Chain mail jamming exosuit for spine rehabilitation: a comprehensive analysis and optimization

Variable stiffness actuators have the ability to change stiffness while retaining the advantages of soft actuators, it can be used in an environment requiring a large load. There are many materials used in variable stiffness actuators, among which shape memory polymers (SMP) can change from glassy state to rubber state under temperature change, and its modulus can realize large-span change. At the same time, shape memory polymers under the acrylic acid system have good 3D printable characteristics, so it is more suitable as variable stiffness material. Many researchers have used SMP to make variable stiffness actuators. However, the method of making these reports includes multiple steps, which is very time-consuming and requires high equipment. Our team recently reported a variable stiffness actuator based on digital light processing 3D printing technology (DLP), which can be printed using commercial printers or self-built printers. The variable stiffness layer and actuator cavity can be manufactured by DLP printing technology. At the same time, the materials used can be commercially purchased. The scheme of preparing polymer precursors is very friendly to users without chemical background. The method proposed in this study can quickly and conveniently fabricate variable stiffness actuators based on shape memory polymers.

We present variable negative stiffness actuation (VnSA), an alternative method of achieving variable stiffness actuation based on the nonlinear deflection characteristics of buckling beams. The approach exploits transverse stiffness variations of axially loaded beams around their critical buckling load to achieve an actuator with adjustable stiffness. In particular, transverse stiffness of buckled beams are positive under tensile loading and for compressive loading below their first critical buckling load, while they display negative stiffness above this critical value. Furthermore, for small deflections transverse stiffness of buckled beams depends linearly on the amount of axial loading. Consequently, the stiffness of a variable stiffness actuator can be modulated (i) by decreasing the transverse stiffness through an increase of the axial compressive loading on a beam, up to values above the first critical buckling load where the overall stiffness of the actuator approaches its lowest negative value, and (ii) by increasing the transverse stiffness through application of tensile axial loading. Capitalizing on the concept of negative stiffness, the lowest stiffness of VnSA can be set arbitrarily close to zero or even to negative values (when counterbalanced), while very high stiffness values are also achievable by tensile loading of the beam. As a result, VnSA can modulate its stiffness over a uniquely large range that includes zero and negative stiffness values. Furthermore, thanks to the negative stiffness characteristics, the stiffness of VnSA can be kept very low without sacrificing the mechanical integrity and load bearing capacity of the actuator. We introduce the design of VnSA, theoretically analyze its stiffness modulation response, and provide implementation details of a prototype. We also provide experimental results detailing range of stiffness modulation and force tracking performance achieved with this prototype and discuss its correspondence with the theory.

The safety of human-robot interaction is an essential requirement for designing collaborative robotics. Thus, this paper aims to design a novel variable stiffness actuator (VSA) that can provide safer physical human-robot interaction for collaborative robotics. VSA follows the idea of modular design, mainly including a variable stiffness module and a drive module. The variable stiffness module transmits the motion from the drive module in a roundabout manner, making the modularization of VSA possible. As the key component of the variable stiffness module, a stiffness adjustment mechanism with a symmetrical structure is applied to change the positions of a pair of pivots in two levers linearly and simultaneously, which can eliminate the additional bending moment caused by the asymmetric structure. The design of the double-deck grooves in the lever allows the pivot to move freely in the groove, avoiding the geometric constraint between the parts. Consequently, the VSA stiffness can change from zero to infinity as the pivot moves from one end of the groove to the other. To facilitate building a manipulator in the future, an expandable electrical system with a distributed structure is also proposed. Stiffness calibration and control experiments are performed to evaluate the physical performance of the designed VSA. Experiment results show that the VSA stiffness is close to the theoretical design stiffness. Furthermore, the VSA with a proportional-derivative feedback plus feedforward controller exhibits a fast response for stiffness regulation and a good performance for position tracking.

This paper presents a biologically-inspired real-time balance recovery control strategy that is applied to a lower body exoskeleton with variable physical stiffness actuators at its ankle joints. For this purpose, a torsional spring-loaded flywheel model is presented to encapsulate both approximated angular momentum and variable physical stiffness, which are crucial parameters in describing the postural balance. In particular, the incorporation of physical compliance enables us to provide three main contributions: i) A mathematical formulation is developed to express the relation between the dynamic balance criterion ZMP and the physical ankle joint stiffness. Therefore, balancing control can be interpreted in terms of ankle joint stiffness regulation. ii) ‘Variable physical’ stiffness is utilized in the bipedal robot balance control task for the first time in the literature, to the authors' knowledge. iii) The variable physical stiffness strategy is compared with the optimal constant stiffness strategy by conducting experiments on our exoskeleton robot. The results indicate that the proposed method provides a favorable balancing control performance to cope with unperceived perturbations, in terms of center of mass position regulation, ZMP error and mechanical power.

In this paper, the structural design of a variable stiffness actuator (VSA) is proposed, and the variable stiffness characteristics of the VSA are studied. The VSA is compact and can be used for humanoid robots. Firstly, the structure of the VSA is designed. Then the stiffness model of the structure is derived in theory and the dynamic simulation is performed in ADAMS. The stiffness results of dynamic simulation and theoretical calculation are highly consistent, which verified the correctness of each other. Finally, the influence of the curve equation of the worm gear disc on the stiffness of the system is studied: the radius of the curve is a function of the angle, and when the order of the curve equation is higher, the stiffness adjustment range of the system is wider. Under the premise of meeting the same stiffness requirements, when the order of the curve equation increases, the radius of the higher-order curve equation is only half of that of the lower-order curve equation, and a more compact VSA can be obtained. The results are of great significance to the prototype design, that is, without changing the main design dimensions of each component, the stiffness of the system can reach the design value simply by changing the order of the curve equation.

PurposeTo achieve variable stiffness, this paper aims to design a flexible actuator with variable stiffness by using the magnetorheological effect of magnetorheological fluid. The variable stiffness actuator can well meet the safety requirements of human–robot interaction and be more adaptable to unknown or complex environments. The variable stiffness actuator designed in this study can realize the continuous and controllable change of stiffness compared with the existing actuator.Design/methodology/approachThe principle of variable stiffness actuator is illustrated in detail; the three-dimensional model and mechanical model of the flexible actuator are provided. The magnetic field distribution of the actuator coil is analyzed, and the dynamic model of the actuator is provided.FindingsOutput torque test suggests that the magnetorheological fluid variable stiffness actuator (VSAMF) can output a stable torque which meets the designing requirements of the test; sinusoidal follow-up test shows that VSAMF can implement sinusoidal follow-up; variable stiffness test shows that VSAMF can achieve real-time variable stiffness adjustment; the crash test suggests that VSAMF can well protect machines when meeting obstacles.Originality/valueIn this paper, a new variable stiffness joint is proposed through changing the current to change the performance of the stiffness, and it can realize the continuous and controllable change of stiffness.

Among many types of flexible robot actuators, the variable stiffness actuator (VSA) is an actuator that can adjust the compliance of the actuator output shaft by adjusting the equivalent stiffness of its internal elastic element. Compared with the traditional rigid actuators, the VSAs have inherent flexibility and adjustable stiffness because they contain elastic elements and stiffness adjusting mechanisms. They have advantages in human-robot physical interaction security and task adaptability. The independent controllability of position and stiffness and the ability of stiffness adjustment make the VSAs have research value and application prospects in the fields of rehabilitation training equipment, prosthetics, wearable devices and so on. The mechanical scheme design of the VSA is an open research field. At present, there is no perfect mechanical structure design of any type of VSA. Optimizing and improving the mechanical structure design of the VSA is helpful to improve its actuation characteristics and application value. Due to the limitation of the mechanical structure design, most of the existing VSAs have limited rotation angle range of the output shaft, which limits their application. The purpose of this paper is to design the parallel driven VSA whose rotation angle range of output shaft is not limited. Moreover, inspired by the mechanical structure design ideas of some stiffness adjustment mechanisms with good implementation schemes and elastic elements with good force transmission characteristics, this paper makes some improvement, synthesis and innovation in the mechanical structure design of the VSA, so as to improve the structural compactness design, assembly modular design, mechanical transmission reliability design and actuation characteristics. In this paper, six types of parallel driven VSAs with different mechanical structure design schemes are proposed. Their common point is that the rotation angle range of the output shaft is not limited, and the differences are that they have different implementation schemes of variable stiffness mechanisms and elastic elements. The transmission structure diagrams of the designed VSAs show the working principle and stiffness adjustment principle. The actuation characteristics of the designed VSAs are analyzed and their differences are compared. The detailed mechanical structure design of the VSA is shown. In the designed VSAs, the model of the VSA based on the symmetrical Archimedes spiral cam groove mechanism is printed and assembled to show the feasibility of the implementation of the designed mechanical structure scheme. Finally, a manual adjustment experiment verifies the stiffness adjustment ability of the assembled VSA model, and shows that the rotation angle range of the output shaft of the assembled VSA model is unlimited.

Variable Stiffness Actuator (VSA) is the core mechanism to achieve physical human–robot interaction, which is an inevitable development trend in robotic. The existing variable stiffness actuators are basically single degree-of-freedom (DOF) rotating joints, which are achieving multi-DOF motion by cascades and resulting in complex robot body structures. In this paper, an integrated 2-DOF actuator with variable stiffness is proposed, which could be used for bionic wrist joints or shoulder joints. The 2-DOF motion is coupling in one universal joint, which is different from the way of single DOF actuators cascade. Based on the 2-DOF orthogonal motion generated by the spherical wrist parallel mechanism, the stiffness could be adjusted by varying the effective length of the springs, which is uniformly distributed in the variable stiffness unit. The variable stiffness principle, the model design, and theoretical analysis of the VSA are discussed in this work. The independence of adjusting the equilibrium position and stiffness of the actuator is validated by experiments. The results show that the measured actuator characteristics are sufficiently matched the theoretical values. In the future, VSA could be used in biped robot or robotic arm, ensuring the safety of human–robot interaction.

This paper presents a bio-inspired dynamic leg model with a novel variable stiffness element to create a normal body motion during stance phase. The variable stiffness in the model is implemented through structure-controlled stiffness. It allows to decouple the stiffness from joint motion, which makes the stiffness a independent variable. Sensitivity of leg model to the variable stiffness element is investigated through dynamics analysis. Because of the decoupled structure of dynamics equations, the deflection of ankle joint related to variable stiffness element is planned based on generalized forced vibration motion in order to create the leg’s motion. A detailed study to investigate the dynamic characteristics under different generalized vibration parameters, and the desired variable stiffness function are evaluated. It is found that under the effects of variable stiffness, the ground reaction forces of leg model during stance motion have similar characteristics to those observed for mammals. Furthermore, in order to create a normal motion during stance phase, linear stiffness variation characteristics and small stiffness range are needed for the proposed variable stiffness actuator.

Robot-aided rehabilitation training allows patients to receive a more effective and stable rehabilitation process. Exoskeleton devices are superior to the endpoint manipulators and cable suspension devices on the aspect that they can train and measure the angle and torque on each joint of impaired limbs. For robotic devices, physical safety should be guaranteed since the robot-assisted training relies on high human-robot interaction especially for exoskeletons. Traditional robotic devices mainly introduce the stiffness actuator, while the high levels of kinetic energy of robots will induce unsafe. For guaranteeing the safety of patients, compliant actuator such as the series elastic actuator (SEA) and variable stiffness actuator (VSA) design has been involved into these devices. The added compliance can make robots intrinsically safe and realize the energy-efficient actuation. The VSA used a variable stiffness elastic component instead of a constant stiffness elastic component, and VSAs is deemed to a kind of SEAs. A closed-loop interaction control method was used for SEAs to generate low impedance. By comparison, the VSA realizes adaptable compliance properties with inherent mechanical design. Thus, for SEAs, an additional mechanism is needed to adjust the output stiffness. In this paper, two kinds of compliant exoskeleton devices designed with the SEA and VSA respectively are introduced. The mechanical design and control method for each device are introduced; especially the design for guaranteeing patients’ safety.

This paper presents the design and modeling of a modular variable stiffness joint intended for human-robot interaction. The functional concept is based on bidirectional antagonistic variable stiffness (BAVS) principle, in which elastic actuators are connected in parallel to output link, and an internal torque is generated by the antagonistic motion of two motors to adjust the stiffness. Different from conventional variable stiffness actuators (VSAs) that introduce extra motor to adjust stiffness, BAVS concept treats both motors as main actuators, thereby improving the joint's torque density. The mechanical realization of BAVS principle employs a differential mechanism and makes use of two harmonic reducers in a differential manner. The flexibility of the joint is provided by a non-linear elastic element consisting of linear spring and cam roller mechanism. Low torque density and non-modular design are the main reasons limiting VSAs' application in multi-degree-of-freedom robotic systems. In response to this, the proposed joint is designed to be compact and modular. This article describes the basic principles, the mechanical design and the dynamic modeling of the proposed joint. The preliminary simulation results are presented to illustrate the high torque density and wide stiffness range of the joint.

Considerable research effort has gone into the design of variable passive stiffness actuators (VSAs). A number of different mechanical designs have been proposed, aimed at either a biomorphic (i.e., antagonistic) design, compactness, or simplified modelling and control. In this paper, we propose a (model-based) unified control methodology that is able to exploit the benefits of variable stiffness independent of the specifics of the mechanical design. Our approach is based on forming constraints on commands sent to the VSA to ensure that the equilibrium position and stiffness of the VSA are tracked to the desired values. We outline how our approach can be used for tracking stiffness and equilibrium position both in joint and task space, and how it may be used in the context of constrained local optimal control. In our experiments we illustrate the utility of our approach in the context of online teleoperation, to transfer compliant human behaviour to a variable stiffness device.

The high stiffness of conventional robots is beneficial in attaining highly accurate positioning in free space. High stiffness, however, limits a robot's ability to perform constrained manipulation. Because of the high stiffness, geometric conflict between the robot and task constraints during constrained manipulation can lead to excessive forces and task failure. Variable stiffness actuators can be used to adjust the stiffness of robot joints to allow high stiffness in unconstrained directions and low stiffness in constrained directions. Two important design criteria for variable stiffness actuation are a large range of stiffness and a compact size. A new design, the Arched Flexure VSA, uses a cantilevered beam flexure of variable cross-section and a controllable load location. It allows the joint to have continuously variable stiffness within a finite stiffness range, have zero stiffness for a small range of joint motion, and allow rapid adjustment of stiffness. Using finite element analysis, flexure geometry was optimized to achieve high stiffness in a compact size. A proof-of-concept prototype demonstrated continuously variable stiffness with a ratio of high stiffness to low stiffness of 55.

We present a novel application of the variable stiffness actuator (VSA)-based assistance/rehabilitation robot-featured impedance control using a cascaded position torque control loop. The robot follows the adaptive impedance control paradigm, thereby achieving an adaptive assistance level according to human joint torque. The feedforward human joint torque command is used to cooperatively adjust the impedance controller and the stiffness trajectory of the VSA (this functional architecture is referred to as the cooperative control framework). In this way, the task performance during movement training can be improved regarding: 1) safety —for example, when the subject intends to contribute considerable effort, low-gain impedance control is activated with a low stiffness actuator to further decrease output impedance and 2) tracking performance —for example, for the subject with less effort, high-gain impedance control is used while pursuing high stiffness to enhance the torque bandwidth. Regarding the safety aspect, we demonstrate that the torque controller designed at low stiffness can be sensitive to the disturbance for low output impedance while maintaining tracking performance. A precondition for this is to treat the input disturbance separately. This is guaranteed by our previously proposed torque control of the VSA using the linear quadratic Gaussian technique. This approach is also employed here, but with additional discussion on the observer design to serve the proposed cooperative control approach. Here, the effectiveness of the proposed control system is experimentally verified using a VSA prototype and a one-degree-of-freedom lower limb exoskeleton worn by a human test person. Note to Practitioners —Control of “physical human–robot interaction” can be achieved by the mechanical parts of the variable stiffness actuator (VSA). However, the mechanical construction for stiffness variation may limit the capacity to achieve low output stiffness and fast stiffness variation in speed. These limitations may become more evident in the assistance/rehabilitation robot applications. To overcome these limitations, the impedance control scheme can be employed to achieve a programmable impedance range and impedance variation speed. This control scheme has been widely applied on the fixed-compliance joint but lacks a way to be implemented on the VSA joint because of its existing capacity to control the impedance with the mechanical construction. This article presents a novel application of the impedance-controlled VSA used on a lower limb robot. We describe how to adjust the actuator stiffness to cooperatively work with the adaptive impedance control scheme. Based on our approach, the robot with the impedance-controlled VSA joint can extend the capacity of bandwidth and low output impedance. This is an improvement on the impedance-controlled fixed-compliance joint. The cooperative control framework presented here was tested on an exoskeleton system with two healthy test persons and is also applicable to other actuator prototypes. Future research aims to employ this system for actual patient training.

Due to the inherent limitations of soft grippers, such as low stiffness and low load-bearing capacity, it is necessary to incorporate variable stiffness mechanisms to enhance their performance. Inspired by the twisted string actuator, a variable stiffness actuator is proposed, which alters friction through twisting tendons and generates antagonistic force with the pulling force on the driving tendon to achieve stiffness variation. This method combines the principles of fiber jamming and the antagonistic principle. The effectiveness of the bending deformation and variable stiffness design was validated through finite element simulations. Based on this, a hardware platform for the variable stiffness soft gripper was established, and bending tests and stiffness measurements were conducted on the variable stiffness soft fingers. The experiment results align closely with the finite element simulation results, indicating that the proposed variable stiffness actuator provides 333% stiffness enhancement. Additionally, measurements of the peak grasping force and grasping tests of the variable stiffness soft gripper are conducted. The experimental results demonstrate that this variable stiffness actuator can effectively enhance soft grippers’ stiffness and grasping capability.