifies that NFTSMCNDO can ensure low tracking errors and faster convergence under disturbance for the exoskeleton.

FIGURE 11. Angle tracking results of elbow and wrist joints with a participant using NTSMC and NFTSMCNDO
In practical applications, the control accuracy might also be affected by various environmental factors (such as the sensor accuracy or system noises). The NTSMC method [17] and the NFTSMCNDO method proposed in this paper are used to realize the force/position hierarchical controller. A participant subject with a height of 176cm and a weight of 64kg was recruited to wear the upper limb exoskeleton for robot-assisted training, and the subject keeps the forearm and wrist in a relaxed state during the test. The desired angles of the elbow joint and the wrist joint are: ) , and the unit is angle (°). The experimental results are shown in Figure 11.  Table III shows that the tracking errors of the elbow and wrist joints reveals that the force/position hierarchical controller based on NFTSMCNDO has better performance than NTSMC. The maximum error (ME) and the average error (AE) of the angle tracking result are used as indicators to compare the control performance. Taking the elbow joint as an example, the ME and AE of NTSMC is 3.1301° and 1.0272°, respectively, while the ME and AE of NFTSMCNDO is 1.4191° and 0.8724°, respectively. The maximum angle tracking error of the wrist joint using NTSMC is 1.8401° at around 20s, and the maximum angle tracking error of the elbow joint using NFTSMCNDO is 1.5152° at around 20s. In contrast, the ME and AE decreased by 54.7% and 15.07%, respectively. When the subject wears the upper limb exoskeleton under disturbances, the proposed NFTSMCNDO method can achieve low tracking errors, and the AE during the entire rehabilitation is small. The NFTSMCNDO-based hierarchical controller uses PI controller at the inner loop, driving the PMAs in contracted state to track the desired output force. Figures 12 and 13 are the joint torque and output force of PMA tracking results of the force/position hierarchical controller with NFTSMCNDO in position loop and PI controller in force loop, respectively.
The results shown in Figure 12 indicate that the assistance torque of the elbow joint can basically meet the tracking effect, and the maximum tracking error is 0.65N· m. The tracking effect of the wrist joint torque is poor, and the maximum tracking error is 0.0635N· m. However, the desired wrist joint torque is small, and the actual torque is basically in line with the change trend of the desired torque. The output force of PMA tracking results is shown in Figure 13, and the error of force tracking control is larger than that of angle tracking control, Taking the elbow joint as an example, the ME and AE of the force tracking at the left PMA is 3.6374N and 1.5049N, respectively. The ME and AE of the force tracking at the right PMA is 32.3535N and 6.6754N, respectively. The goal of the position/force hierarchical controller is to ensure that the exoskeleton meets the angle control accuracy while the driving ropes of the PMAs maintain stretched state. Though the force tracking accuracy is reduced, the actual contraction force is basically in the state of during the entire rehabilitation, which verifies the feasibility and effectiveness of position/force hierarchical controller.

FIGURE 13. PMA output force results in elbow and wrist joints
According to the above comprehensive analysis, it can be concluded that the proposed force/position hierarchical control based on NFTSMCNDO can achieve high-precision angle control and better tracking performance. In addition, the contraction force of the PMAs in joint space are effectively controlled to ensure that all the driving ropes of the PMAs is kept in tension, and the operation safety of robot during rehabilitation is guaranteed. The configuration of traditional upper limb rehabilitation robot is often fixed. Due to the upper limb rehabilitation exoskeleton with reconfigurable modular mechanism and soft actuators, the uncertainties of the dynamic model will affect the high-precision control. The nonlinear disturbance observer can estimate and compensate the nonlinear disturbance of the system to effectively improve the control accuracy. Current rehabilitation robots driven by soft actuators basically do not consider force control in improving the stability of position control and safety in rehabilitation training. However, the position/force hierarchical control based on NFTSMCNDO can effectively ensure the control stability and safety of the exoskeleton.

V. CONCLUSION
In this paper, we designed a reconfigurable upper limb rehabilitation exoskeleton driven by soft actuators to help patients carry out safe and efficient rehabilitation training. Compared with the mechanism driven by rigid motors, the designed rehabilitation exoskeleton driven by the PMAs has the characteristics of light weight, small space occupation and high compliance. The reconfigurable modular mechanism is adopted in which the modules for elbow and wrist joints can be flexibly reconstructed to meet different rehabilitation needs of different patients with different physical parameters, and reconfigurable modular design has potential to increase the equipment utilization rate and reduce the research cost. Considering the load disturbance after reconstruction, the nonlinear disturbance observer is used to estimate and compensate the disturbance, and a position/force control method based on NFTSMCNDO is formed. The experimental results show that the position/force hierarchical controller can not only achieve precise position control, but also provide appropriate assistance torque, thereby making the rehabilitation training compliant and effective.