THREAD: A programming environment for interactive planning-level robotics applications

THREAD programming language, which was developed to meet the needs of researchers in developing robotics applications that perform such tasks as grasp, trajectory design, sensor data analysis, and interfacing with external subsystems in order to perform servo-level control of manipulators and real time sensing is discussed. The philosophy behind THREAD, the issues which entered into its design, and the features of the language are discussed from the viewpoint of researchers who want to develop algorithms in a simulation environment, and from those who want to implement physical robotics systems. The detailed functions of the many complex robotics algorithms and tools which are part of the language are not explained, but an overall impression of their capability is given

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Basic framework and general contact model

The first paper of this series establishes a unified theoretical framework that lays a solid foundation for developing energy-conserving normal contact models for arbitrarily shaped bodies in the discrete element method. It is derived based solely on the requirement that the potential energy must be conserved for an elastic impact of two shapes under any condition. The resulting general energy-conserving contact model states that the normal force as a vector must be the gradient of a contact potential field. When such a contact potential or energy function is specified, a complete normal contact model for a pair of arbitrarily shaped particles, including the contact normal direction, contact point/line and force magnitude, will be automatically followed without introducing any additional assumptions. In this framework, the contact geometry and contact force are indispensably related and are evaluated in a consistent manner. Due to the paramount role that the energy function plays in the current theory, its fundamental properties are discussed, which serve as general guidance for choosing a valid energy function. In addition, both single and multiple contacts and their evolution can be handled in a seamless way. Some symmetric properties of particle shapes can also be utilised to simplify the contact models.Within the proposed theoretical framework, different choices or combinations of geometric features as variables for the contact energy function can give rise to unique types of energy-conserving contact models with distinct characteristics and features. Two such functions using only one primary feature, which lead to two specialised energy-conserving contact models, will be presented in the subsequent papers of this series

Computing Isodose Curves for Radiotherapy Treatment Plans

Radiation therapy increasingly means Intensity Modulated Radiation Therapy (IMRT) and withit a trend towards inverse treatment planning. The metrics of a treatment consist of important conformality indices such as the Ian Paddick Conformality Index (IPCI), Dose Volume Histograms (DVH), as well as the conformance isodose lines. This final metric, which offers spatial information of radiation dose that the others do not, shows the results of simulating the treatment plan on the CAT scan images. A physician is able to examine this image and ascertain which portions of the anatomy are the recipients of different levels of radiation dose. Computing isodose curves is no simple task, especially when the set of CAT scan images becomes large. Our approach is to first interpolate a surface over a finite mesh of scalar data representing the dose distribution in that plane, then find the set of points which constitute that isodose level by using a variation on an approach called the Hit-and-Run algorithm. We examine the behavior of our algorithm in dealing with sample radiotherapy plans as well as constructed examples to determine the effectiveness of this approach

Geometry for design: approaches to the study of representation and dimension and their contributions to the modeling of phenomena

The difficulties of representation and understanding of the dimension are evident in the different educational levels. University education is no stranger to this situation. This communication was developed within the framework of the graphic design course. This course was designed under the use of specialized software in geometry, which was freely available and intuitive. It should be remembered that the adequate use of representations and attributes proper to the dimension aids in the representations of movement phenomena, as well as in the representations in force diagrams in the teaching of physics. This qualitative research aims to address aspects of representation and dimensionality from the description of some selected tasks of the group participants, who contrast the first representations, with their final activities. That is, these representations showed their evolution in construction, to the extent that the flat representations of objects in the portfolio were built in real dimensions, keeping the proportional relationship between its parts

Geometry-based structural analysis and design via discrete stress functions

This PhD thesis proposes a direct and unified method for generating global static equilibrium for 2D and 3D reciprocal form and force diagrams based on reciprocal discrete stress functions. This research combines and reinterprets knowledge from Maxwell’s 19th century graphic statics, projective geometry and rigidity theory to provide an interactive design and analysis framework through which information about designed structural performance can be geometrically encoded in the form of the characteristics of the stress function. This method results in novel, intuitive design and analysis freedoms. In contrast to contemporary computational frameworks, this method is direct and analytical. In this way, there is no need for iteration, the designer operates by default within the equilibrium space and the mathematically elegant nature of this framework results in its wide applicability as well as in added educational value. Moreover, it provides the designers with the agility to start from any one of the four interlinked reciprocal objects (form diagram, force diagram, corresponding stress functions). This method has the potential to be applied in a wide range of case studies and fields. Specifically, it leads to the design, analysis and load-path optimisation of tension-and compression 2D and 3D trusses, tensegrities, the exoskeletons of towers, and in conjunction with force density, to tension-and-compression grid-shells, shells and vaults. Moreover, the abstract nature of this method leads to wide cross-disciplinary applicability, such as 2D and 3D discrete stress fields in structural concrete and to a geometrical interpretation of yield line theory

Algebraic 3D Graphic Statics: reciprocal constructions

The recently developed 3D graphic statics (3DGS) lacks a rigorous mathematical definition relating the geometrical and topological properties of the reciprocal polyhedral diagrams as well as a precise method for the geometric construction of these diagrams. This paper provides a fundamental algebraic formulation for 3DGS by developing equilibrium equations around the edges of the primal diagram and satisfying the equations by the closeness of the polygons constructed by the edges of the corresponding faces in the dual/reciprocal diagram. The research provides multiple numerical methods for solving the equilibrium equations and explains the advantage of using each technique. The approach of this paper can be used for compression-and-tension combined form-finding and analysis as it allows constructing both the form and force diagram based on the interpretation of the input diagram. Besides, the paper expands on the geometric/static degrees of (in)determinacies of the diagrams using the algebraic formulation and shows how these properties can be used for the constrained manipulation of the polyhedrons in an interactive environment without breaking the reciprocity between the two

Asymptotics of lowest unitary SL(2,C) invariants on graphs

We describe a technique to study the asymptotics of SL(2,C) invariant tensors associated to graphs, with unitary irreps and lowest SU(2) spins, and apply it to the Lorentzian EPRL-KKL (Engle, Pereira, Rovelli, Livine; Kaminski, Kieselowski, Lewandowski) model of quantum gravity. We reproduce the known asymptotics of the 4-simplex graph with a different perspective on the geometric variables and introduce an algorithm valid for any graph. On general grounds, we find that critical configurations are not just Regge geometries, but a larger set corresponding to conformal twisted geometries. These can be either Euclidean or Lorentzian, and include curved and flat 4d polytopes as subsets. For modular graphs, we show that multiple pairs of critical points exist, and there exist critical configurations of mixed signature, Euclidean and Lorentzian in different subgraphs, with no 4d embedding possible.Comment: 40 Pages + 5 Appendices. 11 Figures. v2: Refined presentation of the general algorithm, additional minor amendments. v3: paragraph added in section 5 about curved embedding

2-vertex Lorentzian Spin Foam Amplitudes for Dipole Transitions

We compute transition amplitudes between two spin networks with dipole graphs, using the Lorentzian EPRL model with up to two (non-simplicial) vertices. We find power-law decreasing amplitudes in the large spin limit, decreasing faster as the complexity of the foam increases. There are no oscillations nor asymptotic Regge actions at the order considered, nonetheless the amplitudes still induce non-trivial correlations. Spin correlations between the two dipoles appear only when one internal face is present in the foam. We compute them within a mini-superspace description, finding positive correlations, decreasing in value with the Immirzi parameter. The paper also provides an explicit guide to computing Lorentzian amplitudes using the factorisation property of SL(2,C) Clebsch-Gordan coefficients in terms of SU(2) ones. We discuss some of the difficulties of non-simplicial foams, and provide a specific criterion to partially limit the proliferation of diagrams. We systematically compare the results with the simplified EPRLs model, much faster to evaluate, to learn evidence on when it provides reliable approximations of the full amplitudes. Finally, we comment on implications of our results for the physics of non-simplicial spin foams and their resummation.Comment: 27 pages + appendix, many figures. v2: one more numerical result, plus minor amendment