The Spherical Inverted Pendulum with Pelvis Width in Polar Coordinates for Humanoid Walking Design

The present communication is a follow up and extension of the paper “The Spherical Inverted Pendulum: Exact Solutions of Gait and Foot Placement Estimation Based on Symbolic Computation” by the same author. The walk design is approached by a 3-D inverted pendulum in a polar coordinate system. The advantage of this model is to easily offer indications of the energy expenditure of an efficient walk. However, the disadvantages that were never recognized by authors previously using this model is that the COG trajectory has to pass through the supporting foot location. This causes an unnecessary and unrealistic waving in the frontal plane during gait. The problem is discussed here and solved by extending the model of the inverted pendulum by introducing the pelvis width and the distance between the hips of the two legs, without adding dynamical complexity

Modeling, Simulation and Control of the Walking of Biped Robotic Devices—Part III: Turning while Walking

In part II of this group of papers, the control of the gait of a biped robot during rectilinear walk was considered. The modeling approach and simulation, using Kane’s method with implementation leveraged by Autolev, a symbolic computational environment that is complementary, was discussed in part I. Performing turns during the walk is technically more complex than the rectilinear case and deserves further investigation. The problem is solved in the present part III as an extension of part II. The robot executes a rectilinear walk on a local reference frame whose progression axis is always tangent, and its origin performs the involute of the path curve. The curve is defined by its curvature (osculating circle) and center of curvature (evolute) along the path. Radius of curvature and center can change continuously (in practice at every sampling time). For postural equilibrium, Center of Gravity and Zero Moment Point (COG/ZMP) follow the same preview reference proposed for rectilinear walk (c o g R e f x ( t ) , c o g ˙ R e f x ( t ), c o g R e f y ( t ) , c o g ˙ R e f y ( t )). The effect of the turn on the sagittal plane is negligible and is ignored, while on the frontal plane it is accounted for by an offset on COG reference to compensate for the centrifugal acceleration. The body trunk and local frame rotation, and the generation of the references on this moving frame of the free foot trajectory during the swing deserve attention

Modelling, Simulation and Control of the Walking of Biped Robotic Devices—Part I : Modelling and Simulation Using Autolev

A biped robot is a mechanical multichain system. The peculiar features, that distinguishes this kind of robot with respect to others, e.g., industrial robots, is its switching nature between different phases, each one is the same mechanics subject to a different constraint. Moreover, because these (unilateral) constraints, represented by the contact between the foot/feet and the ground, play a fundamental role for maintaining the postural equilibrium during the gait, forces and torques returned must be continuously monitored, as they pose stringent conditions to the trajectories that the joints of the robot can safely follow. The advantages of using the Kane’s method to approach the dynamical model (models) of the system are outlined. This paper, divided in three parts, deals with a generical biped device, which can be an exoskeleton for rehabilitation or an indipendent robot. Part I is devoted to modelling and simulation, part II approaches the control of walk in a rectilinear trajectory, part III extends the results on turning while walking. In particular, this part I describes the model of the biped robot and the practicalities of building a computer simulator, leveraging on the facilities offered by the symbolic computational environment Autolev that complements the Kane’s method

Modeling, Simulation and Control of the Walking of Biped Robotic Devices, Part II: Rectilinear Walking

This is the second part of a three-part paper. It extends to the free walking results of a previous work on postural equilibrium of a lower limb exoskeleton for rehabilitation exercises. A classical approach has been adopted to design gait (zero moment point (ZMP), linearized inverted pendulum theory, inverse kinematics obtained through the pseudo-inverse of Jacobian matrices). While several ideas exploited here can be found in other papers of the literature, e.g., whole-body coordination, our contribution is the simplicity of the whole control approach that originates logically from a common root. (1) The approximation of the unilateral foot/feet-ground contacts with non-holonomic constraints leads naturally to a modeling and control design that implements a two-phase switching system. The approach is facilitated by Kane’s method and tools as described in Part I. (2) The Jacobian matrix is used to transfer from the Cartesian to the joint space a greater number of variables for redundancy than the degrees of freedom (DOF). We call it the extended Jacobian matrix. Redundancy and the prioritization of postural tasks is approached with weighted least squares. The singularity of the kinematics when knees are fully extended is solved very simply by fake knee joint velocities. (3) Compliance with the contact and accommodation of the swing foot on an uneven ground, when switching from single to double stance, and the transfer of weight from one foot to the other in double stance are approached by exploiting force/torque expressions returned from the constraints. (4) In the center of gravity (COG)/ZMP loop for equilibrium, an extended estimator, based on the linearized inverted pendulum, is adopted to cope with external force disturbances and unmodeled dynamics. Part II treats rectilinear walking, while Part III discusses turning while walking

Smart Grid Technologies in Europe: An Overview

The old electricity network infrastructure has proven to be inadequate, with respect to modern challenges such as alternative energy sources, electricity demand and energy saving policies. Moreover, Information and Communication Technologies (ICT) seem to have reached an adequate level of reliability and flexibility in order to support a new concept of electricity network—the smart grid. In this work, we will analyse the state-of-the-art of smart grids, in their technical, management, security, and optimization aspects. We will also provide a brief overview of the regulatory aspects involved in the development of a smart grid, mainly from the viewpoint of the European Unio

Significance of Elastic Coupling for Stresses and Leakage in Frictional Contacts

We study how the commonly neglected coupling of normal and in-plane elastic response affects tribological properties when Hertzian or randomly rough indenters slide past an elastic body. Compressibility-induced coupling is found to substantially increase maximum tensile stresses, which cause materials to fail, and to decrease friction such that Amontons law is violated macroscopically even when it holds microscopically. Confinement-induced coupling increases friction and enlarges domains of high tension. Moreover, both types of coupling affect the gap topography and thereby leakage. Thus, coupling can be much more than a minor perturbation of a mechanical contact