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Edited by: Guanglin Li, Shenzhen Institutes of Advanced Technology (CAS), China

Reviewed by: Xu Zhang, University of Science and Technology of China, China; Ru-Lan Hsieh, Shin Kong WHS Memorial Hospital, Taiwan

^{†}Co-first authors.

Specialty section: This article was submitted to Stroke, a section of the journal Frontiers in Neurology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Robot-aided rehabilitation has become an important technology to restore and reinforce motor functions of patients with extremity impairment, whereas it can be extremely challenging to achieve satisfactory tracking performance due to uncertainties and disturbances during rehabilitation training. In this paper, a wire-driven rehabilitation robot that can work over a three-dimensional space is designed for upper-limb rehabilitation, and sliding mode control with nonlinear disturbance observer is designed for the robot to deal with the problem of unpredictable disturbances during robot-assisted training. Then, simulation and experiments of trajectory tracking are carried out to evaluate the performance of the system, the position errors, and the output forces of the designed control scheme are compared with those of the traditional sliding mode control (SMC) scheme. The results show that the designed control scheme can effectively reduce the tracking errors and chattering of the output forces as compared with the traditional SMC scheme, which indicates that the nonlinear disturbance observer can reduce the effect of unpredictable disturbances. The designed control scheme for the wire-driven rehabilitation robot has potential to assist patients with stroke in performing repetitive rehabilitation training.

Stroke, an acute cerebrovascular disease typically caused by hemorrhage or blockage in brain blood vessels, is a major cause of motor dysfunction or even permanent disability (

Mechanical structure is one of the most important factors that can affect the effectiveness of the robot-assisted rehabilitation. In the past two decades, many robotic systems have been designed and applied in rehabilitation training. Conventional rehabilitation robots usually consist of several rigid links. MIT-MANUS has two degrees-of-freedom (DOF) and can guide the upper-limb over a horizontal plane (

Control scheme is another important factor affects the effectiveness of robot-assisted rehabilitation. When delivering task-oriented rehabilitation training, the control scheme is required to assist the robot in guiding the paretic limb to finish predefined movements or trajectory accurately and compliantly. Linear control techniques such as PID (

In this paper, a wire-driven rehabilitation robot is designed to deliver task-oriented training exercises for upper-limb, which can work over a three-dimensional space. First, sliding mode control with nonlinear disturbance observer (SMCNDO) is designed for the wire-driven rehabilitation robot against unpredictable disturbances. Then, simulation of tracking a predefined trajectory is conducted to investigate the performance of the designed control scheme. Moreover, a square-shaped and a circle-shaped trajectory are designed, and the forearm of the subject is controlled by the robot to follow the predefined trajectories. Both simulation and experimental results of the designed SMCNDO are compared with that of a traditional SMC.

Mechanical architecture of the designed wire-driven rehabilitation robot is shown in Figure

A wire-driven rehabilitation robot.

The geometry of the designed wire-driven rehabilitation robot is shown in Figure _{i}, y_{i}, z_{i}

According to Table _{i}, y_{i}, z_{i}

Parameters of the designed wire-driven rehabilitation robot.

Parameter | Symbol | Value |
---|---|---|

End-effector mass | 2.5 kg | |

The length of |
0.81 m | |

The length of |
1.78 m | |

The length of |
1.36 m | |

Gravity acceleration | 9.8 m/s^{2} |

Differentiating the length of each wire with respect to time leads to velocity of each wire:

Moreover, the relation between

Moreover, in this study, we assume that the motion is within the workspace and the gravity of the end-effector is able to keep all the wires under tension. Therefore, the relation between externally applied forces and the wire tensile forces can be expressed as follows (_{x}, d_{y}_{z}

Note that ^{T} and _{d}_{d} y_{d} z_{d}^{T} represents the actual and the desired position in a three-dimensional space, respectively. For the sake of control scheme design, the vector of sliding surfaces is defined as follows:
_{d} x_{d} x_{d}^{T} is the vector of tracking errors in a three-dimensional space, _{x} s_{y} s_{z}^{T} and _{x}_{y}_{z}^{T} are positive symmetric diagonal matrices. Taking the derivative of _{x}_{y}_{z}^{T}, _{x} k_{y} k_{z}_{x}_{y}_{z}

According to Eqs

A nonlinear disturbance observer has been introduced in many studies (_{x}_{y}_{z}

The derivative of

Substitute Eq.

Therefore,

In this study, _{i}

As mentioned previously that

To investigate the effectiveness of the presented SMCNDO for the wire-driven rehabilitation robot, first, simulation is carried out in Matlab/Simulink. Both SMCNDO and the traditional SMC are considered in the simulation, and the results of tracking a predefined trajectory _{d}_{1}_{T}, _{2}

Both the traditional SMC and SMCNDO can be designed according to Eq. _{1} = 0.1, η_{2} = 80, β = 0.5, and proper control parameters for SMCNDO are given as: _{1} = 0.1, η_{2} = 80, β = 0.5.

Experiments are carried out based on a real-time system to verify the performance of the presented controller for practical applications. It has been approved by the ethics committee of the Injury Rehabilitation Hospital of Guangdong Province. During the experiments, a healthy subject (23 years old, height of 173 cm, and weight of 60 kg) is seated beside the wire-driven rehabilitation robot with his forearm placed on the splint. The subject is instructed to keep relaxed during the experiments. Then, the forearm of the subject is controlled by the robot to follow predefined trajectories, and two different types of trajectories are considered in this section, including a square-shaped and a circle-shaped trajectory. The results of SMCNDO are compared with that of the traditional SMC. The traditional SMC and SMCNDO are designed according to Eq. _{1} = 2,000, η_{2} = 500, β = 0.1, and proper control parameters for SMCNDO is chosen as: _{1} = 2,000, η_{2} = 500, β = 0.1,

Predefined square-shaped and circle-shaped trajectories in experiments. The side length of square-shaped trajectory is

The desired velocity and acceleration can be obtained by differentiating the desired position once and twice, respectively, each experiment of tracking the circle-shaped trajectory lasts 62.8 s. The predefined circle-shaped trajectory is visually shown in Figure

Tracking performance of the traditional SMC and SMCNDO in simulation are shown in Figure

Tracking performance in the three coordinate directions

The output forces for the three wires

The tracking errors of the two applied control schemes in the three coordinate directions when a healthy subject follows the predefined square-shaped trajectory are shown in Figure

Comparison of tracking errors in the three coordinate directions by implementation of sliding mode control (SMC) and sliding mode control with nonlinear disturbance observer (SMCNDO) when a healthy subject follows a square-shaped trajectory.

Root mean square errors (cm) in the three coordinate directions by implementation of sliding mode control (SMC) and sliding mode control with nonlinear disturbance observer (SMCNDO) when a healthy subject follows a square-shaped and a circle-shaped trajectory.

Type of trajectory | ||||||
---|---|---|---|---|---|---|

SMC | SMCNDO | SMC | SMCNDO | SMC | SMCNDO | |

Square-shaped | 0.301 | 0.047 | 0.177 | 0.061 | 0.389 | 0.071 |

Circle-shaped | 0.411 | 0.075 | 0.214 | 0.066 | 0.313 | 0.081 |

Comparison of output forces for the three wires by implementation of sliding mode control (SMC) and sliding mode control with nonlinear disturbance observer (SMCNDO) when a healthy subject follows a square-shaped trajectory.

Comparison of tracking errors in the three coordinate directions by implementation of sliding mode control (SMC) and sliding mode control with nonlinear disturbance observer (SMCNDO) when a healthy subject follows a circle-shaped trajectory.

The tracking errors along the three coordinate directions when tracking the predefined circle-shaped trajectory by implementation of SMC and SMCNDO are shown in Figure

Comparison of the output forces for the three wires by implementation of sliding mode control (SMC) and sliding mode control with nonlinear disturbance observer (SMCNDO) when a healthy subject follows a circle-shaped trajectory.

The designed wire-driven rehabilitation in this paper has three DOF and its architecture makes it possible to assist the subject in performing predefined movements in a three-dimensional space. Coordinate system that applied in the control scheme design procedure is considered in this paper, which can be classified into the wire length coordinate system and the task space coordinate system. In the wire length coordinate system, the length of each wire is measured by scaling the associated motor encoder count; however, due to the unavailable flexibility of wires, using the wire length coordinate system is not reliable when the implementation may require high accuracy. In this paper, this problem can be effectively addressed by using the task space coordinates (

From the results of both simulation and experiments, the traditional SMC has degraded tracking performance and can cause high chattering in all the three coordinate directions, while tracking performance can be obviously improved and chattering can be effectively reduced

There are a few limitations of this study that should be addressed in the future. The positions of the wires should be well arranged to ensure enough workspace and the safety for upper-limb rehabilitation in clinical application. In this pilot study, we mainly focus on the investigation of the feasibility of the wire-driven rehabilitation robot using SMCNDO, in the future, we will recruit enough patients after stroke to investigate its clinical effectiveness in rehabilitation training.

In this paper, a wire-driven rehabilitation robot is designed for upper-limb rehabilitation training, and SMCNDO is designed for this robot. Simulation and experimental results of trajectory tracking show that the wire-driven rehabilitation robot with the designed control scheme has exhibited two superiorities including tracking performance improvement and chattering reduction as compared with the traditional sliding mode control scheme. The wire-driven rehabilitation robot with the designed control scheme may have great potential in robot-aided rehabilitation training.

This study was approved by the ethics committee of the Injury Rehabilitation Hospital of Guangdong Province.

JN and RS conceived and designed the study. JN and QY performed the experiments, wrote the paper, contributed to the work equally, and should be regarded as cofirst authors. RS reviewed and edited the manuscript. XW made a contribution to experiments. All authors had read and approved the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

SMC, sliding mode control; SMNDO, sliding mode control with nonlinear disturbance observer.