High-Order Splines on Riemannian Manifolds

被引：4

作者：

Camarinha, Margarida ^{[1
]}

Silva Leite, Fatima ^{[2
,3
]}

Crouch, Peter E. ^{[4
]}

机构：

[1] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra, Portugal

[2] UC, Inst Syst & Robot, P-3030290 Coimbra, Portugal

[3] Univ Coimbra, Dept Math, P-3000143 Coimbra, Portugal

[4] Univ Texas Arlington, Coll Engn, Arlington, TX 76019 USA

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2023年 / 321卷 / 01期

关键词：

Riemannian polynomial splines; variational problems; Euler-Lagrange equations; generalized Jacobi fields and conjugate points; -exponential; optimal control; Hamiltonian equations; FITTING SMOOTH PATHS; VARIATIONAL-PROBLEMS; BEZIER CURVES; LIE-GROUPS; CUBICS; REDUCTION; INTERPOLATION; INTEGRATORS; GEOMETRY; SYSTEMS;

D O I：

10.1134/S0081543823020128

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is an overview of the work of the authors about generalized polynomial curves and splines on Riemannian manifolds. The emphasis is put on the variational approach that gives rise to such curves, and on the Hamiltonian formulation for the cubic case.

引用

页码：158 / 178

页数：21

共 68 条

[1] Cubic polynomials on Lie groups: reduction of the Hamiltonian system [J].

Abrunheiro, L. ;

Camarinha, M. ;

Clemente-Gallardo, J. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (35)

[2]

Agrachev A. A., 2004, Control Theory from the Geomeric Viewpoint

[3] Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric [J].

Altafini, C .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2004, 10 (04) :526-548

[4]

[Anonymous], 1967, The Theory of Splines and Their Applications

[5] Unit speed stationary points of the acceleration [J].

Arroyo, J. ;

Garay, O. J. ;

Mencia, J. J. .

JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (01)

[6] ABOUT SIMPLE VARIATIONAL SPLINES FROM THE HAMILTONIAN VIEWPOINT [J].

Balseiro, Paula ;

Stuchi, Teresinha J. ;

Cabrera, Alejandro ;

Koiller, Jair .

JOURNAL OF GEOMETRIC MECHANICS, 2017, 9 (03) :257-290

[7] STRICT ABNORMAL EXTREMALS IN NONHOLONOMIC AND KINEMATIC CONTROL SYSTEMS [J].

Barbero-Linan, Maria ;

Munoz-Lecanda, Miguel C. .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2010, 3 (01) :1-17

[8] Geometric mean and geodesic regression on Grassmannians [J].

Batzies, E. ;

Hueper, K. ;

Machado, L. ;

Leite, F. Silva .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 466 :83-101

[9]

BLOCH AM, 1994, IEEE DECIS CONTR P, P2584, DOI 10.1109/CDC.1994.411534

[10]

Bloch AM, 1999, MATHEMATICAL CONTROL THEORY, P268

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