Universal Dynamics of Damped-Driven Systems: The Logistic Map as a Normal Form for Energy Balance

Damped-driven systems are ubiquitous in engineering and science. Despite the diversity of physical processes observed in a broad range of applications, the underlying instabilities observed in practice have a universal characterization which is determined by the overall gain and loss curves of a given system. The universal behavior of damped-driven systems can be understood from a geometrical description of the energy balance with a minimal number of assumptions. The assumptions on the energy dynamics are as follows: the energy increases monotonically as a function of increasing gain, and the losses become increasingly larger with increasing energy, i.e. there are many routes for dissipation in the system for large input energy. The intersection of the gain and loss curves define an energy balanced solution. By constructing an iterative map between the loss and gain curves, the dynamics can be shown to be homeomorphic to the logistic map, which exhibits a period doubling cascade to chaos. Indeed, the loss and gain curves allow for a geometrical description of the dynamics through a simple Verhulst diagram (cobweb plot). Thus irrespective of the physics and its complexities, this simple geometrical description dictates the universal set of logistic map instabilities that arise in complex damped-driven systems. More broadly, damped-driven systems are a class of non-equilibrium pattern forming systems which have a canonical set of instabilities that are manifest in practice.Comment: 26 pages, 31 figure

Humanoid Robots

For many years, the human being has been trying, in all ways, to recreate the complex mechanisms that form the human body. Such task is extremely complicated and the results are not totally satisfactory. However, with increasing technological advances based on theoretical and experimental researches, man gets, in a way, to copy or to imitate some systems of the human body. These researches not only intended to create humanoid robots, great part of them constituting autonomous systems, but also, in some way, to offer a higher knowledge of the systems that form the human body, objectifying possible applications in the technology of rehabilitation of human beings, gathering in a whole studies related not only to Robotics, but also to Biomechanics, Biomimmetics, Cybernetics, among other areas. This book presents a series of researches inspired by this ideal, carried through by various researchers worldwide, looking for to analyze and to discuss diverse subjects related to humanoid robots. The presented contributions explore aspects about robotic hands, learning, language, vision and locomotion

Hiroshima University Research and Technology Guide 2012 Version : Physical Science & Engineering

II Environment/Energy III Design and Manufacturing IV Material/Device V Mechanical Engineering VI Civil Engineering/Architecture VII Computer Science, Information, Communication and System Engineering VIII Measurement & Control/Scientific Analyse

Feedback Control Design for MARLO, a 3D-Bipedal Robot.

This work develops feedback controllers for bipedal walking in 3D on level ground, both in simulation and experimentally. MARLO is a new robot that has been designed for the study of 3D-bipedal locomotion, with the aim of combining energy efficiency, speed, and robustness with respect to natural terrain variations in a single platform. The robot is highly underactuated, having six actuators and, in single support, 13 degrees of freedom. Its sagittal plane dynamics are designed to embody the spring loaded inverted pendulum (SLIP), which has been shown to provide a dynamic model of the body center of mass during steady running gaits in a wide diversity of terrestrial animals. A detailed dynamic model is used to optimize walking gaits with respect to the cost of mechanical transport (cmt), a dimensionless measure of energetic efficiency. A feedback controller is designed that balances the robot during the quiet standing mode, and another feedback policy is developed such that the robot can take a transition step from quiet standing to walking. A feedback controller is designed that stabilizes steady-state 3D walking gaits, despite the high degree of underactuation of the robot. These controllers are combined through a state machine that handles switching among the three controllers controllers. In experiments on planarized (2D) and untethered (3D) versions of the robot with point feet and passive feet (prosthetic feet) walking over flat ground or on a ramp with a shallow slope, the adaptability of the designed controller to the environment (planar or untethered, flat ground or ramp), and to the morphology of the robot (point feet or passive feet), is demonstrated. In experiments on a planarized version of the robot with passive feet, the controller yielded stable walking after starting from quiet standing, autonomously and without any intervention from the operator. In experiments on an untethered (3D) version of the robot, the controller was able to balance the robot over flat ground or on a shallow ramp during the quiet standing mode. In addition, the controller yielded six-untethered ``human-like'' steps after starting from quiet standing, autonomously without any intervention from the operator.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102339/1/aramez_1.pd