scholarly journals The Configuration Space of n-Tuples of Equiangular Unit Vectors for n=3, 4, and 5

2018 ◽  
Vol 2018 ◽  
pp. 1-4
Author(s):  
Yasuhiko Kamiyama
Keyword(s):  
Configuration Space ◽  
Dimensional Space ◽  
Topological Type ◽  
Unit Vectors

Let Mn(θ) be the configuration space of n-tuples of unit vectors in R3 such that all interior angles are θ. The space Mn(θ) is an (n-3)-dimensional space. This paper determines the topological type of Mn(θ) for n=3, 4, and 5.

scholarly journals The Topological Type of Equilateral and Almost Equiangular Polygon Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Yasuhiko Kamiyama
Keyword(s):  
Configuration Space ◽  
Topological Type ◽  
Bond Angles

Let Pn be the configuration space of equilateral spatial n-gons. For θ∈0,π and k∈0,1,…,n, let Pnkθ be the subspace of Pn consisting of elements whose first k bond angles are θ. Recently, the topological type of Pnkθ was determined for small n, special θ, and k=n or n−2. In this paper, we determine the topological type of Pnn−3θ for general n and θ.

Study on dual peg-in-hole insertion using of constraints formed in the environment

2017 ◽  
Vol 44 (6) ◽  
pp. 730-740 ◽  
Author(s):  
Jianhua Su ◽  
Rui Li ◽  
Hong Qiao ◽  
Jing Xu ◽  
Qinglin Ai ◽  
...  
Keyword(s):  
Configuration Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Force Sensor ◽  
High Dimensional ◽  
Content Type ◽  
Attractive Region ◽  
Low Dimensional ◽  
The Cost ◽  
Yaw Angle

Purpose The purpose of this paper is to develop a dual peg-in-hole insertion strategy. Dual peg-in-hole insertion is the most common task in manufacturing. Most of the previous work develop the insertion strategy in a two- or three-dimensional space, in which they suppose the initial yaw angle is zero and only concern the roll and pitch angles. However, in some case, the yaw angle could not be ignored due to the pose uncertainty of the peg on the gripper. Therefore, there is a need to design the insertion strategy in a higher-dimensional configuration space. Design/methodology/approach In this paper, the authors handle the insertion problem by converting it into several sub-problems based on the attractive region formed by the constraints. The existence of the attractive region in the high-dimensional configuration space is first discussed. Then, the construction of the high-dimensional attractive region with its sub-attractive region in the low-dimensional space is proposed. Therefore, the robotic insertion strategy can be designed in the subspace to eliminate some uncertainties between the dual pegs and dual holes. Findings Dual peg-in-hole insertion is realized without using of force sensors. The proposed strategy is also used to demonstrate the precision dual peg-in-hole insertion, where the clearance between the dual-peg and dual-hole is about 0.02 mm. Practical implications The sensor-less insertion strategy will not increase the cost of the assembly system and also can be used in the dual peg-in-hole insertion. Originality/value The theoretical and experimental analyses for dual peg-in-hole insertion are proposed without using of force sensor.

FluxTracer: A 3D-Partitioning and Radiant Flux Computer Tool to Analyse the Optical Behaviour of Light Collection and Concentration Subsystems Using High Performance Computers

2018 ◽  
Author(s):  
Manuel Blanco ◽  
Evgeny Votyakov ◽  
Chariton Christou ◽  
Costas N. Papanicolas ◽  
Clotilde Corsi ◽  
...  
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Traditional Approach ◽  
Dimensional Space ◽  
Radiant Energy ◽  
Light Collection ◽  
Analysis Tools ◽  
Cost Competitiveness ◽  
The Cost ◽  
High Performance Computers

The light collection and concentration subsystem (LCCS) of any concentrating solar thermal (CST) system is composed of the surfaces that collect and concentrate the sunlight and of the input surfaces of the receivers, or receivers’ envelopes, where the light is concentrated. For all commercial CST technologies the LCCS is, together with the power block, the subsystem that has more influence in the overall performance and cost. Thus, its optimization is critical to increase the cost-competitiveness of these systems. This optimization requires, in many cases, the optimization of the position, geometry and size of a very large number of solar collecting and concentrating surfaces as well as the optimization of the shape and size of the input surfaces of the receivers where the sunlight is concentrated. Because a full optimization requires the exploration of a configuration space with a very large number of dimensions, the traditional approach consist in making many initial assumptions to drastically reduce the number of dimensions of the configuration space to a handful, so that the optimization can be carried out using conventional high-end workstations in a matter of hours. However, to achieve relevant breakthroughs and to substantially increase the cost-competitiveness of CST systems a bolder approach is needed, where sophisticated design and analysis tools, engineered from the start to be used in High Performance Computers (HPC), will be combined with sophisticated optimization strategies targeted to explore and find optimal solutions in very high dimensional configuration spaces. This paper presents the first of a series of such design and analysis tools. The tool, call Flux Tracer, partitions the three-dimensional space in which the LCC subsystem under analysis is immersed into volumetric pixels (voxels) and computes the radiant energy flux that traverses each voxel as a function of time. It integrates the energy density in every voxel overtime, providing detailed information regarding how the radiant energy flows in space in a given LCC subsystem and in a given period of time. This information is the cornerstone of the highly sophisticated computational LCC subsystem optimization framework The Cyprus Institute (CYI) is developing, in collaboration with the Australian National University (ANU), targeted to be used in HPC’s.

scholarly journals Crossfertilization Between Plasma, Stellar Dynamics and Hydrodynamics

1975 ◽  
Vol 69 ◽  
pp. 177-194
Author(s):  
M. R. Feix
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Dimensional Space ◽  
Stellar Dynamics ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stokes Fluid ◽  
Gravitating Systems ◽  
Space Phase

We present results on four different mediums characterised by their ‘density conservation’ in a two dimensional space (phase space for unidimensional plasma and self gravitating systems, configuration space for two dimensional Navier Stokes fluid and guiding center rod plasma).

scholarly journals Generating the Isocurve Representation for Configuration Space of Mechanisms

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Weirui Kang ◽  
Jiani Zeng ◽  
Qinghua Liu ◽  
Zhengdong Huang
Keyword(s):  
Configuration Space ◽  
Dimensional Space ◽  
Forward Direction ◽  
Solution Component ◽  
First Order ◽  
Sampling Points ◽  
Solution Point ◽  
Lower Dimensional Space ◽  
Tracing Method ◽  
Lower Dimensional

This paper proposes an approach for generating a set of isocurves as a representation for configuration space (CS) of a mechanism. An isocurve here is a curve in CS with some parameters fixed. Compared with conventional methods like box approximations, sampling points, and boundary tessellations, the isocurve-based representation has some advantages in space parameterization and data management. This approach directly formulates the joint loop equations in the form of kinematic matrices, which does not need any extra conversions and solves the equations with an isocurve-tracing method applying ODE solvers. Since the isocurves are connected in certain orders with the guide isocurves in a lower-dimensional space, tracing all the isocurves only needs one initial solution point for an isolated solution component. In addition, the proposed approach includes an interference-handling step, which trims off the collision portions of the isocurves by checking their feasibility according to the previously defined half-space constraints, and a measure for identifying the forward direction at singular points where the first-order derivatives vanish. The approach is implemented through programming and the results for a few examples show its effectiveness.

scholarly journals Robot Motion Planning Method Based on Incremental High-Dimensional Mixture Probabilistic Model

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Fusheng Zha ◽  
Yizhou Liu ◽  
Xin Wang ◽  
Fei Chen ◽  
Jingxuan Li ◽  
...  
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Probabilistic Model ◽  
Environmental Changes ◽  
Dimensional Space ◽  
Model Fitting ◽  
High Dimensional ◽  
Planning Problem ◽  
Robot Configuration ◽  
Model Training

The sampling-based motion planner is the mainstream method to solve the motion planning problem in high-dimensional space. In the process of exploring robot configuration space, this type of algorithm needs to perform collision query on a large number of samples, which greatly limits their planning efficiency. Therefore, this paper uses machine learning methods to establish a probabilistic model of the obstacle region in configuration space by learning a large number of labeled samples. Based on this, the high-dimensional samples’ rapid collision query is realized. The influence of number of Gaussian components on the fitting accuracy is analyzed in detail, and a self-adaptive model training method based on Greedy expectation-maximization (EM) algorithm is proposed. At the same time, this method has the capability of online updating and can eliminate model fitting errors due to environmental changes. Finally, the model is combined with a variety of sampling-based motion planners and is validated in multiple sets of simulations and real world experiments. The results show that, compared with traditional methods, the proposed method has significantly improved the planning efficiency.

11-DIMENSIONAL SUPERMEMBRANE IN A SPINOR MOVING REPERE FORMALISM

1993 ◽  
Vol 08 (06) ◽  
pp. 1081-1092 ◽  
Author(s):  
I.A. BANDOS ◽  
A.A. ZHELTUKHIN
Keyword(s):  
Configuration Space ◽  
Dimensional Space ◽  
Space Time ◽  
Covariant Description ◽  
Dimensional Space Time

Twistor-like formulations for super p-brane theories in the D-dimensional space-time including D=11 supermembrane are suggested in an extended configuration space. This extension is carried out by the addition of auxiliary spinor coordinates of the moving repere (the Newman-Penrose dyades for D=4). The spinor coordinates are realized as the Lorentz harmonics and necessary for the irreducible covariant description of the κ-symmetry. Using this harmonical realization a generalization of the Newman-Penrose dyades for the case D=11 is suggested.

scholarly journals The Topology of the Configuration Space of a Mathematical Model for Cycloalkenes

2021 ◽  
Author(s):  
Yasuhiko Kamiyama
Keyword(s):  
Mathematical Model ◽  
Configuration Space ◽  
Topological Type ◽  
Closed Surface ◽  
Positive Genus

As a mathematical model for cycloalkenes, we consider equilateral polygons whose interior angles are the same except for those of the both ends of the specified edge. We study the configuration space of such polygons. It is known that for some case, the space is homeomorphic to a sphere. The purpose of this chapter is threefold: First, using the h-cobordism theorem, we prove that the above homeomorphism is in fact a diffeomorphism. Second, we study the best possible condition for the space to be a sphere. At present, only a sphere appears as a topological type of the space. Then our third purpose is to show the case when a closed surface of positive genus appears as a topological type.

Optimization in Mental Configuration Space

2012 ◽  
pp. 140-155
Author(s):  
Huahai Yang
Keyword(s):  
Configuration Space ◽  
Motor Behavior ◽  
Dimensional Space ◽  
Geometric Approach ◽  
Human Cognition ◽  
Important Class ◽  
Two Dimensional ◽  
Performance Models ◽  
Space Concept

This chapter describes a geometric approach to human cognition centering on the concept of mental configuration space. As a case study of the approach, this work details a study that derives performance models for an important class of motor behavior—pointing in the two dimensional space. The five derived models and three existing models in the literature are compared using an experimental study. It is found that the models developed on the basis of mental configuration space fit the empirical data better than other models. It is argued that the mental configuration space concept points to a potentially fruitful direction of research. Finally, the chapter discusses the implications of such an approach for user interface research and development.

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