A path planning method of 6-DOF robot for mirror therapy based on A* algorithm

Abstract

BACKGROUND:

With the population aging, post-stroke patients suffering from hemiplegia are also rapidly increasing. It is essential to provide valid rehabilitation methods for hemiplegia patients. Mirror therapy is an effective rehabilitation method and is widely applied in many rehabilitation robots.

OBJECTIVE:

The aim of this paper is to present a path planning method to guarantee the robot’s motion performance during mirror therapy.

METHODS:

The kinematic framework of the proposed rehabilitation system is detailed, then the reference motion path of the manipulator is calculated according to kinematic transformation. The concept of manipulability is introduced to describe the motion performance of the manipulator. Based on the above work, a path planning method based on A* algorithm is proposed to quantitatively analyze and optimize the motion performance of the manipulator.

RESULTS:

Preliminary experiments with the proposed rehabilitation system are conducted to verify the proposed path planning method. The characteristics of the proposed method are analyzed through two typical situations. The results showed that the proposed method can build a new path for manipulator, which can ensure the robot’s motion performance and is highly consistent with the reference path.

CONCLUSION:

The results showed that the manipulator could achieve the task with acceptable error, which indicates the potential of the proposed path planning method for mirror therapy.

Keywords

Mirror therapy path planning A* algorithm manipulability stroke

1. Introduction

Stroke is a disease of the central nervous system caused by partial loss of brain function [1]. It is the leading cause of death [2] and can also lead to high rates of disability [3]. However, after conventional rehabilitation treatment, only 5% $\sim$ 20% of patients recover [4]. Long-term rehabilitation can significantly improve various movement disorders and reduce the disability rate [5]. Mirror therapy (MT), first proposed by Ramachandran [6], is widely used in upper limb rehabilitation of hemiplegic patients. With the development of technology, many devices offer mirror therapy for rehabilitation without an actual mirror. Du et al. [7] estimate the movement of the patient’s upper limbs through kinematic calculation, and use a 5-DOF manipulator to control the movement of the patient’s affected limb. Lenzi et al. [8] designed an “EMG-based exercise assistance” controller based on the “NEUROExos elbow” rehabilitation system. The system collects EMG signals from the biceps and triceps of the patient’s upper limb and output the assistance torque of the elbow joint. Wang et al. [9] designed a system with the IMU measurement system and the exoskeleton robot to monitor the movement of the unaffected limb of the patient, therefore that system can be measured and controlled over a larger range of motion (ROM) with high safety.

A common task in robot rehabilitation training is to plan a path from the initial pose to the target pose. Obstacle avoidance path planning refers to planning a path from the initial pose to the target pose under the condition of given obstacles, therefore the robot can pass all obstacles safely and without collision [10]. Berg et al. [11] proposed a path planning method for dynamic environments, which takes all the prior information of both static and dynamic elements in the environment into account, and it efficiently updates the solution when changes to either are observed. Kala et al. [12] proposed a path planning method by combining A* algorithm and Fuzzy Inference. The A* algorithm is used on a probability-based map and the Fuzzy Inference System (FIS) is used on lower level planning. All generated paths are optimal in terms of path length and smoothness. The method proposed by Jan et al. [13]can not only search for the optimal path in various terrains. Furthermore, the method can be easily extended to dynamic path planning in 3-D space among multiple robots.

This paper proposes a path planning method for manipulator in upper limb mirror therapy rehabilitation. The paper is constructed as follows. The research status of path planning method of multi-DOF robot is introduced in Section 1. In Section 2, tasks and problems of the path planning method are proposed. In Section 3, the structure of the proposed upper limb rehabilitation system is introduced, and the kinematic modeling of VR handle, VR helmet, system base and manipulator tip is analyzed. In order to ensure the continuity of joint angles, a verification method is proposed. In Section 4, the reference path is calculated and the path planning method is proposed based on the reference path. In Section 5, experiments under two typical situations are conducted and the experimental results are analyzed. Finally, the conclusions of this paper are briefly discussed.

2. Problem description

2.1 Task description

The basic procedure of mirror therapy is to make sure the symmetrical movement of the affected limb and unaffected limb while blocking vision of affected limb. Visual and motor coordination leads to the perception that the affected limb is fully functional. The perception induces cortical reorganization with positive motor recovery [14]. Traditionally, a mirror is used to block view of the affected limb, therefore the patient can only see his/her unaffected limb and the mirror image of the unaffected limb. However, actual mirrors cannot display all directions. Besides, it is difficult to ensure symmetry of limbs movement when the affected limb moves with the assistance of the therapist.

2.2 The limits of moving performance of the robot

Many modern devices are used in mirror therapy [15]. Among them, VR devices have rich training scenes, low development costs and high accuracy, which is very suitable for the collection of unaffected limb data and the display of rehabilitation scenes. The characteristics of the manipulator made it suitable for assisting the movement of the affected limb instead of the therapist. It should be noticed that most VR developer software is based on the left-handed coordinate system; however, robot kinematic models are based on the right-handed coordinate system. Therefore, it is necessary to calculate the conversion relationship between VR devices and robots. Besides, it is necessary to calculate and guarantee the motion performance of the manipulator during mirror therapy rehabilitation because manipulator has limited working space.

The task is usually to find the shortest path between the starting point and the end point in a typical path planning method. However, mirror therapy is a trajectory-based rehabilitation training, the movement of both sides of the patient needs to be as symmetrical as possible to achieve the rehabilitation effect. If the typical path planning method is adopted, the new path will be quite different from the original path and will not be efficient. Therefore, the new path should be highly consistent with the reference path if the motion performance of the manipulator is good.

3. Establishment and analysis of the kinematical model

3.1 General description of the rehabilitation system

The rehabilitation system is designed to assist patients in mirror therapy rehabilitation. The system consists of a 6-DOF robot and a series of VR devices. The patient equipped with the manipulator will receive virtual reality scenes in the VR headset, such as picking fruit and opening the refrigerator door. During the training, the patient completes the task with the unaffected limb. Then the manipulator drives the patients’ affected limb to reproduce the symmetrical path of the unaffected limb. The motion path is mirrored according to the patients’ position. Therefore, the kinematics calculation is needed to obtain the reference path of the manipulator. All analyses assumed that the left limb is the affected limb

3.2 Reference frames in the rehabilitation system

As shown in Fig. 1, the studied rehabilitation system has the following frames:

Robot base coordinate system (BCS) {V}: $O_{B}X_{B}Y_{B}Z_{B}$ . The base coordinate system of rehabilitation system, which is fixed in the base of manipulator. Robot tip coordinate system (TCS) {T}: $O_{T}X_{T}Y_{T}Z_{T}$ . The tip coordinate system of the manipulator is fixed on the tip of the manipulator. Affected hands coordinate system (ACS) {A}: $O_{A}X_{A}Y_{A}Z_{A}$ . The system to describe the pose of affected hands. It has specified displacement along $Z_{T}$ . Mirror plane coordinate system (MCS) {M}: $O_{M}X_{M}Y_{M}Z_{M}$ . It is calibrated by VR handle after the installation of system. $O_{M}$ is set on projection to the ground from the patient’s position. Axis $Z_{M}$ is along the vertical direction, $Z_{M}=0$ in VCS. The axis $X_{M}$ is a horizontal line from the affected limb to the unaffected limb. MCS is the coordinate system for calculating symmetrical path. VR base coordinate system (VCS) {V}: $O_{V}X_{V}Y_{V}Z_{V}$ . The base coordinate system for all VR devices, VCS is a left-handed coordinate system. Right-handed VR base coordinate system (RCS) {R}: $O_{R}X_{R}Y_{R}Z_{R}$ . Right-handed coordinate system to describe all VR devices. The only difference between RCS and VCS is that the axis $Z_{V}$ is reversed. VR handle coordinate system (HCS) {H}: $O_{H}X_{H}Y_{H}Z_{H}$ . The coordinate system of VR handle, which is for recording the motion of patients’ unaffected hand. HCS is a left-handed coordinate system. Unaffected hands coordinate system (UCS) {U}: $O_{U}X_{U}Y_{U}Z_{U}$ . The system to describe poses of unaffected hands. UCS has specified displacement along $Z_{H}$ . UCS is a left-handed coordinate system.

Figure 1.

Structure and reference frames of the rehabilitation system.

3.3 Pose transformation in the rehabilitation system

The symmetrical pose of the affected limb can be described by six parameters: $x_{A},y_{A},z_{A},a_{A},b_{A},c_{A}$ , the rotation is described in $z-y-x$ Euler angle.

Assuming UCS pose in VCS is [ $x_{V},y_{V},z_{V},\gamma_{V},\beta_{V},\alpha_{V}$ ], the location and orientation of unaffected limbs described in VCS is as follows:

${}_{U}^{V}T={}_{H}^{V}T{}_{U}^{H}T$ ${}_{H}^{V}T=\left[\begin{array}[]{cccc}\cos\alpha&-\sin\alpha&0&0\\ \sin\alpha&-\cos\alpha&0&0\\ 0&0&1&0\\ 0&0&0&1\\ \end{array}\right]\left[\begin{array}[]{cccc}\cos\beta&0&\sin\beta&0\\ 0&1&0&0\\ -\sin\beta&0&\cos\beta&0\\ 0&0&0&1\\ \end{array}\right]\left[\begin{array}[]{cccc}1&0&0&0\\ 0&\cos\gamma&-\sin\gamma&0\\ 0&\sin\gamma&\cos\gamma&0\\ 0&0&0&1\\ \end{array}\right]$ (1) ${}_{U}^{H}T=\left[\begin{array}[]{*{20}c}1&0&0&0\\ 0&1&0&0\\ 0&0&1&Z_{A}\\ 0&0&0&1\\ \end{array}\right]$

where ${}_{H}^{V}T$ is defined as the transformation matrix between HCS and VCS, ${}_{U}^{H}T$ is defined as the transformation matrix between UCS and HCS VR developer software is based on the left-handed coordinate system, yet robot kinematics transformation is based on the right-handed coordinate system. Based on the conversion method proposed by Yang et al. [16], the transformation of UCS in RCS can be expressed as follows:

${}_{U}^{R}T={}^{M}T{}_{U}^{V}T{}^{M}T$ (2)

where ${}_{U}^{R}T$ is defined as the transformation matrix between RCS and UCS. Because RCS and VCS have the opposite $Z$ axis, ${}^{M}T$ can be expressed as follows:

$\displaystyle{}^{M}T=\left[\begin{array}[]{*{20}c}1&0&0&0\\ 0&1&0&0\\ 0&0&-1&0\\ 0&0&0&1\\ \end{array}\right]$

Poses are transformed to MCS to achieve the symmetry of motion path, which can be expressed as follows:

${}_{U}^{M}T={}_{R}^{M}T{}_{U}^{R}T$ (3) ${}_{R}^{M}T=\left({{}_{M}^{R}T}\right)^{-1}=\left({{}_{V}^{R}T{}_{M}^{V}T}% \right)^{-1}$ (4)

${}_{M}^{V}T$ is calibrated during the initiation of the rehabilitation system. Based on above work, poses should transform into ACS to get mirrored by reversing $x_{U},a_{U},b_{U}$ , which can be expressed as follows:

${}_{A}^{M}T=\left[\begin{array}[]{llll}C_{\alpha}C_{-\beta}&C_{\alpha}S_{-% \beta}S_{-\gamma}&C_{\alpha}S_{-\beta}C_{-\gamma}+S_{a}S_{-\gamma}&-x\\ S_{\alpha}C_{-\beta}&S_{\alpha}S_{-\beta}S_{-\gamma}+C_{\alpha}C_{-\gamma}&S_{% \alpha}S{-\beta}C_{-\gamma}-C_{\alpha}S_{-\gamma}&y\\ -S_{-\beta}&C_{\beta}S_{-\gamma}&C_{-\beta}C_{-\gamma}&z\\ 0&0&0&1\\ \end{array}\right]$ (5)

where $c_{\alpha}$ is $\cos\alpha$ , $s_{\alpha}$ is $\sin\alpha$ , $\alpha$ is $\textit{arctan}2\left({{}_{U}^{M}T_{2,3},{}_{U}^{M}T_{1,3}}\right)$ , $\beta$ is $\textit{arctan}2\left({\sqrt{{}_{U}^{M}T_{3,1}+{}_{U}^{M}T_{3,2}},{}_{U}^{M}T_% {3,3}}\right)$ , $\gamma$ is $\textit{arctan}2\left({{}_{U}^{M}T_{3,2},-{}_{U}^{M}T_{3,1}}\right)$ , $x$ is ${}_{U}^{M}T_{4,1}$ , $y$ is ${}_{U}^{M}T_{4,2}$ , $z$ is ${}_{U}^{M}T_{4,3}$ .

We can get transformation matrix ${}_{R}^{B}T$ by fixing a VR positioner (PCS) at the tip of the manipulator. ${}_{R}^{B}T$ can be expressed as follows:

${}_{R}^{B}T={}_{P}^{B}T\left({{}_{P}^{R}T}\right)^{-1}$ ${}_{P}^{B}T={}_{T}^{B}T{}_{P}^{T}T$ (6) ${}_{P}^{T}T=\left[\begin{array}[]{*{20}c}1&0&0&0\\ 0&1&0&0\\ 0&0&1&Z_{P}\\ 0&0&0&1\\ \end{array}\right]$

$z_{P}$ is the distance between $o_{T}$ and $o_{P}$ , we can get ${}_{P}^{R}T$ by ${}_{P}^{V}T$ and Eq. (2). Based on above calculation, symmetrical pose in BCS can be expressed as follows:

${}_{T}^{B}T={}_{R}^{B}T{}_{M}^{R}T{}_{A}^{M}T{}_{T}^{A}T$ (7) ${}_{T}^{A}T=\left[\begin{array}[]{*{20}c}1&0&0&0\\ 0&1&0&0\\ 0&0&1&Z_{T}\\ 0&0&0&1\\ \end{array}\right]$

After we get the reference pose of the manipulator in BCS, it is necessary to ensure the continuity of the robot posture. The range of posture angle is [ $-\pi,\pi$ ]. There will be mutation in posture data if any posture angle reaches the border, which may lead to errors during the calculation of the robot joint angle. Therefore, the proposed method is as follows to avoid the truncating of pose data and make robot joint continuous: Normally, there will be several groups of solutions during robotic inverse kinematics calculation. The usual way is to calculate the sum differences between current joint angles and joint angles from the last moment, then choose the best solution according to minimum differences. The above method can be expressed as follows:

$\displaystyle q_{n}=\min\left(\mathop{\sum}\limits_{j=1}^{6}\left|{q^{\prime}_% {j}-q_{j}}\right|\right)$ (8)

$q^{\prime}$ is defined as robot joint angles from last moment. The method adopted in this paper is to set $q_{n}=q_{n}-2\pi$ to make joint angle continuous when $q_{n}$ is bigger than the threshold value, which can be expressed as follows:

$\displaystyle\mathop{\sum}\limits_{j=1}^{6}\left|{q^{\prime}_{j}-q_{j}}\right|% =\mathop{\sum}\limits_{j=1}^{6}\left|{q^{\prime}_{j}-q_{j}}\right|-2\pi$ (9)

The condition of Eq. (9) is expressed as follows:

$\displaystyle\left|{\textit{joint}_{\left({\textit{last},j}\right)}-\textit{% joint}_{\left({i,j}\right)}}\right|>2\pi\pm 0.1\pi$ (10)

The above methods can make sure robot joint angles are continuous without being affected by the overflowing posture data.

4. Path planning method

According to the task description of mirror recovery in Chapter II, the manipulator needs to reproduce the symmetrical path with restricted motion performance. In order to evaluate the motion performance, the variable to describe motion performance of the multi-DOF manipulator is needed. The physical meaning of manipulability is a comprehensive measure of the omnidirectional mobility of a robot. It can be used to measure the overall flexibility of the robot. Yoshikawa defined manipulability as follows [17]:

$\displaystyle\omega=\sqrt{\textit{det}({J(q)J^{T}(q)})}$ (11)

where $q$ is defined as the joint angles, $J(q)$ is defined as the Geometric Jacobian matrix, $J^{T}(q)$ is defined as the transpose matrix of the Geometric Jacobian matrix.

In order to quantitatively describe the robotics’ motion performance, the variable $O_{i}$ is proposed as follows:

$\displaystyle O_{i}=\frac{\omega_{i}}{\omega_{m}}$ (12)

where $\omega_{i}$ is defined as manipulability of posture $i$ , $\omega_{m}$ is defined as maximum manipulability among the whole set of poses of manipulator. Apparently the range of $O_{i}$ is 0 to 1, poses with larger $O_{i}$ have better motion ability.

A* (a-star) algorithm is the most effective direct search method for shortest path in static road network, which is widely used in the problem of optimal path solution [18]. It adds heuristic information related to the task, which can lead the search into the most promising direction. The core of the A* algorithm is the design of the valuation function. The valuation function is used when selecting the best successor nodes, successor node which has a minimum $f(p)$ value will be chosen as the next node. Generally, the evaluation function $f(p)$ can be expressed as follows:

$\displaystyle f(p)=g(p)+h(p)$ (13)

$g(p)$ is defined as the actual cost of an optimal path from the initial position to present position, $h(p)$ is the cost of an optimal path from present position to target position. The evaluation function calculates the position difference of manipulator. According to the characteristics of manipulator path planning, $g_{i}(p)$ and $h_{i}(p)$ can be expressed as follows:

$\displaystyle g_{i}(p)=\mathop{\sum}\limits_{x=1}^{i}\left(\mathop{\sum}% \limits_{y=1}^{3}\left|{p_{y}^{x}-p_{y}^{x-1}}\right|\right)$ (14) $\displaystyle h_{i}(p)=\max({|{p_{x}-p_{l}}|}),x=1,2,\ldots,i$ (15)

where $i$ is defined as the index of position data, $p$ is defined as the position of manipulators’ tip, $l$ is defined as data from the last moment.

According to the characteristics of robot path planning, the following improvements is added to the standard A* algorithm: We set up three lists, set $l_{o}$ as list open, $l_{c}$ as list close and $l_{s}$ as successor list to facilitate analysis. Before path planning, initial position $p_{0}$ is put into $l_{o}$ , $f({p_{0}})$ is set as $h({p_{0}})$ , $l_{c}$ is set as an empty list, $p_{j}$ is set as the position note nearest to present position, $K$ is set as the capacity of $l_{s}$ and $s$ is set as step length to generate the successor node. The child nodes of $p_{i}$ are set as $p_{c}$ .

Before calculating $f({p_{c}})$ , threshold value of manipulability $O_{i}$ should be set to filter poses which may cost robots lose DOF. According to the step length $s$ , the successor nodes of current pose are generated and added into $l_{s}$ . The node with the smallest $f(p)$ value is selected as the optimal successor node of $p_{i}$ . We repeat this process to get the optimal pose for each step. The estimated function with heuristic information is used to calculate the optimal path from the initial pose to the target pose. The threshold value $D$ is set as 0.01 m to judge if $p$ coincides with ${p}^{\prime}$ . The whole process of proposed path planning method is as followed.

Repeat the following process until the distance between target position and current position is less than $D$ . If $l_{o}$ is an empty table, path planning failed; otherwise, the following loop begins:

Select $p_{i}$ from $l_{o}$ with the smallest $f(p)$ as the present node, put it into $l_{c}$ and delete it from $l_{o}$ ;

If $p_{i}$ is coincidence with $p_{l}$ , path planning is successful and the loop ends; otherwise, go to 3).

Set the position closest to the current position in the reference path to $p_{j}$ ;

Generate $S$ based on $p_{j}$ then put $p_{i+1}$ , $p_{i+2}\ldots p_{i+k}$ into $l_{s}$ by letting $p_{i}$ move $S$ toward $p_{j+1}$ , $p_{j+2}\ldots p_{j+k}$ , then impose the following judgment rules for each node in $l_{s}$ :

IF $O$ is bigger than threshold value ${O}^{\prime}$ :

Remove this $p_{c}$ node and add $p_{i+k+1}$ into $l_{s}$

Pick $p_{c}$ with minimum $f(p)$ from $l_{s}$

IF $p_{c}$ in $l_{c}$ AND $h(p_{c})$ is smaller than $h(p_{c})$ of $p_{c}$ in $l_{c}$ :

Clear $p$ after $p_{c}$ in $l_{c}$ recalculate $f({p_{c}})$ set $p_{i+1}=p_{c}$ , add $p_{i+1}$ into $l_{o}$

At the end of the loop, the data in $l_{c}$ is the new path with restricting the motion performance of manipulator.

5. Experiment and results

In order to verify the effectiveness of the proposed path planning method, we designed experiments that simulate the real mirror therapy rehabilitation process. After the subjects put on the VR helmet, they receive a certain order to finish a task, such as picking up fruit, or opening the door of a refrigerator in a virtual reality environment (Fig. 2). After finishing the mission with the VR handle held by their unaffected limb, the manipulator will reproduce the mirrored path with the affected limb. During the experiment, data such as the robotic tip’s poses and joint angles are recorded, processed, and analyzed. The experimental rehabilitation system mainly consists of an UR5 6DOF robot and Samsung VR devices.

Figure 2.

A healthy male subject during the tests.

The tip pose of the manipulator should be calculated with robot joint angles and D-H parameters to evaluate the proposed method, then we can get the maximum manipulability $\omega_{\max}$ of the manipulator after calculation of all $\omega$ . When $O_{i}<0.4$ , the path planning method will plan the motion path of the manipulator.

Sample the data during the movement of the manipulator. The data format is set as follows: sample time, joint angles, the pose of TCS in BCS, $O_{i}$ .

The maximum manipulability of the manipulator in the sample is $\omega_{\max}=1.1974\times 10^{8}$ , which can be calculated by Eq. (12), $k$ is set as 3. We can get $O_{i}=\frac{\omega_{i}}{\omega_{\max}}$ by real-time calculation of $\omega_{i}$ , then we compare the manipulability of the manipulator before and after the path planning method added.

As shown in Fig. 3, the red curve is defined as the change trends in manipulability value after the path planning method is added and the blue curve is the change trends in manipulability value before the path planning method is added. After setting $O_{i}=0.4$ , optimized path restricting the movement performance of the manipulator is compensated by the proposed path planning method. The minimum manipulability value of the robotic after the constraint is added is bigger than before, which means the constraint can prevent the manipulator from the low motion performance area. After the constraint is added, the manipulability of the manipulator $O_{i}$ is bigger than 0.4 at $t=$ 1.535 s and $t=$ 9.725 s, then the constraint is applied and the motion path manipulator starts to deviate from the reference path.

Figure 3.

The manipulability value of the robotic tip over time.

The improvement of robot motion performance is also shown in Figs 4–6. A few seconds after $t=$ 1.535 s and $t=$ 9.725 s, poses that will cause manipulator in low motion performance are avoided by the path planning method, which achieves the purpose of performance constraint. Due to the characteristics of the path planning method, the new path reached the target position in advance.

Figure 4.

The $x$ coordinate of the robotic tip over time.

Figure 5.

The $y$ coordinate of the robotic tip over time.

Figure 6.

The $z$ coordinate of the robotic tip over time.

Figure 7 shows the distance between poses from the reference path and the corresponding poses from the new path. Instead of generating the shortest path from start position to stop position, the new path coincides with the reference path when the manipulability $O_{i}\geqslant 0.4$ . Therefore, the distance between the reference path and the new path is very small. When the manipulator approaches the low motion performance area where $t=$ 1.535 s and $t=$ 9.725 s, a smooth path is planned to replace the reference path, making the task-driven path has less distortion in rehabilitation work. It can also be seen from Fig. 8, which describes a change trends in manipulability value. When the robot arm motion performance is good during the entire task, the reference path and the new path are highly fitted.

Figure 7.

The distance of the corresponding point over time.

Figure 8.

The manipulability value of the robotic tip over time.

In Figs 9–11, the reference path and the new path are highly fitted in three directions, and the coordinate difference is always small. The phase difference caused by the characteristics of path planning method is fixed at 0.2 s.

Figure 9.

The $x$ coordinate of the robotic tip over time.

Figure 10.

The $y$ coordinate of the robotic tip over time.

Figure 11.

The $z$ coordinate of the robotic tip over time.

According to the experimental results, the addition of performance constraints improves the motion performance of the manipulator. When the manipulator tip gets close to lower motion performance poses, the path planning method would generate a new path which can restrict the motion performance. In addition, in order to ensure the characteristics of a trajectory-based task, this method can ensure a high consistency of old and new paths when the manipulability $O_{i}$ meets the requirements.

6. Conclusion

The rehabilitation system with the proposed path planning method has been tested in the experimental study, and the results showed that the manipulator could achieve the task with acceptable error, which indicates the following conclusions. Firstly, the proposed path planning method for the manipulator can enhance its motion performance. Secondly, the new path is highly coincident with the reference path when the motion performance meets the requirements. Thirdly, the proposed path planning method has the potential to be applied to different devices for mirror therapy. The proposed rehabilitation system is furthermore a potential device to enhance human mobility.

Footnotes

Acknowledgments

This work was supported by the National Key Research and Development Program of China [Grant No. 2018YFC2001600] and the National Natural Science Foundation of China [Grant No. 61973205].

Conflict of interest

None to report.

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