Efficient Cartesian path approximation for robots using trigonometric splines

2005 ◽  
Author(s):  
D. Simon ◽  
C. Isik
Keyword(s):  
Trigonometric Splines ◽  
Path Approximation

scholarly journals Maritime Autonomous Surface Ship’s Path Approximation Using Bézier Curves

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1704
Author(s):  
Anna Miller ◽  
Szymon Walczak
Keyword(s):  
Tracking System ◽  
Control Points ◽  
System Research ◽  
Path Modeling ◽  
Time Data ◽  
Trajectory Prediction ◽  
Rational Bézier Curve ◽  
Real Time Data ◽  
Path Approximation ◽  
Drift Path

This work is devoted to the second order rational Bézier curve coefficients estimation. We present the methodology of unique coefficients for each type of ship computation. In the presented formulas of ship’s length, a draft and angular path combined with a drift path are used. This approach leads to the simplest and most accurate Maritime Autonomous Surface Ships (MASS) path modeling. Three rational curve control points are waypoints (WPT). Using WPTs as curve control points allows integrating a trajectory intuitive for the navigator with a path predicting model used as a reference in the control system. Research was done based on real-time data originating from the MASS autonomous trajectory tracking system. The presented mathematical modeling tool may be treated as the best way of future trajectory prediction due to low computation power required.

scholarly journals Hole dynamics in a quantum antiferromagnet: Extension of the retraceable-path approximation

1994 ◽  
Vol 49 (9) ◽  
pp. 6408-6411 ◽  
Author(s):  
Q. F. Zhong ◽  
S. Sorella ◽  
A. Parola
Keyword(s):  
Path Approximation ◽  
Quantum Antiferromagnet

Nuclear Level Densities in the Static-Path Approximation

1988 ◽  
Vol 61 (25) ◽  
pp. 2835-2838 ◽  
Author(s):  
B. Lauritzen ◽  
P. Arve ◽  
G. F. Bertsch
Keyword(s):  
Nuclear Level ◽  
Level Densities ◽  
Path Approximation

scholarly journals A Self-Consistent Treatment of Damped Motion for Stable and Unstable Collective Modes

1998 ◽  
Vol 07 (02) ◽  
pp. 243-274 ◽  
Author(s):  
H. Hofmann ◽  
D. Kiderlen
Keyword(s):  
Harmonic Approximation ◽  
Linear Response Theory ◽  
Collective Modes ◽  
Fluctuation Dissipation ◽  
Second Moments ◽  
Fluctuation Dissipation Theorem ◽  
Dissipative Tunneling ◽  
Self Consistent ◽  
Path Approximation ◽  
Consistent Treatment

We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the fluctuations are governed by diffusion coefficients Dμν. The latter are obtained through a fluctuation dissipation theorem generalized to allow for a treatment of unstable modes. Numerical evaluations of the Dμν are presented. We discuss briefly how this picture may be used to describe global motion within a locally harmonic approximation. Relations to other methods are discussed, like "dissipative tunneling", RPA at finite temperature and generalizations of the "Static Path Approximation".

t-J MODEL FOR TRIPLET HOLES

1991 ◽  
Vol 05 (01n02) ◽  
pp. 131-142 ◽  
Author(s):  
Andrzej M. Oleś ◽  
Jan Zaanen ◽  
Vaclav Drchal
Keyword(s):  
Conventional Wisdom ◽  
Coherent Motion ◽  
Additional Dimension ◽  
Hund’S Rule ◽  
Back Ground ◽  
Path Approximation ◽  
Hund's Rule

If a t—J model applies, conventional wisdom tells that the vacancies are singlets in the high-Tc superconductors. Recent experiments indicate, however, that doping induces significant amounts of 3d3z2 - 1 holes character and this should be attached to the vacancies because of Hund’s rule coupling. This motivates us to consider the motion of a triplet hole in a spin S=1/2 background. We analyze this problem on the level of the nonretracable path approximation and we find that also for J=0 coherent motion is possible. The triplet hole has a branched hopping history. This weakens the band singularities in a ferromagnetic background, while in an antiferromagnetic back-ground this adds nearly an additional dimension to the effective electronic dimensionality.

Diffusion-path approximation in nonlocal electron kinetics

2017 ◽  
Vol 11 (1) ◽  
pp. 106-111 ◽  
Author(s):  
Yu. B. Golubovskii ◽  
K. M. Rabadanov ◽  
V. O. Nekuchaev
Keyword(s):  
Diffusion Path ◽  
Electron Kinetics ◽  
Path Approximation

Ternary approximating non-stationary subdivision schemes for curve design

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
Shahid Siddiqi ◽  
Muhammad Younis
Keyword(s):  
Trigonometric Polynomials ◽  
Asymptotic Equivalence ◽  
Conic Sections ◽  
Subdivision Schemes ◽  
Linear Spaces ◽  
Curve Design ◽  
Trigonometric Splines ◽  
Stationary Subdivision

AbstractIn this paper, an algorithm has been introduced to produce ternary 2m-point (for any integer m ≥ 1) approximating non-stationary subdivision schemes which can generate the linear spaces spanned by {1; cos(α.); sin(α.)}. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the schemes. The proposed algorithm can be consider as the non-stationary counter part of the 2-point and 4-point existing ternary stationary approximating schemes, for different values of m. Moreover, the proposed algorithm has the ability to reproduce or regenerate the conic sections, trigonometric polynomials and trigonometric splines.

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