A PDE viewpoint on basic properties of coordination algorithms with symmetries

Several recent control applications consider the coordination of subsystems through local interaction. Often the interaction has a symmetry in state space, e.g. invariance with respect to a uniform translation of all subsystem values. The present paper shows that in presence of such symmetry, fundamental properties can be highlighted by viewing the distributed system as the discrete approximation of a partial differential equation. An important fact is that the symmetry on the state space differs from the popular spatial invariance property, which is not necessary for the present results. The relevance of the viewpoint is illustrated on two examples: (i) ill-conditioning of interaction matrices in coordination/consensus problems and (ii) the string instability issue. ©2009 IEEE.

Coordination on Lie groups

This paper studies the coordinated motion of a group of agents evolving on a Lie group. Left-or rightinvariance with respect to the absolute position on the group lead to two different characterizations of relative positions and two associated definitions of coordination (fixed relative positions). Conditions for each type of coordination are derived in the associated Lie algebra. This allows to formulate the coordination problem on Lie groups as consensus in a vector space. Total coordination occurs when both types of coordination hold simultaneously. The discussion in this paper provides a common geometric framework for previously published coordination control laws on SO(3), SE(2) and SE(3). The theory is illustrated on the group of planar rigid motion SE(2). © 2008 IEEE.

Group coordination and cooperative control of steered particles in the plane

The paper overviews recent and ongoing efforts by the authors to develop a design methodology to stabilize isolated relative equilibria in a kinematic model of identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles about the same center with fixed relative headings. © Springer-Verlag Berlin Heidelberg 2006.

Feedback mechanisms for global oscillations in Lure systems

The paper presents two mechanisms for global oscillations in feedback systems, based on bifurcations in absolutely stable systems. The external characterization of the oscillators provides the basis for a (energy-based) dissipativity theory for oscillators, thereby opening new possibilities for rigorous stability analysis of high-dimensional systems and interconnected oscillators. © 2004 Elsevier B.V. All rights reserved.

Failure mechanisms in fibrous scaffolds

Polymeric fibrous scaffolds have been considered as replacements for load-bearing soft tissues, because of their ability to mimic the microstructure of natural tissues. Poor toughness of fibrous materials results in failure, which is an issue of importance to both engineering and medical practice. The toughness of fibrous materials depends on the ability of the microstructure to develop toughening mechanisms. However, such toughening mechanisms are still not well understood, because the detailed evolution at the microscopic level is difficult to visualize. A novel and simple method was developed, namely, a sample-taping technique, to examine the detailed failure mechanisms of fibrous microstructures. This technique was compared with in situ fracture testing by scanning electron microscopy. Examination of three types of fibrous networks showed that two different failure modes occurred in fibrous scaffolds. For brittle cracking in gelatin electrospun scaffolds, the random network morphology around the crack tip remained during crack propagation. For ductile failure in polycaprolactone electrospun scaffolds and nonwoven fabrics, the random network deformed via fiber rearrangement, and a large number of fiber bundles formed across the region in front of the notch tip. These fiber bundles not only accommodated mechanical strain, but also resisted crack propagation and thus toughened the fibrous scaffolds. Such understanding provides insight for the production of fibrous materials with enhanced toughness. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

In situ observations of the atomistic mechanisms of Ni catalyzed low temperature graphene growth.

The key atomistic mechanisms of graphene formation on Ni for technologically relevant hydrocarbon exposures below 600 °C are directly revealed via complementary in situ scanning tunneling microscopy and X-ray photoelectron spectroscopy. For clean Ni(111) below 500 °C, two different surface carbide (Ni2C) conversion mechanisms are dominant which both yield epitaxial graphene, whereas above 500 °C, graphene predominantly grows directly on Ni(111) via replacement mechanisms leading to embedded epitaxial and/or rotated graphene domains. Upon cooling, additional carbon structures form exclusively underneath rotated graphene domains. The dominant graphene growth mechanism also critically depends on the near-surface carbon concentration and hence is intimately linked to the full history of the catalyst and all possible sources of contamination. The detailed XPS fingerprinting of these processes allows a direct link to high pressure XPS measurements of a wide range of growth conditions, including polycrystalline Ni catalysts and recipes commonly used in industrial reactors for graphene and carbon nanotube CVD. This enables an unambiguous and consistent interpretation of prior literature and an assessment of how the quality/structure of as-grown carbon nanostructures relates to the growth modes.

An analysis of competing toughening mechanisms in layered and particulate solids

The relative potency of common toughening mechanisms is explored for layered solids and particulate solids, with an emphasis on crack multiplication and plasticity. First, the enhancement in toughness due to a parallel array of cracks in an elastic solid is explored, and the stability of co-operative cracking is quantified. Second, the degree of synergistic toughening is determined for combined crack penetration and crack kinking at the tip of a macroscopic, mode I crack; specifically, the asymptotic problem of self-similar crack advance (penetration mode) versus 90 ° symmetric kinking is considered for an isotropic, homogeneous solid with weak interfaces. Each interface is treated as a cohesive zone of finite strength and toughness. Third, the degree of toughening associated with crack multiplication is assessed for a particulate solid comprising isotropic elastic grains of hexagonal shape, bonded by cohesive zones of finite strength and toughness. The study concludes with the prediction of R-curves for a mode I crack in a multi-layer stack of elastic and elastic-plastic solids. A detailed comparison of the potency of the above mechanisms and their practical application are given. In broad terms, crack tip kinking can be highly potent, whereas multiple cracking is difficult to activate under quasi-static conditions. Plastic dissipation can give a significant toughening in multi-layers especially at the nanoscale. © 2013 Springer Science+Business Media Dordrecht.

Corrugated all-composite sandwich structures. Part 2: Failure mechanisms and experimental programme

A novel corrugated composite core, referred to as a hierarchical corrugation, has been developed and tested experimentally. Hierarchical corrugations exhibit a range of different failure modes depending on the geometrical properties and the material properties of the structures. In order to understand the different failure modes the analytical strength model, developed in part 1 of this paper, was used to make collapse mechanism maps for the different corrugation configurations. If designed correctly, the hierarchical structures can have more than 7 times higher weight specific strength compared to its monolithic counter part. The difference in strength arises mainly from the increase in buckling resistance of the sandwich core members compared to the monolithic version. The highest difference in strength is seen for core configurations with low overall density. As the density of the core increases, the monolithic core members get stockier and more resistant to buckling and thus the benefits of the hierarchical structure reduces. © 2008 Elsevier Ltd. All rights reserved.

Optimal displacement mechanisms beneath shallow foundations on linear-elastic perfectly plastic soil

An energy method for a linear-elastic perfectly plastic method utilising the von Mises yield criterion with associated flow developed in 2013 by McMahon and co-workers is used to compare the ellipsoidal cavity-expansion mechanism, from the same work, and the displacement fields of other research by Levin, in 1995, and Osman and Bolton, in 2005, which utilise the Hill and Prandtl mechanisms respectively. The energy method was also used with a mechanism produced by performing a linear-elastic finite-element analysis in Abaqus. At small values of settlement and soil rigidity the elastic mechanism provides the lowest upper-bound solution, and matches well with finite-element analysis results published in the literature. At typical footing working loads and settlements the cavity-expansion mechanism produces a more optimal solution than the displacement fields within the Hill and Prandtl mechanisms, and also matches well with the published finite-element analysis results in this range. Beyond these loads, at greater footing settlements, or soil rigidity, the Prandtl mechanism is shown to be the most appropriate.

A trichordal temporal approach to digital coordination: the sociomaterial mangling of the CERN grid

This paper develops a sociomaterial perspective on digital coordination. It extends Pickering’s mangle of practice by using a trichordal approach to temporal emergence. We provide new understanding as to how the nonhuman and human agencies involved in coordination are embedded in the past, present, and future. We draw on an in-depth field study conducted between 2006 and 2010 of the development, introduction, and use of a computing grid infrastructure by the CERN particle physics community. Three coordination tensions are identified at different temporal dimensions, namelyobtaining adequate transparency in the present, modeling a future infrastructure, and the historical disciplining of social and material inertias. We propose and develop the concept of digital coordination, and contribute a trichordal temporal approach to understanding the development and use of digital infrastructure as being orientated to the past and future while emerging in the present.

Mechanisms of projectile penetration in Dyneema® encapsulated aluminum structures

Polymer composites comprising ultra-high molecular weight polyethylene (UHWMPE) fibers in a compliant matrix are now widely used in ballistic applications with varying levels of success. This is primarily due to a poor understanding of the mechanics of penetration of these composites in ballistic protection systems. In this study, we report experimental observations of the penetration mechanisms in four model systems impacted by a 12.7 mm diameter spherical steel projectile. The four model targets designed to highlight different penetration mechanisms in Dyneema® UHWMPE composites were: (i) a bare aluminum plate; (ii) the same plate fully encased in a 5.9 mm thick casing of Dyneema®; (iii) the fully encased plate with a portion of the Dyneema® removed from the front face so that the projectile impacts directly the Al plate; and (iv) the fully encased plate with a portion of the Dyneema® removed from the rear face so that the projectile can exit the Al plate without again interacting with the Dyneema®. A combination of synchronized high speed photography with three cameras, together with post-test examination of the targets via X-ray tomography and optical microscopy was used to elucidate the deformation and perforation mechanisms. The measurements show that the ballistic resistance of these targets increases in the order: bare Al plate, rear face cutout target, fully encased target and front face cutout target. These findings are explained based on the following key findings: (a) the ballistic performance of Dyneema® plates supported on a foundation is inferior to Dyneema® plates supported along their edges; (b) the apparent ballistic resistance of Dyneema® plates increases if the plates are given an initial velocity prior to the impact by the projectile, thereby reducing the relative velocity between the Dyneema® plate and projectile; and (c) when the projectile is fragmented prior to impact, the spatially and temporally distributed loading enhances the ballistic resistance of the Dyneema®. The simple model targets designed here have elucidated mechanisms by which Dyneema® functions in multi-material structures. © 2014 Elsevier Ltd.

Surface contact and design of fibrillar 'friction pads' in stick insects (Carausius morosus): mechanisms for large friction coefficients and negligible adhesion.

Many stick insects and mantophasmids possess tarsal 'heel pads' (euplantulae) covered by arrays of conical, micrometre-sized hairs (acanthae). These pads are used mainly under compression; they respond to load with increasing shear resistance, and show negligible adhesion. Reflected-light microscopy in stick insects (Carausius morosus) revealed that the contact area of 'heel pads' changes with normal load on three hierarchical levels. First, loading brought larger areas of the convex pads into contact. Second, loading increased the density of acanthae in contact. Third, higher loads changed the shape of individual hair contacts gradually from circular (tip contact) to elongated (side contact). The resulting increase in real contact area can explain the load dependence of friction, indicating a constant shear stress between acanthae and substrate. As the euplantula contact area is negligible for small loads (similar to hard materials), but increases sharply with load (resembling soft materials), these pads show high friction coefficients despite little adhesion. This property appears essential for the pads' use in locomotion. Several morphological characteristics of hairy friction pads are in apparent contrast to hairy pads used for adhesion, highlighting key adaptations for both pad types. Our results are relevant for the design of fibrillar structures with high friction coefficients but small adhesion.

Sensing through body dynamics

It has been shown that sensory morphology and sensory-motor coordination enhance the capabilities of sensing in robotic systems. The tasks of categorization and category learning, for example, can be significantly simplified by exploiting the morphological constraints, sensory-motor couplings and the interaction with the environment. This paper argues that, in the context of sensory-motor control, it is essential to consider body dynamics derived from morphological properties and the interaction with the environment in order to gain additional insight into the underlying mechanisms of sensory-motor coordination, and more generally the nature of perception. A locomotion model of a four-legged robot is used for the case studies in both simulation and real world. The locomotion model demonstrates how attractor states derived from body dynamics influence the sensory information, which can then be used for the recognition of stable behavioral patterns and of physical properties in the environment. A comprehensive analysis of behavior and sensory information leads to a deeper understanding of the underlying mechanisms by which body dynamics can be exploited for category learning of autonomous robotic systems. © 2006 Elsevier Ltd. All rights reserved.