Growing super stable tensegrity frameworks

This paper discusses methods for growing tensegrity frameworks akin to what are now known as Henneberg constructions, which apply to bar-joint frameworks. In particular, the paper presents tensegrity framework versions of the three key Henneberg constructions of vertex addition, edge splitting and framework merging (whereby separate frameworks are combined into a larger framework). This is done for super stable tensegrity frameworks in an ambient two or three-dimensional space. We start with the operation of adding a new vertex to an original super stable tensegrity framework, named vertex addition. We prove that the new tensegrity framework can be super stable as well if the new vertex is attached to the original framework by an appropriate number of members, which include struts or cables, with suitably assigned stresses. Edge splitting can be secured in R2 (R3) by adding a vertex joined to three (four) existing vertices, two of which are connected by a member, and then removing that member. This procedure, with appropriate selection of struts or cables, preserves super-stability. In d dimensional ambient space, merging two super stable frameworks sharing at least d + 1 vertices that are in general positions, we show that the resulting tensegrity framework is still super stable. Based on these results, we further investigate the strategies of merging two super stable tensegrity frameworks in IRd; (d 2 f2; 3g)that share fewer than d + 1 vertices, and show how they may be merged through the insertion of struts or cables as appropriate between the two structures, with a super stable structure resulting from the merge

Constructing tensegrity frameworks and related applications in multi-agent formation control

In deze thesis bestuderen we hoe tensigrity structuren te ontwerpen en de toepassing ervan in formaties van multi-agent systemen. Als eerste dragen we verschillende manieren voor om rigide, infinitesimaal rigide, en super stabiele tensigrity structuren te laten ‘groeien’. Hierna hebben we de virtueel tensigrity structuren toegepast voor het oplossen van formatie problemen. Verschillende regel-algoritmes zijn voorgedragen voor het manoeuvreren van de formatie. Als laatst is een gedistribueerde formatie volg-regelaar ontworpen waarbij tegelijkertijd de formatie vorm kan worden bereikt terwijl de formatie een externe referentie signaal volgt

Singularity degree of non-facially exposed faces

In this paper, we study the facial structure of the linear image of a cone. We define the singularity degree of a face of a cone to be the minimum number of steps it takes to expose it using exposing vectors from the dual cone. We show that the singularity degree of the linear image of a cone is exactly the number of facial reduction steps to obtain the minimal face in a corresponding primal conic optimization problem. This result generalizes the relationship between the complexity of general facial reduction algorithms and facial exposedness of conic images under a linear transform by Drusvyatskiy, Pataki and Wolkowicz to arbitrary singularity degree. We present our results in the original form and also in its nullspace form. As a by-product, we show that frameworks underlying a chordal graph have at most one level of stress matrix

Design and analysis of geodesic tensegrity structures with agriculture applications.

"This report aims to promulgate and elucidate the effective application of scientific principles in the design and optimisation of tensegrity structures for practical applications. By developing the intrinsic geometry of the geodesic dome and applying tensegrity design principles, a range of efficient, lightweight, modular structures are developed and broadly classified as geodesic tensegrity structures. Novel systems for clustering domes in two dimensions are considered and the analytical geometry required to generate various dome structures is derived from first principles. Computational methods for performing the design optimisation of tensegrity structures are reviewed and explained in detail. It is shown how an efficient, unified computational framework, suitable for the analysis of tensegrity structures in general, may be developed using computations which involve the equilibrium matrix of a structure. The importance of exploiting symmetry to simplify structural computations is highlighted throughout, as this is especially relevant in the analysis of large dome structures. A novel approach to generating the global equilibrium matrix of a structure from element vectors and implementing symmetry subspace methods is presented, which relies on the choice of an appropriate coordinate system to reflect the symmetry of a structure. A new algorithm is developed for implementing symmetry subspace methods in a computer program which enables the symmetry-adapted vector basis to be generated more efficiently. Methods for analysing kinematically indeterminate tensegrities and prestressed mechanisms and performing the prestress optimisation of a tensegrity structure are briefly reviewed and explained. Efficient tensegrity modular systems are developed for constructing a range of double-layer geodesic tensegrity domes and grids, based on the pioneering work of the artist, Kenneth Snelson. Finally, the cultural significance of tensegrity technology is illustrated by focusing on a range of novel applications in agriculture and sustainable development and adopting the holistic, "design science, "approach advocated by Buckminster Fuller.

Super Ball Bot - Structures for Planetary Landing and Exploration, NIAC Phase 2 Final Report

Small, light-weight and low-cost missions will become increasingly important to NASA's exploration goals. Ideally teams of small, collapsible, light weight robots, will be conveniently packed during launch and would reliably separate and unpack at their destination. Such robots will allow rapid, reliable in-situ exploration of hazardous destination such as Titan, where imprecise terrain knowledge and unstable precipitation cycles make single-robot exploration problematic. Unfortunately landing lightweight conventional robots is difficult with current technology. Current robot designs are delicate, requiring a complex combination of devices such as parachutes, retrorockets and impact balloons to minimize impact forces and to place a robot in a proper orientation. Instead we are developing a radically different robot based on a "tensegrity" structure and built purely with tensile and compression elements. Such robots can be both a landing and a mobility platform allowing for dramatically simpler mission profile and reduced costs. These multi-purpose robots can be light-weight, compactly stored and deployed, absorb strong impacts, are redundant against single-point failures, can recover from different landing orientations and can provide surface mobility. These properties allow for unique mission profiles that can be carried out with low cost and high reliability and which minimizes the inefficient dependance on "use once and discard" mass associated with traditional landing systems. We believe tensegrity robot technology can play a critical role in future planetary exploration

Application of Design Synthesis Technology in Architectural Practice

The use of computational tools and techniques has opened up new possibilities in architectural form generation. In parallel there have also been developments in structural engineering analysis and design methods, with the primary focuses being on accurate modelling of material behaviour and structural stability, and on ensuring economy. Having accepted that form and structure are mutually concomitant, something that is particularly important when considering freeform architecture, there are two distinct design approaches: (i) shapedriven architectural forms and adoption of creative integrated postrationalisation for a predefined freeform, and (ii) form-structure integration from conception, manifested by a growing number of methods for use at various stages in the design process. In this regard, a truss layout optimisation technique is proposed as a versatile design tool. This has a potential role in both these approaches to form generation at the conceptual design stage. A series of design studies are employed for this purpose, and generated forms are discussed. Additionally, further form generation possibilities are explored, using an extended version of the aforementioned technique. As a representative example, ‘tensegrity’ forms are studied in greater detail. The generated forms are extensively tested using a commercial structural analysis package, in order to verify the correctness of the conclusions drawn

Spatial Aspects of Metaphors for Information: Implications for Polycentric System Design

This dissertation presents three innovations that suggest an alternative approach to structuring information systems: a multidimensional heuristic workspace, a resonance metaphor for information, and a question-centered approach to structuring information relations. Motivated by the need for space to establish a question-centered learning environment, a heuristic workspace has been designed. Both the question-centered approach to information system design and the workspace have been conceived with the resonance metaphor in mind. This research stemmed from a set of questions aimed at learning how spatial concepts and related factors including geography may play a role in information sharing and public information access. In early stages of this work these concepts and relationships were explored through qualitative analysis of interviews centered on local small group and community users of geospatial data. Evaluation of the interviews led to the conclusion that spatial concepts are pervasive in our language, and they apply equally to phenomena that would be considered physical and geographic as they do to cognitive and social domains. Rather than deriving metaphorically from the physical world to the human, spatial concepts are native to all dimensions of human life. This revised view of the metaphors of space was accompanied by a critical evaluation of the prevailing metaphors for information processes, the conduit and pathway metaphors, which led to the emergence of an alternative, resonance metaphor. Whereas the dominant metaphors emphasized information as object and the movement of objects and people through networks and other limitless information spaces, the resonance metaphor suggests the existence of multiple centers in dynamic proximity relationships. This pointed toward the creation of a space for autonomous problem solving that might be related to other spaces through proximity relationships. It is suggested that a spatial approach involving discrete, discontinuous structures may serve as an alternative to approaches involving movement and transportation. The federation of multiple autonomous problem-solving spaces, toward goals such as establishing communities of questioners, has become an objective of this work. Future work will aim at accomplishing this federation, most likely by means of the IS0 Topic Maps standard or similar semantic networking strategies

The evolution of diversity in the structure and function of artificial organisms

Life on Earth has been shaped by evolutionary processes into a marvelous diversity of form and function, at all levels from melecules to ecosystems. It can be expected that no single conceptual framework ca encompass all the aspects of the evolution of diversity. This thesis explores this question from three different points of view: the role of developmental processes, the role of evolutionary dynamics, and the interplay between the body's control system