Variable impedance actuators: A review <s> What is a Variable Impedance Actuator? <s> Dynamic interaction with the environment is fundamental to the process of manipulation. This paper describes an approach to the design of ‘interaction controllers’ and contrasts this with an approach to servo design. The need for ‘coupled stability’ and ‘interactive behaviour’ specifications is motivated. A necessary and sufficient condition to ensure the stability of a linear manipulator coupled at a single interaction port to a linear, passive environment is found. It is shown that this condition may be extended to a broad class of active environments, and a simple test for coupled stability, based on the root locus, is presented. Two interaction controller designs for a linear manipulator are presented. Interactive behaviour is analysed in the frequency domain by comparison with the behaviour of a target model. A simple controller shows strong stability properties, but poor behaviour; a more sophisticated design shows that it is possible to achieve desirable behaviour while retaining stability guarantees. <s> BIB001 </s> Variable impedance actuators: A review <s> What is a Variable Impedance Actuator? <s> This book describes the design concept and discusses the control issues related to the performance of a direct-drive robot, specifically, a direct-drive mechanical arm capable of carrying up to 10 kilograms, at 10 meters per second, accelerating at 5 G (a unit of acceleration equal to the acceleration of gravity). These are remarkable achievements compared to current industrial robots that move with speeds on the order of 1 meter per second."Direct-Drive Robot "presents the most current research in manipulator design and control, emphasizing the high-performance direct-drive robot arm in which the shafts of articulated joints are directly coupled to the rotors of motors with high torque. It describes fundamental technologies of key components such as motors, amplifiers and sensors, arm linkage design, and control system design, and makes significant contributions in the areas of power efficiency analysis, dynamic mass balancing, and decoupling theory.The book provides a good balance between theory and practice, covering the practical design and implementation of this special robot as well as the theoretical design tools.Contents: Part I: Direct-Drive Technologies. Introduction. Components. Part II: Arm Design Theory. Power Efficiency. Arm Design for Simplified Dynamics. Actuator Relocation. Design of Decoupled Arm Structures. Part III: Development of the MIT Arm. Mechanisms. Control Systems. Part IV: Selected Papers on Direct-Drive Robot Design and Control.Haruhiko Asada is an Associate Professor, Kyoto University, and Lecturer at MIT He has built two prototypes of the direct-drive arm described here. Kamal Youcef-Toumi is an Assistant Professor, Department of Mechanical Engineering, System Dynamics and Controls Division at MIT. He has worked for three years with Asada on the development of the MIT high speed directdrive robot. <s> BIB002 </s> Variable impedance actuators: A review <s> What is a Variable Impedance Actuator? <s> How could the body influence our thinking when it seems obvious that the brain controls the body? In How the Body Shapes the Way We Think, Rolf Pfeifer and Josh Bongard demonstrate that thought is not independent of the body but is tightly constrained, and at the same time enabled, by it. They argue that the kinds of thoughts we are capable of have their foundation in our embodiment -- in our morphology and the material properties of our bodies. This crucial notion of embodiment underlies fundamental changes in the field of artificial intelligence over the past two decades, and Pfeifer and Bongard use the basic methodology of artificial intelligence -- "understanding by building" -- to describe their insights. If we understand how to design and build intelligent systems, they reason, we will better understand intelligence in general. In accessible, nontechnical language, and using many examples, they introduce the basic concepts by building on recent developments in robotics, biology, neuroscience, and psychology to outline a possible theory of intelligence. They illustrate applications of such a theory in ubiquitous computing, business and management, and the psychology of human memory. Embodied intelligence, as described by Pfeifer and Bongard, has important implications for our understanding of both natural and artificial intelligence. <s> BIB003 </s> Variable impedance actuators: A review <s> What is a Variable Impedance Actuator? <s> Most of today's robots have rigid structures and actuators requiring complex software control algorithms and sophisticated sensor systems in order to behave in a compliant and safe way adapted to contact with unknown environments and humans. By studying and constructing variable impedance actuators and their control, we contribute to the development of actuation units which can match the intrinsic safety, motion performance and energy efficiency of biological systems and in particular the human. As such, this may lead to a new generation of robots that can co-exist and co-operate with people and get closer to the human manipulation and locomotion performance than is possible with current robots. <s> BIB004
To define what a Variable Impedance Actuator (VIA) is, it is useful to start by defining a non-VIA (traditional stiff) actuator. A stiff actuator is a device, able to move to a specific position or track a predefined trajectory. Once a position is reached, the actuator will hold this position, (ideally) whatever the external forces (within the force limits of the device). It is a position source, i.e. a system with a very high (ideally infinite) mechanical impedance. This behavior is obtained when a motor has a high gear ratio (eg servomotors) aiming to be as stiff as possible  . Such actuators have excellent trajectory tracking with a high bandwidth and high accuracy. They are common in industrial robots. A VIA in contrast deviates from its set equilibrium position, depending on the external forces and the mechanical properties of the actuator (mostly inertia, stiffness and damping factors). Equilibrium is defined as the position where the actuator generates zero force or torque (also called virtual position by Hogan  ). This concept is specific to VIA actuators, since it does not exist for stiff actuators. An extreme case is where the impedance is zero and the actuator forms a force/torque source or transparent actuator, eg gravity is a force source. Examples where a force/torque source are approached are direct drive motors BIB002 or constant torque springs. VIAs are important in Embodied Intelligence. Pfeifer and Bongard BIB003 state that adaptive behavior is not just control and computation, but it emerges from the complex and dynamic interaction between the robot's morphology, sensory-motor control, and environment. Through smart design of the body and the actuators part of the computational intelligence can be outsourced to the embodied intelligence making many tasks become simpler. Position control in a task in which a robot interacts with the environment, is not a properly posed problem because the controller is dependent on parameters, which are out of the control potential BIB001  . Yet, controlling the impedance and the equilibrium position is a well-posed problem that is independent of the knowledge of the environment, if within certain boundaries. Applications of VIA are consequently found were robots must physically interact with an unknown and dynamic environment and the control body-actuator system must have abilities like BIB004 : • Efficiency e.g. natural gait generation, adaptation in legged locomotion and prosthetics for lower limbs, explosive motions such as throwing or kicking; • Robustness to external perturbations and unpredictable model errors (changes) of the environment, of the robot kinematics and dynamics, or of the dynamics of a human interacting with it; • Adaptability and force accuracy in the interaction with the operator, in applications in which continuous contact and accurate force exchange is necessary, such as in "hands-on" assistive devices, rehabilitation, exoskeletons and haptics; • Safety to humans (and resilience to self-damage) in operations where the robot has fast, accurate motions, while cooperating, physically interacting or even possibly colliding with the humans and their environment, including other robots. Variable Impedance Actuators will be categorized depending on how their stiffness and damping can be achieved, Fig. 1 . This is a revision of the work by Van Ham et al.  . A first division can be made between active impedance by control, inherent compliance and damping actuators, inertial and a combination of them. In this section the terms impedance, admittance, compliance, stiffness and damping are introduced and a relationship between them is provided. Mechanical interaction between two systems A and B can be modeled looking at the dynamic relation between the variables which characterise the energy exchange and interaction behaviour between the two systems. The resulting interaction force and motion between A and B cannot be attributed solely to one of the systems but is the combination of an intrinsic property (behaviour) of A and an intrinsic property (behaviour) of B. These intrinsic behaviours are referred to as impedance and admittance. If the system A is modelled as an impedance, system B must be modelled as an admittance to complement the other. A mechanical impedance is a dynamic relation which generates a force (in time) as a function of a displacement (in time). This differential relation can be linear (modellable usually with Laplace methods) or non linear (modellable with nonlinear functional analysis tools, such as e.g. jet bundles). Admittance is the complement of impedance. Stiffness is the differential relation between infinitesimal differences in force and po-sition. Compliance is the inverse. Stiffness and compliance are related to elastic energy storage. Damping is a differential relation between infinitesimal changes in force and velocity, and is related to irreversible transduction of mechanical energy to heat and as such takes energy out of the systems.