Bioinspired Musculoskeletal Model-based Soft Wrist Exoskeleton for Stroke Rehabilitation

Exoskeleton robots have demonstrated the potential to rehabilitate stroke dyskinesia. Unfortunately, poor human-machine physiological coupling causes unexpected damage to human of muscles and joints. Moreover, inferior humanoid kinematics control would restrict human natural kinematics. Failing to deal with these problems results in bottlenecks and hinders its application. In this paper, the simplified muscle model and muscle-liked kinematics model were proposed, based on which a soft wrist exoskeleton was established to realize natural human interaction. Firstly, we simplified the redundant muscular system related to the wrist joint from ten muscles to four, so as to realize the human-robot physiological coupling. Then, according to the above human-like musculoskeletal model, the humanoid distributed kinematics control was established to achieve the two DOFs coupling kinematics of the wrist. The results show that the wearer of an exoskeleton could reduce muscle activation and joint force by 43.3% and 35.6%, respectively. Additionally, the humanoid motion trajectories similarity of the robot reached 91.5%. Stroke patients could recover 90.3% of natural motion ability to satisfy for most daily activities. This work provides a fundamental understanding on human-machine physiological coupling and humanoid kinematics control of the exoskeleton robots for reducing the post-stroke complications.


Introduction
Robotic-aided neuro-rehabilitation is a clinically viable option to improve rehabilitation outcomes for stroke dyskinesia [1,2] which can assist 90% of patients to regain motion ability [3] . Upper limb functions are important for Activities of Daily Living (ADLs), like self-feeding and drinking [4,5] , and joints closer to the limb end are the more difficult to recover according to rehabilitation medicine [6] . The motion ability of the wrist joint greatly affects the accuracy and stability of grasping. Therefore, exoskeleton robot for wrist rehabilitation could effectively improve rehabilitative outcomes. However, current exoskeletons, including rigid exoskeletons [7][8][9][10] and soft exoskeletons [11,12] still face the common problem of poor human-robot physiological coupling and humanoid kinematics control.
Rigid exoskeletons are widely used in structural applications and carrying a heavy load of large joints [13,14] . Nevertheless, the problems of rigid exoskeletons, such as poor dynamic responses and misalignment of the motion axes, limit its application in the wrist joint. The Universal Haptic Drive (UHD) [5] is for the rehabilitation of the wrist joint. However, the UHD only can assist joints to move the horizontal plane, which cannot meet the normal range of ADLs. This limitation was overcome by a wrist exoskeleton, RiceWrist [15,16] . This exoskeleton encompasses most of the natural hu-man space. However, the heavy mechanism and fully enclosed structure affected the motion. For this problem, WRES [17] , driven by tendon lines, and SCRIPT6, driven by a steel leaf spring, were designed to simplify the structure. However, these robots showed poor adaptability to different individuals. NU-Wrist [18] is a passive self-aligning wrist rehabilitation robot. However, the lack of a handle and forearm support causes inconvenience. Other robotics devices for wrist neurorehabilitation, such as MIT-MANUS [19] , READAPT [20] , wrist robot [21] , and Wrist Gimbal [22] with large inertia mechanisms still would increase metabolic costs.
Soft exoskeletons have been studied widely to solve the problems of rigid exoskeletons, like poor dynamic responses and motion axes misalignment. The soft exoskeleton is like clothing, which could augment motion ability without restricting natural kinematics. Researchers have developed a variety of soft exoskeletons for motion assistance. A soft exoskeleton, Pneumatic Assist Wear, is designed to reduce a physical burden based on pneumatic soft actuator [23] . However, heavy and slow response of pneumatic control limits its application. To overcome this shortcoming, Exo-Glove Poly [24] , a soft glove is driven by tension lines for assisting patients to grasp objects. Nevertheless, manual key results in complex operations, and the thumb lacking the active drive results in an unnatural motion. Moreover, Soft Exosuit [25][26][27][28] could provide natural walking assistance based on Inertial Measurement Unit (IMU) signals. However, these exoskeletons lack the effect analysis on the human physiological state. Therefore, a soft upper-limb exoskeleton was designed for elbow assistance, considering the physiological and kinematics effects on arm movements [29][30][31] . However, the layout of tension lines does not combine the muscle distribution of the human motion system, which reduces human-robot compliance. Moreover, current researches on soft exoskeletons mainly focus on the lower, upper limbs and hand. Comparatively, research of soft wrist exoskeletons is lacking and overlooked, which affects the accuracy of grasping and self-care ability. Furthermore, previous studies of soft exoskeletons lack in-depth physiological analyses of the body's own musculoskeletal system. Therefore, wearers suffer from the poor human-robot physiological coupling.
Hence, in this paper, the simplified muscle model and bionic kinematics model were proposed, based on which a bionic soft wrist exoskeleton was established to overcome the poor human-robot physiological coupling and humanoid kinematics control for natural human interaction. The research work conducted an in-depth study on the wrist joint. In our previous work [32,33] , we have verified the feasibility of the 7 DOFs of the soft upper limb exoskeleton. Next, the simplified muscle model and bionic kinematics model will be extended to the upper limbs and whole-body exoskeleton robots.

Simplified model of human muscle system
The human motion is a highly nonlinear system which not only causes the difficulty of motion control but also poses major challenges for structural design. Therefore, it is necessary to simplify the muscle system.
We selected the wrist joint for our preliminary study to verify the simplified muscle model. Previous wrist exoskeletons had large and rigid structure [34,35] , which could only facilitate rehabilitation training without daily wearing.

Wrist kinematics
The wrist kinematics includes two DOFs: wrist flexion/extension and wrist adduction/abduction. The annular motion is the compound of two DOFs.
3. The main muscles for wrist adduction muscles include the FCU, the ECU.

Muscle kinematics model simplification
According to the standards of the Wake Forest School of Medicine Institutional Review Board following the ethical standards of the Helsinki Declaration of 1975, revised in 2000, five muscles (ECRL, ECBR, ECU, FCR, and FCU) are mainly responsible for the two DOFs. Meanwhile, the FCR and PL have the consistent action direction and both ends points, which have the similar driving effect. FCR plays the main role during wrist flexion relative to PL, which was simplified and the muscles (FCR and PL) are equivalent to a robust muscle to simplify the model. Combined with the above anatomical analysis and reference standards, we further simplified the human skeletal muscle system according to anatomy and biomechanics. The ECRL and ECBR were simplified into a single muscle owing to the equivalence of the motion effect and position overlap. Moreover, the muscle model was simulated and validated in the human skeletal muscle simulation software, Opensim [36] . The FCU, ECRL, FCR, and ECU work together to ensure the stability of the wrist joint movement.

Biomechanical simulation analysis
First, we use an optical motion capture system, Vicon, to record the motion trajectories of healthy subjects. Then, the motion trajectories were imported into Opensim.

Healthy subject motion analysis
The wrist flexion/extension motions were selected as the reference motion data. The joint angles, muscle force, and joint force were obtained as shown in Figs. 1a-1d. In terms of joint angles in Fig. 1b, the angles of wrist flexion/extension change obviously, and the angle of wrist adduction/abduction hardly changed. It is consistent with the actual motion condition. In terms of muscle forces in Fig. 1c, the amplitude of FCR and FCU is large, which contributes to the main power for the movement. The ECU and ECRL have low amplitude. In the human motion system, muscle force curves indicate the cooperation and antagonistic effects. In terms of joint forces in Fig. 1d, the force curves of X, Y, and Z axes also have obvious motion directivity and shows the direction consistent with the motion.  According to the simulation results, the muscle and joint forces significantly reduced by 43.3% and 35.6% respectively with exoskeleton assistance under the same motion state shown in Table 1. These results demonstrate that the simplified muscle model enables the human run in a low-power state without harm to the physiological structure.

Bionic kinematics model
The robot has the drive space, joint space and task space (Descartes Space). The mapping relations of three spaces are the basis of kinematics control. The articulated robot can achieve good kinematics control based on some traditional methods, such as Denavit-Hartenberg (DH) model. However, the robot in this study adopted the distributed muscle drive mode, whose drive space is not coincident with joint space. Therefore, the bionic kinematics model was proposed to solve the control problem for non-alignment of drive space and joint space.
First, we established the mapping between task space (hand) and joint space (joint angle) based on the DH model. Second, the mapping between the joint space (joint angle) and drive space (tension line) was developed based on the transformation of spatial relations. Finally, the above two mapping relations were combined to connect the above three spaces. Based on the above relationships, we can control the angle of the wrist joint by adjusting the tension line.
The soft exoskeleton robots itself don't have precise DH parameters due to the variability of soft material. But the skeletons of the wearers are rigid with the stable  structure. Therefore, DH parameters of the robot could be determined based on the human skeleton, as shown in Figs. 2a-2c. Therefore, the relationship between the joint space and task space was obtained using the DH matrix as:

R P T = T T T =
(1) where W is center distance from palm to the wrist.

Distribution of muscle tension lines
According to above simplified muscle model, the starting and ending points of tension lines are arranged as shown in Fig. 3.  The symbols used in this paper are listed in Table 2 with their definitions. The length of the l 1 could be obtained from Fig. 3 The variables 1 a should be calculated according to the geometric relationships as: a is obtained by cosine theorem in the triangle (0, 9, 10) of Fig. 3b. b can be calculated based on the sine theorem by substituting a into the triangle (1,9,10) according to Fig. 3d φ 12 is obtained by the angle relationship between parallel lines (line(4-4'), line(9-9')) between φ 11 , φ 12 , φ 2 and β 2 according to Fig. 3d in Eq. (5).
  and 1 a could be obtained from the triangle (6, 9, 9') in Fig. 3d. h is the constant value and from point 6 to the horizontal plane.
Moreover, the distances from the muscle nodes (1-8) to center (0) remain unchanged. The values of a 2 and d would change during motion and could be obtained from the triangle (0, 1, 10) in Fig. 3e.
The above space conversion relation is the kinematics model imitating the human muscle configuration. In the model, the length of lines could be obtained by calibration and calculation. And, angles were calculated as follows: β 1 , β 2 and φ 2 are constants, which determined by the configuration of the robot and need to be identified at the eginning. Other angles varied with the DOFs of the joint angles θ 1 and θ 2 .
where 1 2 ,    Among these parameters, 0 0 0 2 , , ,    and 0  are the initial value of the system, which can be calibrated initially.  could be obtained from the triangle (0, 1, 10) in Fig. 3e based on the δ 0 and ε 0 .
Based on the above parameter, the length of the controlled line could be obtained by Eq. (3) based on the θ 1 and θ 2 . Therefore, the posture of the hand and wrist could be controlled based on the above model. Circular motion of the bionic kinematics is shown in Figs. 4a and 4b. The single DOF motion simulation is shown in Figs. 4c and 4d, and the motion trend of the four points can be seen in Fig. 4e and Fig. 4f, which is consistent with the actual motion pattern. The quadrilateral frame represents the wrist posture. Based on the above motion simulation, the validity of the bionic kinematics model was preliminarily verified.

System design 3.1 Physical humanoid platform design
To better simulate the motion model, a bionic physical platform was designed and established with two DOFs. The wrist joint was simplified as a spherical hinge joint in Fig. 4a. The motion platform was manufactured via 3D printing.

System design
According to the simplified muscle model, the locations of the tension endpoints were arranged. The force stressed structure was manufactured via 3D printing. And the soft structure composition of the exoskeleton robot used a commercial body protector (McDavid, Woodridge, Illinois, USA) as shown in Fig. 5b.
The driver system was designed based on the EtherCAT bus protocol. A PC/104 computer and Maxon motors (Maxon Motor Ag., Sachseln, Switzerland) with Elmo drivers were used to implement position control. A 24 V power supply (SZ DJI Technology Co., Ltd., Shenzhen, China) was used to provide power to the system. Two wireless IMUs (Alubi, Guangzhou, China) recorded joint motion angles as shown in Figs. 5d and 5e. Furthermore, the ligament of the wrist joint was imitated to ensure that the tension lines fitted the human body.

Control scheme
First, we analyze the wrist posture to obtain the trajectories according to tasks. Then, the reference interpolation points were computed on the trajectory path. Next, the reference points were computed using inverse  kinematics to obtain the reference joint angles. These angles were calculated using bionic kinematics based on Eqs. (3)-(8) to obtain the tension line lengths. Further, the motors' rotation angles were calculated based on the line lengths and the wire wheel. Elmo drove the motors to realize robot motion control. Finally, wrist angles were recorded by the IMUs and fed back into the motion control system as shown in Fig. 6.

Participants
Three stroke (hemorrhagic) survivors (3 males, age range 32−57 years) were enrolled for an uncontrolled clinical trial. Table 3 provides the basic information for all the participants. This study was carried out in cooperation with the Rehabilitation Center for the Disabled of Liaoning Province (the fifth author's institution). All of the operations are following rehabilitation regulations and ethical norms. The post-stroke participants in the experiments gave informed consent for the study and for using their identifiable images.

Humanoid platform motion experiments
In the motion trajectory experiments, the 3D motion capture system (VICON, Oxford Metrics, UK) was used to capture the marker points attached to the human body. Firstly, to verify the simplified muscle model and kinematics models, wrist flexion/extension, wrist adduction/abduction and circular motions were carried on the physical humanoid platform as shown in Figs. 5g and 5h. The process involved in a circular motion is shown in Figs. 7a and 7b. The motion range of wrist joint is able to cover the daily living motion range of human wrist (wrist flexion/extension: 115˚; and wrist adduction/abduction: 70˚) [37] . It enables the proposed soft exoskeleton to achieve the similar motion as the previous rigid exoskeleton [38,39] . Meanwhile, the trajectory  similarity experiment was carried out, and the results show that the motion average similarity to the healthy subjects is over 91.5% (x 1 , y 1 , z 1 ), as shown in Fig. 7d.

Healthy subject experiments
Two types of experiments on healthy subjects were carried out: motion trajectory experiments and EMG signal experiments.

Motion trajectory experiments
The wrist motion trajectories of the healthy subjects were captured by VICON and reproduced as shown in Fig. 7b. The Pearson correlation coefficients were determined to evaluate the trajectory similarity between the human and the robot. The average correlation was 0.903 (x 2 , y 2 , z 2 ) in Fig. 7d. These results demonstrate that the robot has a high similarity motion ability with healthy subjects. Meanwhile, the soft exoskeleton has better comfort and portability for daily wearing. And the lightweight isotropic device is an important trend for daily activities [16] . Therefore, some soft wrist exoskeletons were developed. However, our proposed soft exoskeleton makes progress in the functional diversity [40] and kinesthetic feedback [41] .

EMG signal experiments
The amplitude of the EMG (Electromyography) signals is positively related to the muscle output force at the Maximum Voluntary Isometric Contraction (MVIC) level. We used a Trigno™ Wireless System (Delsys, Inc., Natick, Massachusetts, USA) to capture the EMG signals. The decline in the EMG signal amplitude represents the assistance effect.
The EMG signal of healthy subjects was captured during lifting 5 kg weight during wrist flexion with and without exoskeleton assistance in Fig. 5i. The amplitudes of the EMG signals from four muscles (ECRL, FCU, ECU, and FCR) are shown in Fig. 8. These four muscles correspond to the muscles in our simplified muscle model. EMG could be the gold standard for the analysis of human muscle activation [42] , which the evaluated force assistance performance of exoskeleton. Some researches focus on the EMG variation before and after assistance as the input of control information [43,44] . The results show the EMG signal with assistance was reduced by 48.5% compared to that without assistance. The value is slightly lower than that of elbow joint [31,33] . It is because the main function of wrist joint relative to elbow joint is position adjustment function, not to carry Fig. 8 The EMG activation degree of the healthy subjects with and without assistance. Grey Line: Without assistance; Red Line: With assistance. the load. Therefore, in the force assistance experiment, the decreased EMG amplitude is slightly lower. In particular, this value is close to the above simulation value of 43.3% by Opensim in Table 4, which forms a closedloop verification of theory and experiment.

Motion experiments on stroke patients
Tests on stroke patients were carried out to verify the clinical assistance effect. The motion ability of these patients improved with the soft exoskeleton, and ADLs could be restored.

Single-DOF motion experiment
The patients in the experiment totally lost their wrist motion ability owing to stroke complications. The single-DOF motion was restored with exoskeleton assistance, as shown in Fig. 7e. The trajectories were recorded using the VICON system and reproduced as in Figs. 7f and 7g). The similarity between the patients and healthy subjects reaches 93.9% shown in Fig. 7h. The average two DOFs motion range of patients recovered to 90.3% of the healthy subject shown in Table 5. The motion range is slightly lower than the rigid rehabilitation wrist exoskeleton [17] due to deformation of soft structure. Here, the motion range could meet the need of ADLs. Further, the compensation algorithm and structure design are being carried out in the next step work to solve the problem of deformation and displacement.

Daily activity experiment
Drinking action was selected to evaluate the assistance effect of the exoskeleton in Fig. 9. The patient couldn't drink by wrist falling off −65˚. With assistance from the exoskeleton, he could move the cup to the mouth and drink by 20˚ radially wrist bending in Figs. 9e-9h. These results prove the motion function recovery effect of the stroke patient with the exoskeleton in ADLs. And, most of current devices are large in size and need to be fixed and trained in specific positions [45] . The proposed exoskeleton is portable and could be worn when the wearers move around. And, the current wrist exoskeletons are mainly used to rehabilitation training [46] . The exoskeleton in this paper could assist the patients with activities of daily living before restoring their motion ability.
It's well known that rehabilitation is a long-term progress [45] . A lightweight and comfortable exoskeleton robot with high degree of human-robot fusion can be better accepted by patients. The previous exoskeletons used to adopt the rigid structure, and, due to the irregular physiological structure of human joint, additional complex mechanisms need to be designed to ensure the alignment of human and robot joint axes [47] . Thus, this research mainly focuses on three parts: bionic configuration, bionic drive, and bionic control. Compared with previous research on exoskeleton robots, the Table 5 The motion trajectory recovery of patients compared with healthy subject Fig. 9 Drinking water in comparison to the patient without and with the assistance (Volunteer 3). (a-e) The patient failed to drink water independently; (f-j) the patient succeeded in drinking water with assistance. The angles in the figures represent the angle between the hand and the forearm.
proposed robot has the following innovative advantages: (i) Bionic Configuration: Simplified muscle model: Based on anatomy and sport biomechanics, a simplified muscle system was discussed and proposed improving human-machine coupling and assistance efficiency based on the robust and flexible human muscle system.
(ii) Bionic Drive: Soft structure and compliant drive: The overall structure and drive part can be achieved by soft materials and tension lines, similar to human body flexibility based on the simplified muscle system according to biomechanics and anatomy.
(iii) Bionic Control: Bionic kinematics model: A bionic kinematics model was established to solve the problem that the drive space and joint space don't coincide in irregular distribution drive space, which realizes human-robot integration in the control strategy.
Besides, some limitations need to be overcome to further improve the performance of the robot in future studies, for example, the displacement and deformation caused by the soft structure. Compensation algorithm and more stable structure design will be carried out in the next step work. Furthermore, artificial intelligence should be combined to provide personalized assistance [28,[48][49][50] .

Conclusion
Human motion system is a nonlinear system with advantages. However, the complex and redundant system causes the difficulty of motion control and hardware design. In this study, the human muscle system was simplified to an executable model in a soft wrist exoskeleton. Meanwhile, a muscle-liked kinematics model was established to realize humanoid control, which solves the misalignment of drive space and joint space due to muscle-liked irregular distribution drive. The experimental results demonstrate that high-performance humanoid motion ability could improve the motion ability of stroke patients, which has the well-behaved human-robot coupling with the lower muscle activation and joint force. Thus, the proposed exoskeleton could be used in the process of stroke rehabilitation and daily life. And the methods of muscle simplification and bionics kinematic model could provide a thought for exoskeletons and humanoid robots.
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