Dynamic interpolation for obstacle avoidance on Riemannian manifolds

DOI10.1080/00207179.2019.1603400zbMath1480.93302arXiv1809.03168OpenAlexW2892277472WikidataQ115310178 ScholiaQ115310178MaRDI QIDQ5020766

Anthony M. Bloch, Leonardo Colombo, Margarida Camarinha

Publication date: 7 January 2022

Published in: International Journal of Control (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.03168

zbMATH Keywords

Lie groupstrajectory planningobstacle avoidanceinterpolation problemsRiemannian and sub-Riemannian geometry

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Sub-Riemannian geometry (53C17) Model systems in control theory (93C99)

Related Items (9)

Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces ⋮ Geometric control of two quadrotors carrying a rigid rod with elastic cables ⋮ High-order splines on Riemannian manifolds ⋮ Existence of global minimizer for elastic variational obstacle avoidance problems on Riemannian manifolds ⋮ Local minimizers for variational obstacle avoidance on Riemannian manifolds ⋮ Reduction by Symmetry in Obstacle Avoidance Problems on Riemannian Manifolds ⋮ Riemannian cubics close to geodesics at the boundaries ⋮ Finding extremals of Lagrangian actions ⋮ Collision Avoidance of Multiagent Systems on Riemannian Manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher-order smoothing splines versus least squares problems on Riemannian manifolds
• Invariant higher-order variational problems
• Optimal control on Riemannian manifolds by interpolation
• Dynamic coverage optimal control for multiple spacecraft interferometric imaging
• Nonholonomic problems and the theory of distributions
• Elastic curves as solutions of Riemannian and sub-Riemannian control problems.
• Optimal under-actuated kinematic motion planning on the \(\epsilon\)-group
• The dynamic interpolation problem: on Riemannian manifolds, Lie groups, and symmetric spaces
• Variational dynamic interpolation for kinematic systems on trivial principal bundles
• Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. E Crouch, J. E. Marsden and D. Zenkov. With scientific input from P. S. Krishnaprasad and R. M. Murray
• Second-order constrained variational problems on Lie algebroids: applications to optimal control
• A geodesic feedback law to decouple the full and reduced attitude
• Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables
• Higher-order variational problems on Lie groups and optimal control applications
• On gradient dynamical systems
• Cubic Splines on Curved Spaces
• Optimal Control Problems with Symmetry Breaking Cost Functions
• Nonholonomic Control Systems on Riemannian Manifolds
• An analytical theory for Riemannian cubic polynomials
• Motion control of drift-free, left-invariant systems on Lie groups
• Variational time discretization of Riemannian splines
• Finite-time optimal formation control of multi-agent systems on the Lie group SE(3)
• The optimal control problem on SO(4) and its applications to quantum control
• Reduction by group symmetry of second order variational problems on a semidirect product of Lie groups with positive definite Riemannian metric

This page was built for publication: Dynamic interpolation for obstacle avoidance on Riemannian manifolds