Variable impedance actuators: A review <s> Producing nonlinear springs <s> Problems with the control and compliance of pneumatic systems have prevented their widespread use in advanced robotics. However, their compactness, power/weight ratio, and simplicity are factors that could potentially be exploited in sophisticated dextrous manipulator designs. This paper considers the development of a new high power/weight and power/volume braided pneumatic muscle actuator (PMA) having considerable power output potential, combined with controllable motion and inherent compliance to prevent damage to handled objects. Control of these muscles is explored via adaptive pole-placement controllers. Experimental results indicate that accurate position control of 1/spl deg/ is feasible, with power/weight outputs in excess of 1kW/kg at 200kPa. > <s> BIB001 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> This paper is concerned with the design and control of actuators for machines and robots physically interacting with humans, implementing criteria established in our previous work [1] on optimal mechanical-control co-design for intrinsically safe, yet performant machines. In our Variable Impedance Actuation (VIA) approach, actuators control in real-time both the reference position and the mechanical impedance of the moving parts in the machine in such a way to optimize performance while intrinsically guaranteeing safety. In this paper we describe an implementation of such concepts, consisting of a novel electromechanical Variable Stiffness Actuation (VSA) motor. The design and the functioning principle of the VSA are reported, along with the analysis of its dynamic behavior. A novel scheme for feedback control of this device is presented, along with experimental results showing performance and safety of a one-link arm actuated by the VSA motor. <s> BIB002 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> This paper reports on the second generation of the pleated pneumatic artificial muscle (PPAM) which has been developed to extend the lifespan of its first prototype. This type of artificial muscle was developed to overcome dry friction and material deformation which is present in the widely used McKibben muscle. The essence of the PPAM is its pleated membrane structure which enables the muscle to work at low pressures and at large contractions. There is growing interest in this kind of actuation for robotics applications due to its high power to weight ratio and adaptable compliance, especially for legged locomotion and robot applications in direct contact with a human. This paper describes the design of the second-generation PPAM, for which specifically the membrane layout has been changed. In terms of this new layout the mathematical model, developed for the first prototype, has been reformulated. This paper gives an elaborate discussion on this mathematical model that represents the force generation an... <s> BIB003 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> This paper presents design and performance of a novel joint based actuator for a robot run by variable stiffness actuation, meant for systems physically interacting with humans. This new actuator prototype (VSA-II) is developed as an improvement over our previously developed one reported in [9], where an optimal mechanical-control co-design principle established in [7] is followed as well. While the first version was built in a way to demonstrate effectiveness of variable impedance actuation (VIA), it had limitations in torque capacities, life cycle and implementability in a real robot. VSA-II overcomes the problem of implementability with higher capacities and robustness in design for longer life. The paper discusses design and stiffness behaviour of VSA-II in theory and experiments. A comparison of stiffness characteristics between the two actuator is discussed, highlighting the advantages of the new design. A simple, but effective PD scheme is employed to independently control joint-stiffness and joint-position of a 1-link arm. Finally, results from performed impact tests of 1- link arm are reported, showing the effectiveness of stiffness variation in controlling value of a safety metric. <s> BIB004 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> This book provides a comprehensive and updated insight into dielectric elastomers; one of the most promising classes of polymer-based smart materials and technologies. This technology can be used in a very broad range of applications, from robotics and automation to the biomedical field. The need for improved transducer performance has resulted in considerable efforts towards the development of devices relying on materials with intrinsic transduction properties. These materials, often termed as "smart or "intelligent , include improved piezoelectrics and magnetostrictive or shape-memory materials. Emerging electromechanical transduction technologies, based on so-called ElectroActive Polymers (EAP), have gained considerable attention. EAP offer the potential for performance exceeding other smart materials, while retaining the cost and versatility inherent to polymer materials. Within the EAP family, "dielectric elastomers , are of particular interest as they show good overall performance, simplicity of structure and robustness. Dielectric elastomer transducers are rapidly emerging as high-performance "pseudo-muscular actuators, useful for different kinds of tasks. Further, in addition to actuation, dielectric elastomers have also been shown to offer unique possibilities for improved generator and sensing devices. Dielectric elastomer transduction is enabling an enormous range of new applications that were precluded to any other EAP or smart-material technology until recently. This book provides a comprehensive and updated insight into dielectric elastomer transduction, covering all its fundamental aspects. The book deals with transduction principles, basic materials properties, design of efficient device architectures, material and device modelling, along with applications. * Concise and comprehensive treatment for practitioners and academics * Guides the reader through the latest developments in electroactive-polymer-based technology * Designed for ease of use with sections on fundamentals, materials, devices, models and applications <s> BIB005 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> Different, adaptable, passive-compliant actuators have been developed recently such as the antagonistic setup of two Series Elastic Actuators, the Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator, the Actuator with Mechanically Adjustable Series Compliance, and the Variable Stiffness Actuator. The main purpose of these designs is to reduce the energy consumption of walking/running robots and prostheses. This paper presents a design formulation to link the different mechanical designs together, and a study on the power consumption of these actuators. <s> BIB006 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> In this paper we introduce a classification of intrinsically compliant joint mechanisms. Furthermore, we outline design considerations for realizing such devices in order to match the requirements for robust and performant actuation. Based on this elaboration, a new design concept is presented, the DLR QA-Joint. Its performance is investigated by various experiments, covering velocity increase using the elastic energy, joint protection capabilities, and control performance. <s> BIB007 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> Dielectric elastomers are a subclass of electronic EAPs able to produce large deformations (and thus mechanical work) when an external electric field is applied. While the intrinsic compliance of this kind of polymeric actuators have been always addressed as major benefit with respect to traditional electromagnetic motors, unable to fully capture the capabilities and mechanical properties of biological muscles, their polymeric nature poses peculiar challenges in controlling a system which is subject to nonlinearities, hysteresis and viscous creep behavior. In this paper we explore the controllability properties of a simple rotational joint driven by two dielectric elastomer actuators arranged in an antagonistic configuration. A number of sensors are used to obtain information about the state of controlled system: the angular position of the joint is measured by an angular encoder, custom-designed tension sensors are used to monitor the tension of the two driving tendons and linear encoders provide accurate measurements of the displacements generated by the two actuators. Using this feedback information, a control algorithm has been implemented on a microcontroller unit in order to independently activate the two actuators, allowing a closed loop control of both the angular position of the joint (position control) and the tensions of its tendons (force control). A description of the developed control strategy and its performances under different load conditions are discussed in this paper. <s> BIB008 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> An anthropomorphic hand arm system using variable stiffness actuation has been developed at DLR. It is aimed to reach its human archetype regarding size, weight and performance. The main focus of our development is put on robustness, dynamic performance and dexterity. Therefore, a paradigm change from impedance controlled, but mechanically stiff joints to robots using intrinsic variable compliance joints is carried out. <s> BIB009 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> Focusing on the physical interaction between people and machines within safety constraints in versatile situations, this paper proposes a new, efficient actuation approach, continuous-state coupled elastic actuation (CCEA), to provide oncoming human-machine systems with an intrinsic programmable stiffness capacity to shape output force corresponding to the deviation between human motions and set positions of the system. As one of all the possible CCEA systems, a prototype of a 2-DOF coupled elastic actuator is designed to provide a compromise between performance and safety. Using a pair of antagonistic four-bar linkages, the inherent stiffness of the system can be adjusted dynamically. Compared to the state-of-the-art variable stiffness actuators, the CCEA system is unique in that it can achieve near zero mechanical stiffness in an efficient way. In addition, a human-robot interaction model is built to investigate the controlled bandwidth and safety of the CCEA system. For the application of assistive exercises, this study also proposes two kinds of controls for assistive exercises. Finally, a CCEA exoskeleton is built for elbow rehabilitation. Both simulations and experiments are conducted to show some desired properties of the proposed CCEA system. <s> BIB010 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> We propose a prototype of a Variable Stiffness Actuator (VSA) conceived with low cost as its first goal. This approach was scarcely covered in past literature. Many recent works introduced a large number of actuators with adjustable stiffness, optimized for a wide set of applications. They cover a broad range of design possibilities, but their availability is still limited to small quantities. This work presents the design and implementation of a modular servo-VSA multi-unit system, called VSA-CubeBot. It offers a customizable platform for the realization and test of variable stiffness robotic structures with many degrees of freedom. We present solutions relative to the variable stiffness mechanism, embedded electronics, mechanical and electrical interconnections. Characteristics, both theoretic and experimental, of the single actuator are reported and, finally, five units are interconnected to form a single arm, to give an example of the many possible applications of this modular VSA actuation unit. <s> BIB011 </s> Variable impedance actuators: A review <s> Producing nonlinear springs <s> Variable stiffness actuators realize a novel class of actuators, which are capable of changing the apparent output stiffness independently of the output position. This is mechanically achieved by the internal introduction of a number of elastic elements and a number of actuated degrees of freedom (DOFs), which determine how the elastic elements are sensed at the output. During the nominal behavior of these actuators, the power flow from the internal actuated DOFs can be such that energy is undesirably stored in the elastic elements because of the specific kinematic structure of the actuator. In this study, we focus on the analysis of the power flow in variable stiffness actuators. More specifically, the analysis is restricted to the kinematic structure of the actuators, in order to show the influence of the topological structure on the power flow, rather than on the realization choices. We define a measure that indicates the ratio between the total amount of power that is injected by the internal actuated DOFs and the power that is captured by the internal elastic elements which, therefore, cannot be used to do work on the load. In order to define the power-flow ratio, we exploit a generic port-based model of variable stiffness actuators, which highlights the kinematic properties of the design and the power flows in the actuator structure. <s> BIB012
To obtain adaptable stiffness in an antagonistic setup, the springs need to be nonlinear  with a quadratic force-length function forming the most common tendon elastic characteristics  . This design (with two identical antagonistic springs) results in a constant joint stiffness characteristic, independent of the joint angle deflection. Also rubbers and polymers are non-hookean and can be shaped to create nonlinear elastic behavior. Fig. 5 presents some possibilities. A first option is to use variable pitch progressive springs where each coil is spaced differently with a variable spring rate (Fig. 5a ). The different coils are achieved with variable pitch, conical or mixed. When free, the spring initially is easily compressed, however, as more forces are applied, the coils on a progressive spring come closer and at a certain point, coils at the top 1/4 touch, finally becoming inactive, and that makes the spring stiffer. Tonietti et al. BIB002 describe the Variable Stiffness Actuator (VSA) where the nonlinearity is created by a linear spring pushing the tendon into a triangle (Fig. 5b) . The height of this triangle relative to half base determines the stiffness of the mechanism. Disadvantages are the limited life cycle and load capacity of the timing belt. This mechanism has been used in a simplified form in  (Fig. 5c ). To further simplify the design one pulley can act as the mechanism winder as seen in the DLR hand/arm system BIB009 . Others, such as Migliore et al. BIB010 use shaped pieces, over which two wheels roll to transform the characteristic in a nonlinear shape (see Fig.  5d ). The centers of the wheels are interconnected by a linear spring. With this design the spring force-elongation characteristic can be chosen during the design phase, as well as the resulting compliance characteristic of the overall system. The drawback is the size, extra complexity, and friction in the quadratic spring mechanism. The QA joint uses a cam profile with rollers to implement a rotational setup BIB007 . The VSA-II BIB004 and VSA-HD BIB011 have a four-bar mechanism, which is a special case of Grashof four-bar linkage (Grashof neutral linkage), Fig.  5e . By appropriate link lengths selection the nonlinear relationship between input and output link angles can be regulated. Huang et al. BIB010 used an antagonistic pair of four-bar linkages where the linear spring is placed between two opposing nodes and the nonlinear output force is obtained from the two other nodes. Pneumatic designs such as Pneumatic Artificial Muscles (PAM's), with the McKibben muscles the most well-known , which when pressurized, contract axially while expanding radially can also be used (Fig. 5f) [45] BIB001 . Here air compressibility makes them inherently compliant and spring-like, however, braid friction can cause hysteresis problems and dead bands making them difficult to control. The Pleated Pneumatic Artificial Muscle (PPAM, BIB003 [46]) reduces hysteresis and overcomes the threshold of pressure (deadband). Pneumatic muscles have a high power to weight ratio and can be directly coupled to the joint without gearing, but each joint needs two actuators and the resultant characteristic can be highly nonlinear. The drawbacks of a joint actuated by two pneumatic muscles are the nonlinear characteristic, the slow dynamics (especially depressurizing the muscle is slow), the presence of hysteresis, and the need for pressurized air. Electroactive Polymers (EAPs) are another candidate technology that produce large deformations under an external electric field and they have the necessary nonlinear stress-strain relationship. Randazzo et al. BIB008 working on a rotational joint driven by two antagonistic Dielectric Elastomer Actuators (DEA) showed that the joint stiffness change is small. DEAs are superior to traditional electromagnetic actuators in terms of weight and energy efficiency, but they are still slower, produce low forces and require high voltages to operate BIB005 . This subclass uses nonlinear springs, which is often a drawback, but the antagonistic springs also reduce energy efficiency and energy storage capacity. Hurst and Rizzi  abandoned the antagonistic setup in Mabel calculating that this significantly reduced energy storage capacity as energy must transferred from one spring to another rather than directly to the joint. Another study BIB006 described how an antagonistic setup using two SEA consumes more energy for a certain motion compared to a Maccepa actuator (The Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator). Carloni et al. BIB012 developed a metric for comparing the energy efficiency of VSA designs with results in accordance with BIB006 . 