Variable impedance actuators: A review <s> Inertial actuators <s> We have developed a single wheel, gyroscopically stabilized robot. This is a novel concept for a mobile robot that provides dynamic stability for rapid locomotion. The robot is a sharp-edged wheel actuated by a spinning flywheel for steering and a drive motor for propulsion. The spinning flywheel acts as a gyroscope to stabilize the robot and it can be steered by tilting. This robot is nonholonomic in nature, underactuated and inherently unstable in the lateral direction. In this paper, we first develop a three-dimensional (3-D) nonlinear dynamic model and investigate the dynamic characteristics of the robot. We conduct simulations and real-time experiments to verify the model. Both simulations and experiments show that the flywheel has a significant stabilizing effect on the robot. Then, we can decouple the longitudinal and lateral motions of the robot by linearization. We propose a linear state feedback to stabilize the robot at different lean angles, so as to control the steering velocity of the robot indirectly, because the robot steers only by leaning itself to a predefined angle. For the task of path following, we design a controller for tracking any desired straight line without falling. In the controller, we first design the linear and steering velocities for driving the robot along the desired straight line by controlling the path curvature. We then apply the linear state feedback to stabilize the robot at the predefined lean angle such that the resulting steering velocity of the robot converges to the given steering velocity. This work is a significant step toward fully autonomous control of such a dynamically stable but statically unstable system. <s> BIB001 </s> Variable impedance actuators: A review <s> Inertial actuators <s> The purpose of a hybrid powertrain is to reduce fuel consumption and emissions by the regeneration of braking energy and by minimising inefficient part load operation of the engine. This must be accomplished whilst maintaining vehicle acceleration performance as expected by drivers; this currently delivered by a powerful engine, always available. Above all, the additional life cycle costs of a successful hybrid powertrain must not be significantly greater than that of the conventional engine and transmission it replaces otherwise adoption will be greatly inhibited. The majority of hybrid powertrains available commercially and under development rely on a large electrochemical battery and electric motor to provide the second means of propulsion in place of, or to supplement, the engine. The popularity of this approach is based on the availability and mature development status of batteries and electric motors. However, there are serious drawbacks in efficiency and cost, particularly when the hybrid powertrain operates most effectively in surge power mode, providing and absorbing power levels at similar levels to engine maximum output. Inefficiencies occur due to the large number of energy transformations, and battery life is limited by the number of charge and discharge cycles, an effect made worse when current levels are high. A flywheel is proposed as a superior alternative to the battery which can provide power levels as high as the engine, limited only by the capacity of the mechanical drive. High levels of energy capacity are not required as the energy stored need not exceed the kinetic energy of a vehicle travelling at moderate speed. High cost, practicality, safety and gyroscopic effects are often cited as reasons against the use of flywheels in hybrids. These are all addressed in a description of an Imperial College flywheel design that has been developed specifically for hybrid vehicle application. This flywheel has been manufactured and early test results are also reported. Even more robust, lower cost design approaches have been developed by HyKinesys and partners and these also include consideration of the CVT systems used to transmit power from flywheel to vehicle and back. The flywheel designs are better described as flycylinders, and are denoted by the name "PowerBeams" for practical commercial application. In addition to the above, the recent announcement by the FIA to allow energy storage devices to be used in Formula One in just two years time is a substantial force for change. Such systems must also be reasonably lightweight, robust and reliable. The winner in racing is then likely to challenge for supremacy on the road. Kinetic energy storage systems are amongst the potential contenders identified by the FIA. <s> BIB002 </s> Variable impedance actuators: A review <s> Inertial actuators <s> The control of a robot's mechanical impedance is attracting increasing attention of the robotics community. Recent research in Robotics has recognized the importance of Variable Stiffness Actuators (VSA) in safety and performance of robots. An important step in using VSA for safety has been to understand the optimality principles that regulate the synchronized variation of stiffness and velocity when moving in the shortest time while limiting possible impact forces (the safe brachistochrone problem). In this paper, we follow a similar program of understanding the use of VSA in performance enhancement, looking at very dynamic tasks where impacts are maximized. To this purpose we address a new optimization problem that consists in choosing the inputs for maximizing the velocity of a link at a given final position, such as, e.g., for maximizing the effect of a hammer impact. We first study the problem with fixed stiffness, and show that, under realistic modeling assumptions, there does exist an optimal linear spring for the given inertia and motor. We then study optimal control of VSA and show that varying the spring stiffness during the execution of the hammering task improves the final performance substantially. The optimal control law is obtained analytically, thus providing insight in the optimality principles underpinning general VSA control. Finally, we show the practicality of our theoretical results with experimental tests. <s> BIB003
Since impedance is defined as the differential operator relating the time course of reaction force F(t) to the time course of position (P(t), the impedance of a inertia M is (in the Laplace domain for simplicity): So a mass can also be used as a storage of kinetic energy apart from a spring and damper. For example in a hammer kinetic energy can be accumulated to drive a nail in a piece of wood BIB003 . A spinning flywheel is employed to act as a gyroscope to stabilize the robot and it can be steered by tilting BIB001 or used to store and release rotational energy for example used in the vehicles as Formula 1 BIB002 . Modulation of the impedance can be achieved by for example a variable transmission.