Variable Stiffness Actuator Research Articles

Human-Robot Interaction Control for Robot Driven by Variable Stiffness Actuator With Force Self-Sensing

Robots driven by variable stiffness actuators (VSAs) have been an important technology as they could provide intrinsic compliance for safe human-robot interaction. The internal compliance of VSA also makes it possible for the actuator to act as a torque sensor and estimate the external force. This paper presents a physical human-robot interaction control strategy for robots driven by VSA with force self-sensing. The VSA adopted in the robotic system improves the safe performance of physical human-robot interaction. The interaction force is directly estimated by measuring the internal deformation of VSA with a stiffness region control which ensures a better resolution of force estimation and avoids transgressing the limits of deformation simultaneously. Then an online estimation method for the human motion intention is developed to generate the desired trajectory based on the estimated force. The impedance control is designed to enable the robot to actively follow the desired trajectory with compliance. Under the proposed control strategy, the robot is capable of actively tracking the “motion intention” of human with the estimated interaction force, which is demonstrated through experiment studies.

Structure-Controlled Variable Stiffness Robotic Joint Based on Multiple Rotary Flexure Hinges

Variable stiffness actuator (VSA) plays an important role for achieving safety and robustness for robots to physically interact with environments. This article proposes a structure-controlled approach in developing a new variable stiffness robotic joint with the merits of compactness, high stiffness, and high displacement-to-stiffness ratio. Unlike the common methods of using antagonist springs and lever concept, the structure-controlled approach achieves stiffness variation through the adjustment of mechanical structure configuration inside the actuator. Specifically, the stiffness variation is realized by changing the effective second moment of area through rotating a combination of leaf flexure hinges arranged in a radial configuration. A range of configurations are studied and the configuration we identified has the advantages of minimum unbalanced twists in the mechanism while providing high transmission torque, large stiffness, range and minimum lateral buckling effects. The performance characteristics are accomplished through a novel variable stiffness mechanism and a position-based control strategy for both position and torque control modes. A prototype system was implemented to verify the characteristic and performance of the design concept. It demonstrated that the new VSA system is effective for realising independent joint-stiffness and joint-position control of robot joints.

A Novel Rotational Actuator With Variable Stiffness Using S-Shaped Springs

In this article, we propose a novel rotational variable stiffness actuator that uses S-shaped springs as elastic elements. The S-shaped springs are designed based on the principle of variable beam length, which allows for an easily customizable and wide-ranging stiffness regulation from a minimum value to near infinite. The stiffness can be smoothly regulated online by rotating the S-shaped springs, resulting in a compact stiffness regulation mechanism. Moreover, a planetary gear differential is used to drive the stiffness regulation mechanism such that both the stiffness control motor and the main drive motor can be placed at the proximal part. This configuration effectively reduces the reflected inertia of the moving parts, which helps to achieve a compact design and improve the control performance. The proposed actuator ranks high among designs of the similar output power in terms of the power-to-weight ratio and the power-to-volume ratio; therefore, the compactness of the proposed design is verified. Besides, the stiffness regulation speed of the proposed design also ranks high among the designs. Consequently, the actuator can be used for fast stiffness regulation. For robust position tracking under different operating conditions, a disturbance observer is used to estimate the mismatched lumped disturbance caused by the load torque and model uncertainties. To further improve the control performance, a sliding mode control term is introduced to compensate for the disturbance estimation error. The stability of the closed-loop system is proved using the Lyapunov method. Experimental results under different operating conditions have verified the validity of the novel actuator and the proposed controller.

Configuration synthesis of variable stiffness mechanisms based on guide-bar mechanisms with length-adjustable links

A variable stiffness mechanism (VSM) is used to connect the principal motor and the load of a serial-configuration variable stiffness actuator (VSA) and can adjust the intrinsic stiffness of the VSA to improve the dynamic performance, energy efficiency, and safety of robotic systems. This paper presents a new configuration synthesis method to design VSMs based on guide-bar mechanisms through the addition of linear springs and the use of length-adjustable links. The springs are used to constrain the mechanism and generate compliant behaviour, and the length-adjustable links are used to adjust the transmission ratio and modulate the apparent stiffness. The conditions for designing VSMs with symmetrical stiffness characteristics, capable of low-power cost stiffness modulation and decoupled control of equilibrium position and stiffness, are also derived. By selecting different spring-constrained joints, length-adjustable links, initial angles of input joints, and length ranges of the adjustable links, twelve energy-efficient VSMs with different stiffness performance are constructed. In addition, the concept design of a VSA that can vary its stiffness from zero to infinity is presented; this design uses only one linear torsion spring without a preload.

Low Impedance-Guaranteed Gain-Scheduled GESO for Torque-Controlled VSA With Application of Exoskeleton-Assisted Sit-to-Stand

This article investigates a closed-loop torque-controlled variable stiffness actuator (VSA) combined with a disturbance observer for enhancing low output impedance. We implement the generalized extended state observer (GESO) for conveniently testing the stability of the time-varying VSA system. In our application, the GESO is also required to serve the operation of the low- and high-impedance task. Here, the most important aspect is to consider the influence of the physical stiffness on the output impedance, because the VSA has been regulated with the closed-loop torque control. Through the interaction-torque experiments, we verify that using the fast dynamics GESO with the low-stiffness actuator can achieve low output impedance and stable interaction under the reachable frequency of a human. These properties contribute to perform the low-impedance task. When performing the high-impedance task, where a large torque command is needed, the high-stiffness actuator and the slow dynamics GESO are implemented to achieve high bandwidth and proper tracking performance. The continuously variable observer responses in accordance with the stiffness values are achieved via the gain-scheduling control. Moreover, the present closed-loop linear parameter varying system can be verified to be quadratically stable. The VSA system is then implemented on a knee exoskeleton for a sit-to-stand application. The reference command of the exoskeleton is a joint torque, calculated from the inverse dynamics. This torque signal is also used as the reference command of the stiffness motor of the VSA. The effectiveness of the exoskeleton system is experimentally verified with one healthy volunteer. Subsequently, another two healthy volunteers also successfully experienced the system.

Design and Analysis of New Haptic Joysticks for Enhancing Operational Skills in Excavator Control

Abstract The design perspective of interfaces has strong implications on operator intuition and safety. Haptics enabled user interfaces can enhance operator skills and enhance interactivity. In this paper, an innovative method of haptic feedback in joysticks is presented for excavator control. Haptic illusion in the device is generated with the concept of the variable stiffness actuation mechanism. The force feedback (FFB) is rendered through “haptic links,” based on the effect of digging force at each joint. The stiffness in the device varies dynamically with the load and restricts the operator motion with a resistive torque in the range of 0–0.9 Nm. The haptic joystick aims to render high-fidelity kinesthetic feedback that can help to mitigate the operator error in loading operations. The user evaluation with the joystick showed an improvement of 40% in the volume of material removed and a significant drop in error rate related to force patterns and collisions.

Globally optimal passive compliance control for tasks having multiple homotopy classes

Redundant serial manipulators with variable stiffness actuators (VSAs) are capable of passive compliance control, in which the elastic behavior of the end-effector is controlled for robust interaction with a stiff environment. This paper addresses the problem of finding the globally optimal joint manipulation path (sequence of joint positions and compliances) that yields a desired task manipulation path (sequence of end-effector positions and compliances) when there is one degree of redundancy. The space of admissible joint paths can be very complex, with multiple bifurcations resulting in multiple homotopy classes of joint paths. Bifurcations due to singularities in the combined kinematic and compliance joint space are quickly identified using geometric conditions and root-finding. Bifurcations due to joint limits are identified using a novel path planner that traces the solution space boundary edges. With the bifurcations located, joint paths in all homotopy class are generated and deformed into locally optimal paths. The best of these is very likely the globally optimal joint path. Concepts are illustrated in a case study for particle-planar passive compliance control with a 3R-VSA manipulator.

Importing the Human Factor into Safe Human–Robot Interaction Function Using the Bond Graph Method

SUMMARYThe variable stiffness actuator (VSA) is helpful to realize the post-collision safety strategies for safe human–robot interaction.1 The stiffness of the robot will be reduced to protect the user from injury when the collision between the robot and human occurs. However, The VSA has a mechanism limit constraint that can cause harm to users even if the stiffness is minimized. Accordingly, in this article, a concept combining danger index and robust fault detection and isolation is presented and applied to active–passive variable stiffness elastic actuator (APVSEA). APVSEA can actively change joint stiffness with the change of danger index. Experimental results show that this concept can effectively confirm the fault mode and provide additional protection measures to ensure the safety of users when the joint stiffness has been adjusted to the minimum.

Walking with a powered ankle-foot orthosis: the effects of actuation timing and stiffness level on healthy users

BackgroundIn the last decades, several powered ankle-foot orthoses have been developed to assist the ankle joint of their users during walking. Recent studies have shown that the effects of the assistance provided by powered ankle-foot orthoses depend on the assistive profile. In compliant actuators, the stiffness level influences the actuator’s performance. However, the effects of this parameter on the users has not been yet evaluated. The goal of this study is to assess the effects of the assistance provided by a variable stiffness ankle actuator on healthy young users. More specifically, the effect of different onset times of the push-off torque and different actuator’s stiffness levels has been investigated.MethodsEight healthy subjects walked with a unilateral powered ankle-foot orthosis in several assisted walking trials. The powered orthosis was actuated in the sagittal plane by a variable stiffness actuator. During the assisted walking trials, three different onset times of the push-off assistance and three different actuator’s stiffness levels were used. The metabolic cost of walking, lower limb muscles activation, joint kinematics, and gait parameters measured during different assisted walking trials were compared to the ones measured during normal walking and walking with the powered orthosis not providing assistance.ResultsThis study found trends for more compliant settings of the ankle actuator resulting in bigger reductions of the metabolic cost of walking and soleus muscle activation in the stance phase during assisted walking as compared to the unassisted walking trial. In addition to this, the study found that, among the tested onset times, the earlier ones showed a trend for bigger reductions of the activation of the soleus muscle during stance, while the later ones led to a bigger reduction in the metabolic cost of walking in the assisted walking trials as compared to the unassisted condition.ConclusionsThis study presents a first attempt to show that, together with the assistive torque profile, also the stiffness level of a compliant ankle actuator can influence the assistive performance of a powered ankle-foot orthosis.

Knee Compliance Reduces Peak Swing Phase Collision Forces in a Lower-Limb Exoskeleton Leg: A Test Bench Evaluation.

Powered lower limb exoskeletons are a viable solution for people with a spinal cord injury to regain mobility for their daily activities. However, the commonly employed rigid actuation and pre-programmed trajectories increase the risk of falling in case of collisions with external objects. Compliant actuation may reduce forces during collisions, thus protecting hardware and user. However, experimental data of collisions specific to lower limb exoskeletons are not available. In this work, we investigated how a variable stiffness actuator at the knee joint influences collision forces transmitted to the user via the exoskeleton. In a test bench experiment, we compared three configurations of an exoskeleton leg with a variable stiffness knee actuator in (i)compliant or (ii)stiff configurations, and with (iii)a rigid actuator. The peak torque observed at the pelvis was reduced from 260.2Nm to 116.2Nm as stiffness decreased. In addition, the mechanical impulse was reduced by a factor of three. These results indicate that compliance in the knee joint of an exoskeleton can be favorable in case of collision and should be considered when designing powered lower limb exoskeletons. Overall, this could decrease the effort necessary to maintain balance after a collision, and improved collision handling in exoskeletons could result in safer use and benefit their usefulness in daily life.

A Novel Mechatronic Kit of Variable Stiffness Manipulators – Design and Implementation

In the developing fields of wearable devices, rehabilitation, and humanoid robotics, variable stiffness actuators (VSAs) are attracting increasing attention. VSA can minimize forces that are exerted by shocks, and can be safely interacted with by their users. They can store and release energy as passive elastic elements. The main goal of this work is to design a variable stiffness mechanism with a lightweight articulated robot arm. The proposed variable stiffness mechanism is based on lever kinematics. An RC servo motor is used to manipulate the leverage and to adjust the stiffness of the mechanism to control the position of a robot arm. Two spring elements absorb the output force from the lever. Such a design can reduce the number of sensing elements that are used in the robotic system and the damage force that is caused by unpredictable external forces. The designed articulated robotic arm uses a worm gear with a 1:40 high gear ratio to increase the payload capacity and reduce the weight of the robot arm. The worm gear has a self-locking function, which reduces the sliding step of the stepping motor. The advantages of the design in this study are the retention of the strength and loading capacity of the robot arm. The software package LabVIEW is used to build the control and measurement environment in which several control syntheses are tested. Numerous experimental results confirm that the design is reliable and has a low cost of implementation in a shock test. The novel mechatronic kit is ideally suitable for use in advanced mechatronic courses for university students. The discussion of the broad issues deliberated in this investigation will be applied to various systems that require variable stiffness manipulators.

Design, modeling and testing of a compact variable stiffness mechanism for exoskeletons

In this paper, the mechanical design of a novel variable stiffness mechanism (VSM) with reconfigurability is presented. The design of VSM is based on a zero-length base link four-bar linkage, integrated with a linear spring. The VSM is able to achieve variable stiffness in adjustable ranges, due to its reconfigurable design. Compared with other similar designs, the new VSM is compact and light weight, and can be used as a standalone module, or integrated with electric motor to build variable stiffness actuator which can be further applied in wearable exoskeletons. In the paper, mathematical models are developed for VSM to reveal the stiffness/torque performance limits. The mathematical models are validated experimentally with a prototype in both static and dynamic tests. The proposed VSM is finally integrated in a wearable elbow exoskeleton.

Environmental adaptive control of a snake-like robot with variable stiffness actuators

This work investigates adaptive stiffness control and motion optimization of a snake-like robot with variable stiffness actuators. The robot can vary its stiffness by controlling magnetorheological fluid (MRF) around actuators. In order to improve the robot's physical stability in complex environments, this work proposes an adaptive stiffness control strategy. This strategy is also useful for the robot to avoid disturbing caused by emergency situations such as collisions. In addition, to obtain optimal stiffness and reduce energy consumption, both torques of actuators and stiffness of the MRF braker are considered and optimized by using an evolutionary optimization algorithm. Simulations and experiments are conducted to verify the proposed adaptive stiffness control and optimization methods for a variable stiffness snake-like robots.

Virtual and physical prototyping of a beam-based variable stiffness actuator for safe human-machine interaction

Abstract This paper reports about the virtual and physical prototyping of an antagonistic Variable Stiffness Actuator (VSA) to be used on robotic arms specifically realized for physical human-robot interaction. Such antagonistic actuation system, which comprises purposely conceived Compliant Transmission Elements (CTEs) characterized by a nonlinear relation between the deflection and the applied torque, allows to simultaneously control both the joint’s position and stiffness. The CTE’s beams geometry, namely slender spline beams, has been defined by means of an automatic routine leveraging on Matlab and ANSYS and allowing for the shape optimization of complex flexures. The synthesized springs are characterized by a predefined quadratic torque-deflection characteristic, which is shown to guarantee a precise stiffness modulation while avoiding the need for a joint’s position sensor. After shape optimization, the CTE is fabricated via additive manufacturing and subsequently tested. The acquired data show a very good consistency with the numerical results, although highlighting a non-negligible hysteresis due to material damping. Therefore, in order to cope with such unavoidable effect along with other parameter uncertainties and unmodeled effects (e.g. static friction), a robust feedback controller is proposed, allowing for the simultaneous and decoupled regulation of joint position and stiffness. Finally, a VSA prototype is produced and tested. Experimental results confirm that the VSA behaves as expected.

Adaptive Robust Force Position Control for Flexible Active Prosthetic Knee Using Gait Trajectory

Active prosthetic knees (APKs) are widely used in the past decades. However, it is still challenging to make them more natural and controllable because: (1) most existing APKs that use rigid actuators have difficulty obtaining more natural walking; and (2) traditional finite-state impedance control has difficulty adjusting parameters for different motions and users. In this paper, a flexible APK with a compact variable stiffness actuator (VSA) is designed for obtaining more flexible bionic characteristics. The VSA joint is implemented by two motors of different sizes, which connect the knee angle and the joint stiffness. Considering the complexity of prothetic lower limb control due to unknown APK dynamics, as well as strong coupling between biological joints and prosthetic joints, an adaptive robust force/position control method is designed for generating a desired gait trajectory of the prosthesis. It can operate without the explicit model of the system dynamics and multiple tuning parameters of different gaits. The proposed model-free scheme utilizes the time-delay estimation technique, sliding mode control, and fuzzy neural network to realize finite-time convergence and gait trajectory tracking. The virtual prototype of APK was established in ADAMS as a testing platform and compared with two traditional time-delay control schemes. Some demonstrations are illustrated, which show that the proposed method has superior tracking characteristics and stronger robustness under uncertain disturbances within the trajectory error in ± 0 . 5 degrees. The VSA joint can reduce energy consumption by adjusting stiffness appropriately. Furthermore, the feasibility of this method was verified in a human–machine hybrid control model.

Design and Modeling of Parallel Two-degree-of-freedom Variable Stiffness Actuator

In this paper, a new 2-DOF variable stiffness actuator based on a 2-DOF spherical wrist parallel mechanism is proposed. A 2-DOF VSA based on a parallel ball wrist mechanism and a parallel arrangement of leaf spring sets is used. Control its stiffness adjustment, analysis its variable stiffness principle and actuator mechanical structure. The parallel arrangement of the leaf spring groups reduces the mass and volume of the joints, enabling simultaneous adjustment of the stiffness. The analytical formula of the rotational stiffness of the actuator is established according to the geometric nonlinearity of the large deflection of the leaf spring.

An Input Observer-Based Stiffness Estimation Approach for Flexible Robot Joints

This letter addresses the stiffness estimation problem for flexible robot joints, driven by variable stiffness actuators in antagonistic setups. Due to the difficulties of achieving consistent production of these actuators and the time-varying nature of their internal flexible elements, which are subject to plastic deformation over time, it is currently a challenge to precisely determine the total flexibility torque applied to a robot's joint and the corresponding joint stiffness. Herein, by considering the flexibility torque acting on each motor as an unknown signal and building upon Unknown Input Observer theory, a solution for electrically-driven actuators is proposed, which consists of a linear estimator requiring only knowledge about the positions of the joints and the motors as well as the drive's dynamic parameters. Beyond its linearity advantage, another appealing feature of the solution is the lack of need for torque and velocity sensors. The presented approach is first verified via simulations and then successfully tested on an experimental setup, comprising bidirectional antagonistic variable stiffness actuators.

Open-Loop Position Control in Collaborative, Modular Variable-Stiffness-Link (VSL) Robots

Collaborative robots open up new avenues in the field of industrial robotics and physical Human-Robot Interaction (pHRI) as they are suitable to work in close approximation with humans. The integration and control of variable stiffness elements allow inherently safe interaction: Apart from notable work on Variable Stiffness Actuators, the concept of Variable-Stiffness-Link (VSL) manipulators promises safety improvements in cases of unintentional physical collision. However, position control of these type of robotic manipulators is challenging for critical task-oriented motions. In this letter, we propose a hybrid, learning based kinematic modelling approach to improve the performance of traditional open-loop position controllers for a modular, collaborative VSL robot. We show that our approach improves the performance of traditional open-loop position controllers for robots with VSL and compensates for position errors, in particular, for lower stiffness values inside the links: Using our upgraded and modular robot, two experiments have been carried out to evaluate the behaviour of the robot during task-oriented motions. Results show that traditional model-based kinematics are not able to accurately control the position of the end-effector: the position error increases with higher loads and lower pressures inside the VSLs. On the other hand, we demonstrate that, using our approach, the VSL robot can outperform the position control compared to a robotic manipulator with 3D printed rigid links.

Robust tracking control for two classes of variable stiffness actuators based on linear extended state observer with estimation error compensation

In this article, a novel robust tracking control scheme based on linear extended state observer with estimation error compensation is proposed for the tracking control of the antagonistic variable stiffness actuator based on equivalent nonlinear torsion spring and the serial variable stiffness actuator based on lever mechanism. For the dynamic models of these two classes of variable stiffness actuators, considering the parametric uncertainties, the unknown friction torques acting on the driving units, the unknown external disturbances acting on the output links and the input saturation constraints, an integral chain pseudo-linear system with input saturation constraints and matched lumped disturbances is established by coordinate transformation. Subsequently, the matched lumped disturbances in the pseudo-linear system are extended to the new system states, and we obtain an extended integral chain pseudo-linear system. Then, we design the linear extended state observer to estimate the unknown states of the extended pseudo-linear system. Considering the input saturation constraints in the extended pseudo-linear system and the estimation errors of the linear extended state observer with fixed preset observation gains, the adaptive input saturation compensation laws and the novel estimation error compensators are designed. Finally, a robust tracking controller based on linear extended state observer, sliding mode control, adaptive input saturation compensation laws, and estimating error compensators is designed to achieve simultaneous position and stiffness tracking control of these two classes of variable stiffness actuators. Under the action of the designed controller, the semi-global uniformly ultimately bounded stability of the closed-loop system is proved by the stability analysis of the candidate Lyapunov function. The simulation results show the effectiveness, robustness, and adaptability of the designed controller in the tracking control of these two classes of variable stiffness actuators. Furthermore, the simulation comparisons show the effectiveness of the proposed estimation error compensation measures in reducing the tracking errors and improving the disturbance rejection performance of the controller.

Decoupled nonlinear adaptive control of position and stiffness for pneumatic soft robots

This article addresses the problem of simultaneous and robust closed-loop control of joint stiffness and position, for a class of antagonistically actuated pneumatic soft robots with rigid links and compliant joints. By introducing a first-order dynamic equation for the stiffness variable and using the additional control degree of freedom, embedded in the null space of the pneumatic actuator matrix, an innovative control approach is introduced comprising an adaptive compensator and a dynamic decoupler. The proposed solution builds upon existing adaptive control theory and provides a technique for closing the loop on joint stiffness in pneumatic variable stiffness actuators. Under a very mild assumption involving the inertia and actuator matrices, the solution is able to cope with uncertainties of the model and, when the desired stiffness is constant or slowly varying, also of the pneumatic actuator. Position and stiffness decoupling is achieved by the introduction of a first-order differential equation for an internal state variable of the controller, which takes into account the time derivative of pressure in the stiffness dynamics. A formal proof of the stability of the position and stiffness tracking errors is provided. An appealing property of the approach is that it does not require higher derivatives of position or any derivatives of stiffness. The solution is validated with respect to several use-cases, first in simulation and then via a real pneumatic soft robot with McKibben muscles. A comparison with respect to existing techniques reveals a more robust position and stiffness tracking skill.