Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane
From MaRDI portal
Publication:3060046
DOI10.1051/cocv/2009031zbMath1208.49003arXiv0903.0727OpenAlexW2127787309WikidataQ115334472 ScholiaQ115334472MaRDI QIDQ3060046
Publication date: 30 November 2010
Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0903.0727
optimal controlsub-Riemannian geometryconjugate timecut timedifferential-geometric methodsrototranslationsgroup of motions of a planeleft-invariant problem
Geometric methods (93B27) Variational problems in a geometric measure-theoretic setting (49Q20) Existence theories for optimal control problems involving ordinary differential equations (49J15) Sub-Riemannian geometry (53C17)
Related Items (38)
On extensions of sub-Riemannian structures on Lie groups ⋮ Controlling of a mobile robot with a trailer and its nilpotent approximation ⋮ Relation between Euler's elasticae and sub-Riemannian geodesics on \(\mathrm{SE}(2)\) ⋮ Cut locus and optimal synthesis in sub-Riemannian problem on the Lie group SH(2) ⋮ Pontryagin maximum principle, (co)adjoint representation, and normal geodesics of left-invariant (sub-)Finsler metrics on Lie groups ⋮ On sub-Riemannian and Riemannian structures on the Heisenberg groups ⋮ Cut time in the sub-Riemannian problem on the Cartan group ⋮ Maxwell strata and conjugate points in the sub-Riemannian problem on the Lie group SH(2) ⋮ On sub-Riemannian geodesics in \(\mathrm{SE}(3)\) whose spatial projections do not have cusps ⋮ Unnamed Item ⋮ Control of a mobile robot with a trailer based on nilpotent approximation ⋮ Geodesics in the Heisenberg group \(H ^{n }\) with a Lorentzian metric ⋮ Cut time in sub-riemannian problem on engel group ⋮ Cuspless Sub-Riemannian Geodesics within the Euclidean Motion Group SE(d) ⋮ A Nonholonomic Model and Complete Controllability of a Three-Link Wheeled Snake Robot ⋮ Control systems on the Engel group ⋮ The geometry of Riemannian curvature radii ⋮ Symmetries in left-invariant optimal control problems ⋮ Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems ⋮ Sub-Riemannian structures on 3D Lie groups ⋮ Conjugate points in nilpotent sub-Riemannian problem on the Engel group ⋮ Extremal trajectories and Maxwell strata in sub-Riemannian problem on group of motions of pseudo-Euclidean plane ⋮ Data-Driven Sub-Riemannian Geodesics in SE(2) ⋮ Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane ⋮ Maxwell strata in sub-Riemannian problem on the group of motions of a plane ⋮ Conjugate time in the sub-Riemannian problem on the Cartan group ⋮ Association fields via cuspless sub-Riemannian geodesics in SE(2) ⋮ Asymptotic solution of a singularly perturbed optimal control problem related to the reconstruction of a defective curve ⋮ Cost-extended control systems on Lie groups ⋮ Sub-Riemannian geodesics on the three-dimensional solvable non-nilpotent Lie group \(\mathrm{SOLV}^-\) ⋮ Symmetric Riemannian problem on the group of proper isometries of hyperbolic plane ⋮ A PDE Approach to Data-Driven Sub-Riemannian Geodesics in $SE$(2) ⋮ Comparison theorems for conjugate points in sub-Riemannian geometry ⋮ Stable Feedback Control of a Fast Wheeled Robot ⋮ Homogeneous sub-Riemannian geodesics on a group of motions of the plane ⋮ Bicycle paths, elasticae and sub-Riemannian geometry ⋮ Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry ⋮ On the Gamma-convergence of some polygonal curvature functionals
Uses Software
Cites Work
- Maxwell strata in the Euler elastic problem
- Conjugate points in the Euler elastic problem
- The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
- Control theory from the geometric viewpoint.
- Small sub-Riemannian balls on \(\mathbf R^3\)
- Exponential mappings for contact sub-Riemannian structures
- Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane
- Complete description of the Maxwell strata in the generalized Dido problem
- Maxwell strata in sub-Riemannian problem on the group of motions of a plane
- Exponential map in the generalized Dido problem
- Discrete symmetries in the generalized Dido problem
- The Maxwell set in the generalized Dido problem
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane
