Adjustable Tensegrity Robot Based on Assur Graph Principle

2009 ◽  
Author(s):  
Offer Shai ◽  
Itay Tehori ◽  
Avner Bronfeld ◽  
Michael Slavutin ◽  
Uri Ben-Hanan
Keyword(s):  
Control System ◽  
Projective Geometry ◽  
Efficient Algorithm ◽  
Degrees Of Freedom ◽  
Theoretical Foundation ◽  
Main Idea ◽  
Output Data ◽  
Promising Application ◽  
External Loads

The paper introduces a tensegrity robot consisting of cables and actuators. Although this robot has zero degrees of freedom, it is both mobile, and capable of sustaining massive external loads. This outcome is achieved by constantly maintaining the configuration of the robot at a singular position. The underlying theoretical foundation of this work is originated from the concept of Assur Trusses (also known as Assur Groups), which are long known in the field of kinematics. During the last three years, the latter concept has been reformulated by mathematicians from rigidity theory community, and new theorems and algorithms have been developed. Since the topology of the robot is an Assur Truss, the work reported in the paper relies on Assur Trusses theorems that have been developed this year resulting in an efficient algorithm to constantly keep the robot at the singular position. In order to get an efficient characterization of the desired configurations, known techniques from projective geometry were employed. The main idea of the control system of the device, that was also mathematically proved, is that changing the length of only one element, causes the robot to be at the singular position. Therefore, the system measures the force in only one cable, and its length is modified accordingly by the control system. The topology of the device is an Assur Truss — a 3D triad, but the principles introduced in the paper are applicable to any robot whose topology is an Assur Truss, such as: tetrad, pentad, double triad and so forth. The paper includes several photos of the device and the output data of the control system indicating its promising application.

scholarly journals Efficient Search for Optimal Diffusion Layers of Generalized Feistel Networks

2019 ◽  
pp. 218-240
Author(s):  
Patrick Derbez ◽  
Pierre-Alain Fouque ◽  
Baptiste Lambin ◽  
Victor Mollimard
Keyword(s):  
Lower Bound ◽  
Open Problem ◽  
Building Block ◽  
Efficient Algorithm ◽  
Main Idea ◽  
Diffusion Layers ◽  
Round Function ◽  
Feistel Networks ◽  
Impossibility Proof

The Feistel construction is one of the most studied ways of building block ciphers. Several generalizations were then proposed in the literature, leading to the Generalized Feistel Network, where the round function first applies a classical Feistel operation in parallel on an even number of blocks, and then a permutation is applied to this set of blocks. In 2010 at FSE, Suzaki and Minematsu studied the diffusion of such construction, raising the question of how many rounds are required so that each block of the ciphertext depends on all blocks of the plaintext. They thus gave some optimal permutations, with respect to this diffusion criteria, for a Generalized Feistel Network consisting of 2 to 16 blocks, as well as giving a good candidate for 32 blocks. Later at FSE’19, Cauchois et al. went further and were able to propose optimal even-odd permutations for up to 26 blocks.In this paper, we complete the literature by building optimal even-odd permutations for 28, 30, 32, 36 blocks which to the best of our knowledge were unknown until now. The main idea behind our constructions and impossibility proof is a new characterization of the total diffusion of a permutation after a given number of rounds. In fact, we propose an efficient algorithm based on this new characterization which constructs all optimal even-odd permutations for the 28, 30, 32, 36 blocks cases and proves a better lower bound for the 34, 38, 40 and 42 blocks cases. In particular, we improve the 32 blocks case by exhibiting optimal even-odd permutations with diffusion round of 9. The existence of such a permutation was an open problem for almost 10 years and the best known permutation in the literature had a diffusion round of 10. Moreover, our characterization can be implemented very efficiently and allows us to easily re-find all optimal even-odd permutations for up to 26 blocks with a basic exhaustive search

scholarly journals GALOIS THEORY OF THE CANONICAL THETA STRUCTURE

2011 ◽  
Vol 07 (01) ◽  
pp. 173-202
Author(s):  
ROBERT CARLS
Keyword(s):  
Galois Theory ◽  
Theoretical Foundation ◽  
Abelian Varieties ◽  
Geometric Mean ◽  
Null Point ◽  
Point Counting ◽  
Characteristic 2 ◽  
Theoretic Characterization ◽  
Generalized Arithmetic

In this article, we give a Galois-theoretic characterization of the canonical theta structure. The Galois property of the canonical theta structure translates into certain p-adic theta relations which are satisfied by the canonical theta null point of the canonical lift. As an application, we prove some 2-adic theta identities which describe the set of canonical theta null points of the canonical lifts of ordinary abelian varieties in characteristic 2. The latter theta relations are suitable for explicit canonical lifting. Using the theory of canonical theta null points, we are able to give a theoretical foundation to Mestre's point counting algorithm which is based on the computation of the generalized arithmetic geometric mean sequence.

Characterization of Piezoelectric Nanofiber Composites Acoustic Emission Sensor for Structure Health Monitoring

2012 ◽  
Author(s):  
Xi Chen ◽  
Yong Shi
Keyword(s):  
Acoustic Emission ◽  
Lead Zirconate Titanate ◽  
High Sensitivity ◽  
Lead Zirconate ◽  
Steel Bar ◽  
Promising Application ◽  
Soft Polymer ◽  
Active Fiber Composites ◽  
The Mathematical Model

A nanoscale active fiber composites (NAFCs) based acoustic emission (AE) sensor with high sensitivity is developed. The lead zirconate titanate (PZT) nanofibers, with the diameter of approximately 80 nm, were electrospun on a silicon substrate. Nanofibers were parallel aligned on the substrate under a controlled electric field. The interdigitated electrodes were deposited on the PZT nanofibers and packaged by spinning a thin soft polymer layer on the top of the sensor. The hysteresis loop shows a typical ferroelectric property of as-spun PZT nanofibers. The mathematical model of the voltage generation when the elastic waves were reaching the sensor was studied. The sensor was tested by mounting on a steel surface and the measured output voltage under the periodic impact of a grounded steel bar was over 35 mV. The small size of the developed PZT NAFCs AE sensor shows a promising application in monitoring the structures by integration into composites.

Variational characterization of real eigenvalues in linear viscoelastic oscillators

2017 ◽  
Vol 23 (10) ◽  
pp. 1377-1388 ◽  
Author(s):  
Seyyed Abbas Mohammadi ◽  
Heinrich Voss
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Eigenvalue Problem ◽  
Eigenvalues And Eigenvectors ◽  
Variational Characterization ◽  
Viscoelastic System ◽  
New Approach ◽  
Motion Equations ◽  
Multiple Degrees Of Freedom ◽  
Linear Viscoelastic

This paper proposes a new approach for computing the real eigenvalues of a multiple-degrees-of-freedom viscoelastic system in which we assume an exponentially decaying damping. The free-motion equations lead to a nonlinear eigenvalue problem. If the system matrices are symmetric, the eigenvalues allow for a variational characterization of maxmin type, and the eigenvalues and eigenvectors can be determined very efficiently by the safeguarded iteration, which converges quadratically and, for extreme eigenvalues, monotonically. Numerical methods demonstrate the performance and the reliability of the approach. The method succeeds where some current approaches, with restrictive physical assumptions, fail.

Unified Rotational and Translational Stiffness Characterization of Compliant Shell Mechanisms

2018 ◽  
Author(s):  
Joost R. Leemans ◽  
Charles J. Kim ◽  
Werner W. P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Characterization Methods ◽  
Six Degrees Of Freedom ◽  
Thin Walled Structures ◽  
Spatial Mechanisms ◽  
Eigen Decomposition ◽  
Comprehensive Characterization

Compliant shell mechanisms utilize spatially curved thin-walled structures to transfer or transmit force, motion or energy through elastic deformation. To design with spatial mechanisms designers need comprehensive characterization methods, while existing methods fall short of meaningful comparisons between rotational and translational degrees of freedom. This paper presents two approaches, both of which are based on the principle of virtual loads and potential energy, utilizing properties of screw theory, Plücker coordinates and an eigen-decomposition, leading to two unification lengths that can be used to compare and visualize all six degrees of freedom directions and magnitudes of compliant mechanisms in a non-arbitrary physically meaningful manner.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

Globalized Dual Heuristic Dynamic Programming in Control of Robotic Manipulator

2016 ◽  
Vol 817 ◽  
pp. 150-161 ◽  
Author(s):  
Marcin Szuster ◽  
Piotr Gierlak
Keyword(s):  
Neural Networks ◽  
Dynamic Programming ◽  
Control System ◽  
Degrees Of Freedom ◽  
Dynamic Programming Algorithm ◽  
Robotic Manipulator ◽  
Iteration Step ◽  
Programming Algorithm ◽  
Heuristic Dynamic Programming ◽  
The Stability

The article focuses on the implementation of the globalized dual-heuristic dynamic programming algorithm in the discrete tracking control system of the three degrees of freedom robotic manipulator. The globalized dual-heuristic dynamic programming algorithm is included in the approximate dynamic programming algorithms family, that bases on the Bellman’s dynamic programming idea. These algorithms generally consist of the actor and the critic structures realized in a form of artificial neural networks. Moreover, the control system includes the PD controller, the supervisory term and an additional control signal. The structure of the supervisory term derives from the stability analysis, which was realized using the Lyapunov stability theorem. The control system works on-line and the neural networks’ weight adaptation process is realized in every iteration step. A series of computer simulations was realized in Matlab/Simulink software to confirm performance of the control system.

FINITELY SUBSEQUENTIAL TRANSDUCERS

2003 ◽  
Vol 14 (06) ◽  
pp. 983-994 ◽  
Author(s):  
CYRIL ALLAUZEN ◽  
MEHRYAR MOHRI
Keyword(s):  
Speech Recognition ◽  
Finite Number ◽  
Efficient Algorithm ◽  
Experimental Results ◽  
Theoretical Formulation ◽  
Large Vocabulary ◽  
Finite State Transducers ◽  
Finite State ◽  
Large Vocabulary Speech Recognition

Finitely subsequential transducers are efficient finite-state transducers with a finite number of final outputs and are used in a variety of applications. Not all transducers admit equivalent finitely subsequential transducers however. We briefly describe an existing generalized determinization algorithm for finitely subsequential transducers and give the first characterization of finitely subsequentiable transducers, transducers that admit equivalent finitely subsequential transducers. Our characterization shows the existence of an efficient algorithm for testing finite subsequentiability. We have fully implemented the generalized determinization algorithm and the algorithm for testing finite subsequentiability. We report experimental results showing that these algorithms are practical in large-vocabulary speech recognition applications. The theoretical formulation of our results is the equivalence of the following three properties for finite-state transducers: determinizability in the sense of the generalized algorithm, finite subsequentiability, and the twins property.

Sign in / Sign up

Export Citation Format

Share Document