A Differential-Geometric Approach for Bernstein’s Degrees-of-Freedom Problem

2007 ◽  
pp. 1-28 ◽  
Author(s):  
Suguru Arimoto
Keyword(s):  
Degrees Of Freedom ◽  
Geometric Approach

CONTROL OF A COMPLIANT HUMANOID ROBOT IN DOUBLE SUPPORT PHASE: A GEOMETRIC APPROACH

2012 ◽  
Vol 09 (01) ◽  
pp. 1250004 ◽  
Author(s):  
GUSTAVO MEDRANO CERDA ◽  
HOUMAN DALLALI ◽  
MARTIN BROWN
Keyword(s):  
Energy Efficiency ◽  
Degrees Of Freedom ◽  
Geometric Approach ◽  
Research Problem ◽  
Bipedal Walking ◽  
Constrained Motion ◽  
Double Support ◽  
Compliant Actuators ◽  
Support Phase ◽  
Double Support Phase

Enhancing energy efficiency of bipedal walking is an important research problem that has been approached by design of recently developed compliant bipedal robots such as CoMan. While compliance leads to energy efficiency, it also complicates the walking control system due to further under-actuated degrees of freedom (DoF) associated with the compliant actuators. This problem becomes more challenging as the constrained motion of the robot in double support is considered. In this paper this problem is approached from a multi-variable geometric control aspect to systematically account for the compliant actuators dynamics and constrained motion of the robot in double support phase using a detailed electro-mechanical model of CoMan. It is shown that the formulation of constraint subspace is non-trivial in the case of non-rigid robots. A step-wise numerical algorithm is provided and the effectiveness of the proposed method is illustrated via simulation, using a ten DoF model of CoMan.

Inverse Kinematics Simulation for a Surgical Robot Using CATIA

2015 ◽  
Vol 780 ◽  
pp. 49-54
Author(s):  
Shao Gang Liu ◽  
Edris Farah
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
3D Model ◽  
Geometric Approach ◽  
Surgical Robot ◽  
Six Degrees Of Freedom ◽  
Kinematics Simulation ◽  
Kinematics Modeling ◽  
Model Equations ◽  
The Mathematical Model

Robotic arm with six degrees of freedom can be successfully used to do a surgical task through a small incision called (RCM point) on the patient's body. Inverse Kinematics modeling and simulating of a 6 DOF surgical robot is developed in this paper. The mathematical model equations are built using geometric approach and the Denavit-Hartenberg convention. The 3D model of the robot is created by CATIA5 to simulate the motion of the robot in surgical environments. The inverse kinematics equations model is validated through the simulating model. Result confirms that the proposed robot mechanism is applicable for minimally invasive surgery applications.

scholarly journals The Planar Thirring Model with Kähler-Dirac Fermions

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1523
Author(s):  
Simon Hands
Keyword(s):  
Degrees Of Freedom ◽  
Differential Forms ◽  
Continuum Theory ◽  
Geometric Approach ◽  
Mass Term ◽  
Thirring Model ◽  
Dirac Fermions ◽  
Long Wavelength ◽  
Fermion Fields ◽  
Lattice Fermions

Kähler’s geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U(N)⊗U(N) field transformations and has a parity-invariant mass term, which are symmetries shared in common with staggered lattice fermions. The formalism is used to construct a version of the Thirring model with contact interactions between conserved Noether currents. Under reasonable assumptions about field rescaling after quantum corrections, a more general interaction term is derived, sharing the same symmetries but now including terms which entangle spin and taste degrees of freedom, which exactly coincides with the leading terms in the staggered lattice Thirring model in the long-wavelength limit. Finally, truncated versions of the theory are explored; it is found that excluding scalar and pseudoscalar components leads to a theory of six-component fermion fields describing particles with spin 1, with fermion and antifermion corresponding to states with definite circular polarisation. In the UV limit, only transverse states with just four non-vanishing components propagate. Implications for the description of dynamics at a strongly interacting renormalisation group fixed point are discussed.

scholarly journals A geometric approach for follow-the-leader motion of serpentine manipulator

2019 ◽  
Vol 16 (5) ◽  
pp. 172988141987463 ◽  
Author(s):  
Haibo Xie ◽  
Cheng Wang ◽  
Shusen Li ◽  
Liang Hu ◽  
Huayong Yang
Keyword(s):  
Path Planning ◽  
Real Time ◽  
Obstacle Avoidance ◽  
Degrees Of Freedom ◽  
Mechanical Design ◽  
Computation Time ◽  
Geometric Approach ◽  
Real Time Control ◽  
Time Control ◽  
The Ideal

This article presents a geometric approach for path planning of serpentine manipulator for real-time control in confined spaces. Firstly, the mechanical design of a serpentine manipulator is introduced, and its kinematics is analyzed. As the serpentine manipulator usually has more than 10 degrees of freedom, the motion control and obstacle avoidance are difficult considering its inverse kinematics. Follow-the-leader is an ideal path planning method for serpentine manipulator, as the manipulator moves forward, all the sections follow the path that the tip of manipulator has passed, which simplifies the obstacle avoidance. The realization of follow-the-leader method is to find the new configurations of the manipulator that can fit the ideal path with small errors. In this article, a novel geometric approach for follow-the-leader motion is proposed to solve new configurations with high precision of location and less computation time. The method is validated through simulation and the deviation from the ideal path is analyzed, simulation results show that calculation time for per step is less than 0.5 ms for a serpentine manipulator with 10 sections. To verify the follow-the-leader method, a 13-degree-of-freedom serpentine manipulator system with 6 sections was built, and 12 magnetic rotary encoders were embedded into the universal joints to collect data of rotation angles of each section. Experimental results show that the manipulator can carry out follow-the-leader motion as expected in real time.

scholarly journals Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
K. Eder ◽  
H. Sahlmann
Keyword(s):  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Chiral Limit ◽  
Geometric Approach ◽  
Simons Theory ◽  
New Developments ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory ◽  
Topological Term

Abstract In this article, the Cartan geometric approach toward (extended) supergravity in the presence of boundaries will be discussed. In particular, based on new developments in this field, we will derive the Holst variant of the MacDowell-Mansouri action for $$ \mathcal{N} $$ N = 1 and $$ \mathcal{N} $$ N = 2 pure AdS supergravity in D = 4 for arbitrary Barbero-Immirzi parameters. This action turns out to play a crucial role in context of boundaries in the framework of supergravity if one imposes supersymmetry invariance at the boundary. For the $$ \mathcal{N} $$ N = 2 case, it follows that this amounts to the introduction of a θ-topological term to the Yang-Mills sector which explicitly depends on the Barbero-Immirzi parameter. This shows the close connection between this parameter and the θ-ambiguity of gauge theory.We will also discuss the chiral limit of the theory, which turns out to possess some very special properties such as the manifest invariance of the resulting action under an enlarged gauge symmetry. Moreover, we will show that demanding supersymmetry invariance at the boundary yields a unique boundary term corresponding to a super Chern-Simons theory with OSp($$ \mathcal{N} $$ N |2) gauge group. In this context, we will also derive boundary conditions that couple boundary and bulk degrees of freedom and show equivalence to the results found in the D’Auria-Fré approach in context of the non-chiral theory. These results provide a step towards of quantum description of supersymmetric black holes in the framework of loop quantum gravity.

A Geometric Approach to Hyper-Redundant Manipulator Obstacle Avoidance

1992 ◽  
Vol 114 (4) ◽  
pp. 580-585 ◽  
Author(s):  
G. S. Chirikjian ◽  
J. W. Burdick
Keyword(s):  
Differential Geometry ◽  
Obstacle Avoidance ◽  
Infinite Number ◽  
Degrees Of Freedom ◽  
Geometric Approach ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Redundant Robots ◽  
Geometric Algorithm

The term hyper-redundant refers to redundant manipulators with a very large or infinite number of degrees of freedom. These manipulators are analogous in morphology to snakes, elephant trunks, and tentacles. While a variety of obstacle avoidance algorithms for nonredundant and mildly redundant manipulators exist, little analysis has been performed for hyper-redundant robots. This paper presents a strictly geometric algorithm for hyper-redundant manipulator obstacle avoidance which relies on the use of “tunnels” in the obstacle-filled workspace. Methods of differential geometry are used to formulate equations which guarantee that sections of the manipulator are confined to the tunnels, and therefore avoid obstacles. A general formulation is presented with an example to illustrate this approach.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

A Geometric Approach to Homology Theory

1976 ◽  
Author(s):  
S. Buonchristiano ◽  
C. P. Rourke ◽  
B. J. Sanderson
Keyword(s):  
Geometric Approach ◽  
Homology Theory

Das Experten-Novizen-Paradigma und die Vertrauenskrise in der Psychologie

2016 ◽  
Vol 23 (4) ◽  
pp. 131-140 ◽  
Author(s):  
Philip Furley ◽  
Karsten Schul ◽  
Daniel Memmert
Keyword(s):  
Degrees Of Freedom

Zusammenfassung. Das Ziel des vorliegenden Beitrages ist es anhand eines vielverwendeten Paradigmas in der Sportwissenschaft – dem Experten-Novizen-Vergleich – zu prüfen, ob die momentane Vertrauenskrise in der Psychologie ebenfalls die Sportpsychologie betreffen könnte. Anhand einer exemplarischen Studie zeigen wir, dass es innerhalb dieses Paradigmas zu kontroversen Befunden kommt, welche durch die vermuteten Ursachen der Vertrauenskrise (Researcher Degrees of Freedom, kleine Stichprobengrößen) erklärt sein könnten. Zusätzlich argumentieren wir, dass weitere Faktoren (Konfundierung, Stichprobengrößen, Rosenthal Effekt, Expertise-Definition) innerhalb dieses Paradigmas die Reproduzierbarkeit von Erkenntnissen in Frage stellen. Wir diskutieren mögliche Maßnahmen, wie die dargestellten Probleme des Experten-Novizen-Paradigmas in zukünftigen Forschungsarbeiten gelöst werden können.

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