Local geometric control of a certain mechanism with the growth vector \((4,7)\)

DOI10.1007/s10883-019-09460-7zbMath1439.53034arXiv1802.08480OpenAlexW2971405135WikidataQ127297574 ScholiaQ127297574MaRDI QIDQ2174253

Jaroslav Hrdina, Lenka Zalabová

Publication date: 21 April 2020

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.08480

zbMATH Keywords

nilpotent Lie groupPontryagin's maximum principlesub-Riemannian geometrylocal control

Mathematics Subject Classification ID

Control problems involving ordinary differential equations (34H05) Control/observation systems governed by ordinary differential equations (93C15) Sub-Riemannian geometry (53C17)

Related Items (3)

Symmetries in geometric control theory using Maple ⋮ Local control of 2-link robotic worms based on additional symmetries ⋮ On symmetries of a sub-Riemannian structure with growth vector \((4, 7)\)

Uses Software

• DifferentialGeometry
• CLUCalc

Cites Work

• Sard property for the endpoint map on some Carnot groups
• Control theory on Lie groups
• Nilpotent \((3, 6)\) sub-Riemannian problem
• Vector fields with distributions and invariants of ODEs
• Geometric control of the trident snake robot based on CGA
• New symbolic tools for differential geometry, gravitation, and field theory
• Generic one-step bracket-generating distributions of rank four
• Nilpotent Approximations of Control Systems and Distributions
• A Comprehensive Introduction to Sub-Riemannian Geometry
• Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning
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