15 citations · 43 across the 6 of their papers we have counts for
6 papers · 1 filter
Collision Free Motion Planning on Graphs
Michael Farber
A topological theory initiated recently by the author uses methods of algebraic topology to estimate numerically the character of instabilities arising in motion planning algorithm…
Topological Robotics: Subspace Arrangements and Collision Free Motion Planning
Michael Farber, Sergey Yuzvinsky
We study an elementary problem of the topological robotics: collective motion of a set of distinct particles which one has to move from an initial configuration to a final conf…
Topological robotics: motion planning in projective spaces
Michael Farber, Serge Tabachnikov, Sergey Yuzvinsky
We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial positi…
Lusternik - Schnirelman theory and dynamics
Michael Farber
In this paper we study a new topological invariant $\Cat(X,ξ)$, where is a finite polyhedron and is a real cohomology class. $\Cat(X,ξ)$ is defined using open…
Topological complexity of motion planning
Michael Farber
In this paper we study a notion of topological complexity for the motion planning problem. The topological complexity is a number which measures discontinuity of the process of mot…
Topology of billiard problems, II
Michael Farber
We give topological lower bounds on the number of periodic and closed trajectories in strictly convex smooth billiards. We use variational reduction admitting a finite group of sym…