MOTION PLANNING IN SPACES WITH SMALL FUNDAMENTAL GROUPS

DOI10.1142/S0219199710003750zbMath1215.55001arXiv0806.4113MaRDI QIDQ5306081

A. E. Costa, Michael S. Farber

Publication date: 29 March 2010

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.4113

zbMATH Keywords

configuration spacestopological complexitycomplexity of motion planning algorithms

Mathematics Subject Classification ID

Control/observation systems involving computers (process control, etc.) (93C83) Automated systems (robots, etc.) in control theory (93C85) Control of mechanical systems (70Q05) Robot dynamics and control of rigid bodies (70E60) Discriminantal varieties and configuration spaces in algebraic topology (55R80) Classical topics in algebraic topology (55M99)

Related Items (17)

On the topological complexity of manifolds with abelian fundamental group ⋮ On the topological complexity and zero-divisor cup-length of real Grassmannians ⋮ Motion planning in connected sums of real projective spaces ⋮ Topological complexity of the Klein bottle ⋮ An upper bound for higher topological complexity and higher strongly equivariant complexity ⋮ Lusternik-Schnirelmann theory to topological complexity from \(A_{\infty}\)-view point ⋮ On the topological complexity of aspherical spaces ⋮ Topological complexity of motion planning in projective product spaces ⋮ On topological complexity of twisted products ⋮ Sequential motion planning algorithms in real projective spaces: an approach to their immersion dimension ⋮ Path homotopy invariants and their application to optimal trajectory planning ⋮ Cohomological dimension, self-linking, and systolic geometry ⋮ Topological complexity of configuration spaces ⋮ Topological complexity of real Grassmannians ⋮ On the sectional category of subgroup inclusions and Adamson cohomology theory ⋮ Bredon cohomology and robot motion planning ⋮ A mapping theorem for topological complexity

Cites Work

• Topological complexity of motion planning
• Instabilities of robot motion
• Topological robotics in lens spaces
• Motion planning in tori
• Robot motion planning, weights of cohomology classes, and cohomology operations
• On the Lusternik-Schnirelmann category of spaces with 2-dimensional fundamental group
• Topological complexity of configuration spaces
• On the Lusternik–Schnirelmann category of Grassmannians

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