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Gait rehabilitation is essential for chronic stroke patients to regain independent walking ability and quality of life, of which symmetry is regarded as a gold standard of gait quality. In this letter, a cable-driven lower limb exoskeleton powered by series elastic actuators (SEAs) has been developed, and a generalized gait-phase-based assistive strategy has been presented aiming to enhance the gait symmetry of chronic stroke patients. This strategy features a parameterized assistive force generation method that allows individuals customization to achieve more synchronized assistance with their walking gait patterns. A compliant human-robot interaction is guaranteed by SEA, and the exoskeleton exhibits low passive impedance and good transparency. The proposed assistive strategy was evaluated with five able-bodied subjects walked with the assistance from exoskeleton while adding artificial impairments to mimic a pathological gait with deficits (i.e., reduced knee flexion and foot-drop). Experimental results proved its efficacy in enhancing temporal walking gait symmetry to levels comparable to participants normal gait.

In recent years, cable-driven parallel manipulators (CDPM) become more and more interesting topics of robot researchers due to its outstanding advantages. Unlike traditional parallel robots, CDPMs use many flexible cables in order to connect the robot fixed frame and the moving platform instead of using conventional rigid links. Since cables used in CDPM is very light compared to rigid links, its workspace can be very large. Besides, CDPMs are often enhanced load capacity by adding redundant actuators. They also help to widen the singularity-free workspace of CDPM. On the other hand, the redundant actuators produce the underdetermined system i.e. the system has non-unique solutions. Moreover, the elasticity and bendability of flexible cable caused by self-weight and external forces act on it, resulting in the kinematic problem of CDPMs are no longer related to the geometric problem. Therefore, the system of CDPM become non-linear when the deformation of cable is considered. In this study, we introduce the simplified static cable model and use it to linearize the static model of redundantly actuated CDPM. The algorithm to solve the force distribution problem is proposed in Sect. 4. The static-workspace and the performance of those are analyzed in a numerical test.

Ankle dysfunction is common in the public following injuries, especially for stroke patients. Most of the current robotic ankle rehabilitation devices are driven by rigid actuators and have problems such as limited degrees of freedom, lack of safety and compliance, and poor flexibility. In this letter, we design a new type of compliant ankle rehabilitation robot redundantly driven by pneumatic muscles (PMs) and cables to provide full range of motion and torque ability for the human ankle with enhanced safety and adaptability, attributing to the PM's high power/mass ratio, good flexibility and lightweight advantages. The ankle joint can be compliantly driven by the robot with full three degrees of freedom to perform the dorsiflexion/plantarflexion, inversion/ eversion, and adduction/abduction training. In order to keep all PMs and cables in tension which is essential to ensure the robot's controllability and patient's safety, Karush-Kuhn-Tucker (KKT) theorem and analytic-iterative algorithm are utilized to realize a hierarchical force-position control (HFPC) scheme with optimal force distribution for the redundant compliant robot. Experiment results demonstrate that all PMs are kept in tension during the control while the position tracking accuracy of the robot is acceptable, which ensures controllability and stability throughout the compliant robot-assisted rehabilitation training.

Considerable attention has been paid to the exploration of moon, especially the construction of lunar habitat. However, few studies are found working on the construction equipment being suitable for trans planetary transportation, assembly, and working in lunar environment. This paper proposed a novel cable-driven printer used to build lunar architecture. The pose measurement and control strategy of the printing system is proposed. To study the reconfiguration characteristic of the cable-driven printer, several trees with arbitrary locations were selected as the rack to reconstruct the system outdoors. The key factors such as the sensitivity of pose deviation to system parameters affecting the reconstruction performance is discussed. The forming space of the cable-driven printer is analyzed theoretically and the forming ability of the system is verified experimentally. It is found that the cable-driven printer has the advantages of simple structure, small weight, large forming space and good reconfiguration characteristic, which shows the great potential of the proposed cable-driven printer in the construction of lunar architecture.

This paper develops the conceptual design and error analysis of a cable-driven parallel robot (CDPR). The earlier error analysis of CDPRs generally regarded the cable around the pulley as a center point and neglected the radius of the pulleys. In this paper, the conceptual design of a CDPR with pulleys on its base platform is performed, and an error mapping model considering the influence of radius of the pulleys for the CDPR is established through kinematics analysis and a full matrix complete differential method. Monte Carlo simulation is adopted to deal with the sensitivity analysis, which can directly describe the contribution of each error component to the total orientation error of the CDPR by virtue of the error modeling. The results show that the sensitivity coefficients of pulleys’ geometric errors and geometric errors of the cables are relatively larger, which confirms that the cable length errors and pulleys’ geometric errors should be given higher priority in design and processing.

The cable-driven flexible arm based on the principle of origami is a new type of non-articulated compliant actuator with high integration, high environmental adaptability, large workspace/large deployment ratio. The forward/reverse kinematic models of joint space, operation space and driving space along with trajectory error model of the cable-driven flexible arm were proposed in this paper. The prototype of the flexible arm was developed capable of realizing bending, torsion and expansion/contraction. The simulation and experiment results of the cable-driven foldable flexible arm verified feasibility of the kinematic models and driving method proposed in this paper. Above research achievements lay necessary foundation for the next step to realize the key service functions of grasping/manipulation, three-dimensional precise movement, non-structural environment interaction/adaptation of the flexible arm with variable stiffness, variable configuration and variable size.

Motion control of the human hand is the most complex part of the human body. It has always been a challenge for a good balance between the cost, weight, responding speed, grasping force, finger extension, and dexterity of prosthetic hand. To solve these issues, a 3D-printed cable driven humanoid hand based on bidirectional elastomeric passive transmission (BEPT) is designed in this paper. A semi-static model of BEPT is investigated based on energy conservation law to analyze the mechanical properties of BEPT and a dynamical simulation of finger grasping is conducted. For a good imitation of human hand and an excellent grasping performance, specific BEPT is selected according to human finger grasping experiments. The advantage of BEPT based humanoid hand is that a good balance between the price and performance of the humanoid hand is achieved. Experiments proved that the designed prosthetic hand’s single fingertip force can reach 33 N and the fastest fingertip grasping speed realized 0.6 s/180°. It also has a good force compliance effect with only 430g’s weight. It can not only grab fragile objects like raw eggs and paper cup, but also achieve strong grasping force to damage metal cans. This humanoid hand has considerable application prospects in artificial prosthesis, human-computer interaction, and robot operation.

This study intends to investigate a dynamic modeling and design of controller for a planar serial chain, performing 2-DoF, in interaction with a cable-driven robot. The under study system can be used as a rehabilitation setup which is helpful for those with arm disability. The latter goal can be achieved by applying the positive tensions of the cable-driven robot which are designed based on feedback linearization approach. To this end, the system dynamics formulation is developed using Lagrange approach and then the so-called Wrench-Closure Workspace (WCW) analysis is performed. Moreover, in the feedback linearization approach, the PD and PID controllers are used as auxiliary controllers input and the stability of the system is guaranteed as a whole. From the simulation results it follows that, in the presence of bounded disturbance based on Roots Mean Square Error (RMSE) criteria, the PID controller has better performance and tracking error of the 2-DoF robot joints are improved 15.29% and 24.32%, respectively.

In order to improve the working performance of the lower limb rehabilitation robot and the safety of the trained object, the mechanical characteristics of a cable-driven lower limb rehabilitation robot (CDLR) are studied. The dynamic model of the designed CDLR was established. Four kinds of cable tension optimization algorithms were proposed to obtain a good rehabilitation training effect, and the quality of the feasible workspace of the CDLR was analyzed. Finally, a real-time evaluation index of the cable tension optimization algorithms was given to measure the calculation speed of the optimization algorithms. The numerical research results were provided to confirm the characteristics of the four kinds of the optimization algorithms. The research results provide a basis for the follow-up research on the safety and compliance control strategy of the CDLR system.

With the widespread development of leg exoskeletons to provide external force-based repetitive training for gait rehabilitation, the prospect of undesired movement adaptation due to applied forces and imposed constraints require adequate investigation. A cable-driven leg exoskeleton, CDLE, presents a lightweight, flexible, and redundantly actuated architecture that enables the possibility of system parameters modulation to alter human–robot interaction while applying the desired forces. In this work, multi-joint stiffness performance of CDLE is formulated to systematically analyze human–CDLE interaction. Further, potential alterations in CDLE architecture are presented to tune human–CDLE interaction that favors the desired human leg movement during a gait rehabilitation paradigm.

The design and control of a cable-driven rehabilitation robot, which can be configured easily for exercising different articulations such as elbows, shoulders, hips, knees and ankles without requiring any orthosis, are introduced. The passive, active-assisted and active-resisted exercises were designed and implemented using impedance control. The controller could switch between exercises according to the force feedback. The effectiveness of the proposed controller was demonstrated by experimental studies. The robot was tested first with a dummy extremity and then with a healthy subject mimicking various types of patients during the tests. Experimental results showed that satisfactory closed-loop performances were achieved.

SUMMARYCable-driven parallel manipulators (CDPMs) offer advantages over traditional parallel manipulators. Though their ability to accelerate is higher than the traditional motion platforms, the capabilities are often not used optimally. The issues of cable slackening (especially at higher accelerations) and the emergence of singularity poses have traditional limitations. This paper analyzes and generates manipulator configurations that reduce the effect of these two essential hindrances of deploying CDPMs. A methodology, inspired by rigid body dynamics of multiple contact problems, used to optimize the positions of attachment points, is shown to be effective.

For high control performance of cable-driven manipulators, we design a new adaptive time-delay control (ATDC) using enhanced nonsingular fast terminal sliding mode (NFTSM). The proposed ATDC uses time-delay estimation (TDE) to acquire the lumped dynamics in a simple way and founds a practical model-free structure. Then, a new enhanced NFTSM surface is developed to ensure fast convergence and high control accuracy. To acquire good comprehensive performance under lumped uncertainties, in this article we propose a novel adaptive algorithm for the control gain, which can regulate itself based on the control errors timely and accurately. Benefitting from the TDE and the proposed enhanced NFTSM surface and adaptive control gain, our proposed ATDC is model-free , fast response , and accurate . Theoretical analysis concerning system stability, and control precision and convergence speed are given based on Lyapunov theory. Finally, the advantages of our ATDC over existing methods are verified with comparative experiments.

Out of all the changes to our daily life brought by the COVID-19 pandemic, one of the most significant ones has been the limited access to health services that we used to take for granted. Thus, in order to prevent temporary injuries from having lingering or permanent effects, the need for home rehabilitation device is urgent. For this reason, this paper proposes a cable-driven device for limb rehabilitation, CUBE2, with a novel end-effector (EE) design and autotuning capabilities to enable autonomous use. The proposed design is presented as an evolution of the previous CUBE design. In this paper, the proposed device is modelled and analyzed with finite element analysis. Then, a novel vision-based control strategy is described. Furthermore, a prototype has been manufactured and validated experimentally. Preliminary test to estimate home position repeatability has been carried out.

Certain satellites with ultralong wings play a crucial role in many fields. However, external disturbance and self-rotation could result in the vibration of flexible wings, which affects the normal operation of the satellites. In severe cases, the satellites will be damaged. Therefore, the vibration of these spatial flexible structures should be suppressed. With the benefits of large workspace, low energy consumption, and small inertia, a cable-driven parallel robot (CDPR) is proposed for vibration suppression of ultralong spatial flexible structures. A controller based on the open-loop control is proposed in this article to rapidly suppress the vibration of flexible structures with quite small controllable force. To enhance the contrast, two sets of passive pretightening schemes (wire ropes and elastic strings with small elastic coefficients) are tested. In view of the small value of the cable force, the influence of friction on the experiment cannot be neglected. Therefore, a friction measurement experiment is also carried out to ensure the accuracy of the experimental data. First, the dynamic model of the CDPR, which is comprised of four cables and a flexible end-effector is established. Furthermore, controller design is detailed. The dynamic response of the scale model under output force of the control low is compared with free vibration, which validates the scheme's ability and effectiveness in vibration suppression. Finally, simulations and experiments are conducted to evaluate the control scheme, and the results are satisfactory.

The transmission error of cable-driven sheaves (CDS) used in space docking locks directly affects the synchronous docking of two spacecraft, which is guaranteed mainly by the preload applied to their serial cables. But it is difficult controlled precisely because of the complicated cable deformation and operating conditions. The synchronous testing efficiency of the docking locks is inevitably influenced, correspondingly. This paper proposes a prediction model for the transmission error of CDS based on their cable deformation. In this model, the deformations of non- and free sectional cables are both modified on finite element analysis, which are respectively derived from classical Capstan equation and Hooke’s law for them without considering the effects of the friction coefficient between wire strands. Based on the proposed model, the relationships between the transmission error and dominating factors are analyzed. Then the preload compensation for transmission error is obtained at the engaging and locking angles of the docking locks, respectively. Experiments validate the model. This can provide a valuable reference in controlling the transmission error of CDS and improving the assembly efficiency of docking locks.

The increasing number of patients with hand disabilities after strokes or peripheral nerve injuries necessitates the continuous development of rehabilitation system devices to accelerate muscle recovery and to help patients regain the motor functions of their hands. This paper introduces the design of a hand rehabilitation system for patients who have a solitary impairment of their hand extension. The system was designed to be portable, simple, and cheap. Using a system based on a cable-driven mechanism instead of traditional rigid links reduces the degrees of freedom of the finger to one. The dielectric elastomer actuator was designed and fabricated as a smart actuator for the system, which supports the low cost of the system. A kinematic analysis of the cable-driven mechanism has been done. Parameters of the actuator were optimized to reach the required output. In order to characterize the performance of the actuator, a uniaxial tension test, isotonic test, and isometric test have been implemented.

Specific satellites with ultralong wings play a crucial role in many fields. However, external disturbance and self-rotation could result in undesired vibrations of the flexible wings, which affect the normal operation of the satellites. In severe cases, the satellites would be damaged. Therefore, it is imperative to conduct vibration suppression for these flexible structures. Utilizing fuzzy-proportional integral derivative control and deep reinforcement learning (DRL), two active control methods are proposed in this article to rapidly suppress the vibration of flexible structures with quite small controllable force based on a cable-driven parallel robot. Inspired by the output law of DRL, a new control method named Tang and Sun control is innovatively presented based on the Lyapunov theory. To verify the effectiveness of these three control methods, three groups of simulations with different initial disturbances are implemented for each method. Besides, to enhance the contrast, a passive pretightening scheme is also tested. First, the dynamic model of the cable-driven parallel robot which comprises four cables and a flexible structure is established using the finite element method. Then, the dynamic behavior of the model under the controllable cable force is analyzed by the Newmark-ß method. Finally, these control methods are implemented by numerical simulations to evaluate their performance, and the results are satisfactory, which validates the controllers’ ability to suppress vibrations.

In this article, an adaptive nonsingular terminal sliding mode control scheme based on fractional order is proposed for a cable-driven manipulator with external disturbances, where the concentration is uncertain and the upper limit is known or unknown. Furthermore, a new adaptive fractional-order nonsingular fast terminal sliding mode algorithm with time-delay estimation is developed. The delay estimation unit can be used to properly compensate the centralized unknown dynamics of the system, thereby obtaining attractive model-free characteristics. A characteristic of the control scheme in this article is that by using the adaptive tuning law, the upper limit of the uncertainty is estimated only by the speed and position measurement so as to achieve the effects of rapid convergence, high accuracy, and vibration reduction. In addition, the proposed controller effectively eliminates the effects of jitter without losing robustness and accuracy. The simulation results show the effectiveness of the proposed control scheme.

A new adaptive time delay estimation technique with sliding mode control method is proposed and investigated in this passage for cable-driven manipulators. Time delay estimation technique is an effective tool to compensate for unmodeled dynamics and unknown disturbance, and adaptive time delay estimation performs better due to its adaptive control gain. The proposed adaptive method is based on the fuzzy logic algorithm which has a great advantage in input–output mapping thank to its flexibility. Tuning procedure is addressed to reveal the implementation of the newly proposed algorithm. Moreover, the desired trajectory is taken as an input of adaptive algorithm and better control performance is obtained through this attempt. The proposed controller is ultimately uniformly bounded and proof using the Lyapunov method is provided. Finally, comparative experiments show the validity and effectiveness of the proposed controller.

Cable-driven parallel robots (CDPRs) are vulnerable to vibration due to the inevitable flexible properties of the cables. Thus, vibration analysis is critical for CDPR’s operation in which highly accurate motion is required. However, most of the current methods related to vibration analysis of CDPRs rely on simple spring models which have limitations in their performance and complexity that are not general to analyze the vibration of various CDPRs. Hence, accurate, simple and general approaches for vibration analysis in CDPRs are need. To solve this problem, this paper presents the finite element method (FEM) and the modified analytical method to analyze the vibration of CDPRs. To validate these methods, free vibration analysis was conducted using the proposed methods for the planar and spatial cable-driven parallel robots. The natural frequencies of these two CDPRs were computed by the proposed two methods and compared with those of the commercial software, SAP2000. The solutions obtained by the FEM and the modified analytical models turned out to be close to SAP2000’s results, thereby verifying the validity of the proposed methods.

This paper aims to solve the problems of the existing limbs rehabilitation robots in terms of configuration limitations, human-machine compatibility, multimodal rehabilitation training. In addition, the control method of the cable tension of cable drive unit (CDU) loading system is studied to improve loading accuracy of cable tension and safety of the rehabilitation training robot. The novelty of this work is to propose a compound correction controller that can not only ensure the tracking accuracy of the cable-driven lower limb rehabilitation robot (CDLR) but also effectively improve the force loading accuracy of the cable tension force. Hence, this paper proposes a CDLR that can realize the active training mode, passive training mode, and assistive training mode. Firstly, the structure and working principle of CDLR is introduced. The dynamic model of the CDU loading system is established and the frequency characteristic of the CDU loading system is analyzed. In order to improve the loading accuracy and response speed of the CDU loading system, a compound correction controller is designed based on the frequency characteristics of the CDU loading system. Finally, the active force servo control experiment and the passive force servo control experiment of the CDU loading system are carried out on the experimental platform. The experimental results show that the compound correction control strategy can meet the requirements of lower limb rehabilitation training in the active force servo control experiment; the compound correction control strategy can significantly improve the loading precision and dynamic performance of the system in the passive force servo control experiment. That is, the compound correction control strategy can meet the requirements of lower limb rehabilitation training. The results provide a basis for the whole robot experiment and human-machine experiments and improve the stability of the CDLR system and patient safety.

This paper presents an adaptive proportional-integral-derivative fractional-order nonsingular terminal sliding mode (PID-FONTSM) control for the cable-driven manipulators using time-delay estimatio...

For accurate position tracking control of cable – driven manipulators under heavy lumped uncertainties, a novel adaptive nonsingular terminal sliding mode (ANTSM) control scheme using time delay es...

In this paper, a mathematical model is presented to numerically simulate the dynamical responses in a multi-cable suspension platform taking into account the slack cables and guiding devices. The s...

Multi-link cable-driven robots (MCDRs) have potential advantages in confined spaces exploration because of their redundancy and flexibility. Operational space wrench and acceleration capability analysis of MCDRs is important for their design, manipulability optimization, and motion planning. However, existing works mainly focus on capability analysis in the joint space. In this paper, we present a zonotope-based iterative method and a simplified capability zonotope to analyze the operational-space wrench and acceleration capability of MCDRs. In the iterative method, the capability generated by some cables can be iteratively added to the initial capability zonotope based on the Minkowski sum. In the simplified zonotope capability representation, a threshold is put forward to reduce redundant vertices and faces with little volume loss. Finally, simulations on a 24 DOFs MCDR are performed to verify the effectiveness of the developed method. The results demonstrate that our iterative algorithm can easily generate the capability zonotope with a few MB ROM, while traditional operational wrench capability evaluation without our iterative algorithm needs 18432 GB ROM. Furthermore, our simplified representation reduces the vertices and faces from 1260 and 2516 to 88 and 172, respectively, but with only 3.3% volume loss, which decreases the constraints of the robot and is conducive to manipulability optimization and motion planning.

Cables are widely used because of their light weight and wide range of arrangement. To guarantee successful deployment and retraction of cable-driven mechanisms, this paper proposes a novel cable-winding device to fulfil particular requirements of a space mission, such as a large driving force output, large cable displacement, and high reliability. The device consists of three parts: the transmission assembly, cable arrangement assembly, and redundancy motor assembly. The transmission assembly transforms the torque of a motor into a large driving force. Cables can be wound layer-by-layer on a winch with the cable arrangement assembly. The redundancy motor assembly ensures normal movement of the mechanism if one motor fails, and can offer greater torque than a single motor. A prototype of the proposed cable-winding device is fabricated, and experiments are conducted to verify the performance of the device. The device has also been used in a large telescopic boom, which further validates its feasibility for actuating deployable mechanisms.

In this work a novel crashworthy cable-driven four-bar link mechanism is designed, manufactured, and tested for the development of robotic landing gear for rotorcraft. The paper will demonstrate ho...