15 citations · 43 across the 6 of their papers we have counts for
4 papers · 1 filter
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…
Instabilities of Robot Motion
Michael Farber
Instabilities of robot motion are caused by topological reasons. In this paper we find a relation between the topological properties of a configuration space (the structure of its…
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…