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Wyświetlanie 1-15 z 31
Tytuł:
Approximation of Jacobian inverse kinematics algorithms
Autorzy:
Tchoń, K.
Karpińska, J.
Janiak, M.
Powiązania:
https://bibliotekanauki.pl/articles/929992.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
kinematyka odwrotna
pseudoodwrotny Jacobian
aproksymacja
robot inverse kinematics
extended Jacobian
Jacobian pseudoinverse
approximation
Opis:
This paper addresses the synthesis problem of Jacobian inverse kinematics algorithms for stationary manipulators and mobile robots. Special attention is paid to the design of extended Jacobian algorithms that approximate the Jacobian pseudoinverse algorithm. Two approaches to the approximation problem are developed: one relies on variational calculus, the other is differential geometric. Example designs of the extended Jacobian inverse kinematics algorithm for 3DOF manipulators as well as for the unicycle mobile robot illustrate the theoretical concepts.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 4; 519-531
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
About some properties of jacobian for polynomial mappings of two complex variables
Autorzy:
Gawroński, B.
Jankowska, J.
Moltzan, R.
Włodarczyk, I.
Biernat, G.
Powiązania:
https://bibliotekanauki.pl/articles/123009.pdf
Data publikacji:
2013
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
polynomial mappings
Jacobian
Opis:
In our article we consider jacobian Jac(f,h) of polynomial mapping f = Xk Yk +…+ f1, h = Xk–1 Yk–1 +…+ h1. We give conditions for coordinate h in which constant jacobian Jac(f,h) = Jac(f1,h1) vanishes.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 4; 41-46
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A counterexample to a conjecture of Drużkowski and Rusek
Autorzy:
van den Essen, Arno
Powiązania:
https://bibliotekanauki.pl/articles/1311428.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
polynomial automorphisms
Jacobian Conjecture
Opis:
Let F = X + H be a cubic homogeneous polynomial automorphism from $ℂ^n$ to $ℂ^n$. Let $p$ be the nilpotence index of the Jacobian matrix JH. It was conjectured by Drużkowski and Rusek in [4] that $deg F^{-1} ≤ 3^{p-1}$. We show that the conjecture is true if n ≤ 4 and false if n ≥ 5.
Źródło:
Annales Polonici Mathematici; 1995, 62, 2; 173-176
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some remarks to the Jacobian conjecture
Autorzy:
Lara-Dziembek, S.
Biernat, G.
Pawlak, E.
Powiązania:
https://bibliotekanauki.pl/articles/122630.pdf
Data publikacji:
2017
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Jacobian
zero at infinity
Jacobian Conjecture
zero w nieskończoności
hipoteza Jakobianowa
odwzorowanie wielomianu
Opis:
This work is related to the Jacobian Conjecture. It contains the formulas concerning algebraic dependence of the polynomial mappings having two zeros at infinity and the constant Jacobian. These relations mean that such mappings are non-invertible. They reduce the Jacobian Conjecture only to the case of mappings having one zero at infinity. This case is already solved by Abhyankar. The formulas presented in the paper were illustrated by the large example.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 1; 87-96
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Regular analytic transformations of $ℝ^2$
Autorzy:
Gubeladze, Joseph
Powiązania:
https://bibliotekanauki.pl/articles/1207913.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
injectivity
regular analytic maps
Jacobian
Opis:
Existence of loops for non-injective regular analytic transformations of the real plane is shown. As an application, a criterion for injectivity of a regular analytic transformation of $ℝ^2$ in terms of the Jacobian and the first and second order partial derivatives is obtained. This criterion is new even in the special case of polynomial transformations.
Źródło:
Annales Polonici Mathematici; 2000, 75, 2; 99-109
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monodromy, differential equations and the Jacobian conjecture
Autorzy:
Friedland, Shmuel
Powiązania:
https://bibliotekanauki.pl/articles/1293854.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Jacobian conjecture
Gauss-Manin connection
monodromy
Opis:
We study certain problems on polynomial mappings related to the Jacobian conjecture.
Źródło:
Annales Polonici Mathematici; 1999, 72, 3; 219-249
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Jacobian Conjecture in case of "non-negative coefficients"
Autorzy:
Drużkowski, Ludwik
Powiązania:
https://bibliotekanauki.pl/articles/1294772.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
polynomial automorphisms
nilpotent matrix
Jacobian Conjecture
Opis:
It is known that it is sufficient to consider in the Jacobian Conjecture only polynomial mappings of the form $F(x₁,...,x_n) = x - H(x) := (x₁ - H₁(x₁,...,x_n),...,x_n - H_n(x₁,...,x_n))$, where $H_j$ are homogeneous polynomials of degree 3 with real coefficients (or $H_j = 0$), j = 1,...,n and H'(x) is a nilpotent matrix for each $x = (x₁,...,x_n) ∈ ℝ^n$.
We give another proof of Yu's theorem that in the case of non-negative coefficients of H the mapping F is a polynomial automorphism, and we moreover prove that in that case $deg F^{-1} ≤ (deg F)^{ind F - 1}$, where $ind F := max{ind H'(x): x ∈ ℝ^n}$. Note that the above inequality is not true when the coefficients of H are arbitrary real numbers; cf. [E3].
Źródło:
Annales Polonici Mathematici; 1997, 66, 1; 67-75
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Differential conditions to verify the Jacobian Conjecture
Autorzy:
Drużkowski, Ludwik
Tutaj, Halszka
Powiązania:
https://bibliotekanauki.pl/articles/1311973.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
jacobian conditions
global injectivity
global stability
Opis:
Let F be a polynomial mapping of ℝ², F(O) = 0. In 1987 Meisters and Olech proved that the solution y(·) = 0 of the autonomous system of differential equations ẏ = F(y) is globally asymptotically stable provided that the jacobian of F is everywhere positive and the trace of the matrix of the differential of F is everywhere negative. In particular, the mapping F is then injective. We give an n-dimensional generalization of this result.
Źródło:
Annales Polonici Mathematici; 1992, 57, 3; 253-263
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse
Autorzy:
Ratajczak, J.
Powiązania:
https://bibliotekanauki.pl/articles/229524.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
redundant manipulator
inverse kinematics
Jacobian
approximation
Opis:
The paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We introduce the approximation of the dynamically consistent Jacobian by the extended Jacobian. In order to do that, we formulate the approximation problem and suitably defined approximation error. By the minimization of this error over a certain region we can design an extended Jacobian inverse which will be close to the dynamically consistent Jacobian inverse. To solve the approximation problem we use the Cholesky decomposition and the Ritz method. The computational example illustrates the theory.
Źródło:
Archives of Control Sciences; 2015, 25, 1; 35-50
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Non-zero constant Jacobian polynomial maps of $ℂ²$
Autorzy:
Chau, Nguyen
Powiązania:
https://bibliotekanauki.pl/articles/1294068.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Jacobian conjecture
polynomial automorphism
Newton-Puiseux expansion
Opis:
We study the behavior at infinity of non-zero constant Jacobian polynomial maps f = (P,Q) in ℂ² by analyzing the influence of the Jacobian condition on the structure of Newton-Puiseux expansions of branches at infinity of level sets of the components. One of the results obtained states that the Jacobian conjecture in ℂ² is true if the Jacobian condition ensures that the restriction of Q to the curve P = 0 has only one pole.
Źródło:
Annales Polonici Mathematici; 1999, 71, 3; 287-310
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global attractor of a differentiable autonomous system on the plane
Autorzy:
Nguyen, Chau
Powiązania:
https://bibliotekanauki.pl/articles/1311425.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Markus-Yamabe Conjecture
asymptotically stable
Jacobian Conjecture
Opis:
We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.
Źródło:
Annales Polonici Mathematici; 1995, 62, 2; 143-154
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the global asymptotic stability problem and the Jacobian conjecture
Autorzy:
Drużkowski, L. M.
Powiązania:
https://bibliotekanauki.pl/articles/1839158.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
hipoteza jakobianu
global stability problem
Jacobian Conjecture
Opis:
In this survey, we recall the formulation of the problems and give a review of some nontrivial results in the area. Let F = (F1,...,Fn] : R^n - --> R^n be a C^1 map and let F'(x) and Jac F(x) = det F'(x) denote the Jacobian matrix and the jacobian of F at a point x belongs to R^n, respectively. The Global Asymptotic Stability Problem (GASP) reads as follows: Assume that F(0] = 0 and at any point x belongs to R^n all eigenvalues of F'(x) have negative real parts. Then consider the associated system of differential equations x'j(t] = Fj(x1(t), ...,Xn(t)), j = 1,...,n. The question is whether the solution x[t] = 0 is globally asymptotically stable. If n > 2, then the answer is negative (even if F is a a polynomial automorphism), so from now on (GASP) denotes (GASP) restricted to R^2. In 1963, Olech showed that under the (GASP) assumption (i. e., Jac F[x) > 0 and Trace F'(x) = [...] < 0 for any x belong to R^2) the conclusion of (GASP) is equivalent to the injectivity of F. In 1994, Fessler, and independently Gutierrez, proved the injectivity of F and, due to the above mentioned Olech's equivalence, gave the affirmative answer to the two-dimensional (GASP). Let K denote R or C, n > 1. The Jacobian Conjecture can be formulated as follows: If F = (F1, ... ,Fn) : K^n --> K^n is a polynomial map with a constant nonzero jacobian, then F is a polynomial automorphism (i.e. there exists F^-1 and F^-1 is also a polynomial map). Although the Jacobian Conjecture is still unsolved even in the case of n = 2, it is convenient, to consider the so called Generalized Jacobian Conjecture (for short (GJC)): the Jacobian Conjecture holds for every n > 1. We give a review of some interesting conditions equivalent to the Jacobian Conjecture, including Meisters and Olech's result on the existence of a poly-flow solution of the associated Ważewski equation x'(t) = [F'(x(t))]^-1 (a). We also present, a reduction of (GJC) to the case of F of degree 3 and of special forms, then some partial results, and (JC)'s relations with other problems.
Źródło:
Control and Cybernetics; 2005, 34, 3; 747-762
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Trajectory planning for kinematically redundant robots using jacobi matrix – an industrial implementation
Autorzy:
Walther, M.
Sewohl, A.
Schlegel, H.
Neugebauer, R.
Powiązania:
https://bibliotekanauki.pl/articles/99976.pdf
Data publikacji:
2017
Wydawca:
Wrocławska Rada Federacji Stowarzyszeń Naukowo-Technicznych
Tematy:
redundant robots
trajectory planning
jacobian matrix
pseudoinverse
Opis:
The widespread use of robots in industry contributes significantly to high productivity. Serial 6-axis robots are used in large quantities, e.g. for assembly or welding. A current emerging trend is the use of robots for classic tasks of a machine tool like finishing of milled workpieces. For such applications, standard robots are usually extended by additional axes like linear axes or rotary tilting tables. Therefore, the overall system becomes kinematically redundant. To be able to calculate the axis quantities via inverse kinematics for a given path, additional degrees of freedom must be bound. In order to automatically and optimally consider the additional axis motion a method, using the pseudoinverse of the Jacobian matrix, is discussed. Due to the dependence of the Jacobi matrix on the robot's current joint position, numerical inaccuracies, which in turn reflect a path error, are inherent to this method. By feedback control of the path error, in the form of a classic control loop, the error can be reduced so that a practical implementation on industrial robot controller is possible. In the article possibilities for parameterisation of the algorithm as well as proof of stability of the closed loop are presented. The results obtained are verified by a concrete application.
Źródło:
Journal of Machine Engineering; 2017, 17, 3; 24-35
1895-7595
2391-8071
Pojawia się w:
Journal of Machine Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Jacobians of non-maximal degree
Autorzy:
Lara-Dziembek, S.
Biernat, G.
Pawlak, E.
Powiązania:
https://bibliotekanauki.pl/articles/973619.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Jacobian
zeros at infinity
jakobian
zero w nieskończoności
Opis:
In the article the leading forms of the polynomial mapping having the Jacobians of non-maximal degree are considered. In particular, the mappings having two zeros at infinity are discussed.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 4; 99-104
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 31

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