Path planning for active tensegrity structures

This paper presents a path planning method for actuated tensegrity structures with quasi-static motion. The valid configurations for such structures lay on an equilibrium manifold, which is implicitly defined by a set of kinematic and static constraints. The exploration of this manifold is difficult with standard methods due to the lack of a global parameterization. Thus, this paper proposes the use of techniques with roots in differential geometry to define an atlas, i.e., a set of coordinated local parameterizations of the equilibrium manifold. This atlas is exploited to define a rapidly-exploring random tree, which efficiently finds valid paths between configurations. However, these paths are typically long and jerky and, therefore, this paper also introduces a procedure to reduce their control effort. A variety of test cases are presented to empirically evaluate the proposed method. (C) 2015 Elsevier Ltd. All rights reserved.Peer ReviewedPostprint (author's final draft

Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm

Tensegrities are spatial, reticulated and lightweight structures that are increasingly investigated as structural solutions for active and deployable structures. Tensegrity systems are composed only of axially loaded elements and this provides opportunities for actuation and deployment through changing element lengths. In cable-based actuation strategies, the deficiency of having to control too many cable elements can be overcome by connecting several cables. However, clustering active cables significantly changes the mechanics of classical tensegrity structures. Challenges emerge for structural analysis, control and actuation. In this paper, a modified dynamic relaxation (DR) algorithm is presented for static analysis and form-finding. The method is extended to accommodate clustered tensegrity structures. The applicability of the modified DR to this type of structure is demonstrated. Furthermore, the performance of the proposed method is compared with that of a transient stiffness method. Results obtained from two numerical examples show that the values predicted by the DR method are in a good agreement with those generated by the transient stiffness method. Finally it is shown that the DR method scales up to larger structures more efficiently. (C) 2010 Elsevier Ltd. All rights reserved

Growth-Adapted Tensegrity Structures: A New Calculus for the Space Economy

We describe a novel approach to create and engineer an economically viable space habitat development technology, for deployment of a lightweight tensegrity habitat structure orbiting at Earth-Moon L2, where onboard robotic assets will use space-based materials to provide water for shielding, irrigation and life support, soil for ecosystem development, and to enable structural maintenance and enhancement. The habitat can become a tourist destination, an economic hub, and a multi-purpose research and support facility for lunar surface development and space ecosystem life sciences

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.

Benelux meeting on systems and control, 23rd, March 17-19, 2004, Helvoirt, The Netherlands

Book of abstract

Rigidity of frameworks with coordinated constraint relaxations

This thesis is concerned with the rigidity of coordinated frameworks. These are considered to be bar-joint frameworks for which the requirement that the lengths of bars be kept fixed is relaxed on some collection of bars, with the caveat that all bars within a coordination class must change length by the same amount. We begin by formulating the conditions for a framework to be continuously coordinated rigid, infinitesimally coordinated rigid, and statically coordinated rigid. We prove that static and infinitesimal rigidity are equivalent for coordinated frameworks, and that for regular coordinated frameworks, continuous rigidity and infinitesimal rigidity are equivalent. We give a characterisation of the rigidity of frameworks in d-dimensional Euclidean space with k coordination classes, based on the rigidity of the structure graph of such a framework. Since minimal infinitesimal rigidity of bar-joint frameworks is characterised in 1- and 2-dimensions, we extend the standard characterisations to a combinatorial characterisation of minimally infinitesimally rigid frameworks with one class of coordinated bars, and with two classes of coordinated bars, in both dimension 1 and dimension 2. We also obtain an inductive characterisation of such minimally infinitesimally rigid frameworks using coordinated analogues to standard inductive constructions. We conclude by considering coordinated frameworks with symmetric realisations, and give some initial results in this area