Homotopy-based formations of robot swarms
Zbigniew Bartosiewicz · 2022 European Control Conference (ECC) · 2022
A problem of transformation of a planar formation of a robot swarm to another formation is considered. Robots are placed in the vertices of a polygon, so the goal is to transform the entire polygon in a continuous way. The proposed solution is based on the topological concept of homotopy. It describes a continuous passage from one closed curve to another one. During the passage the basic structure of the curved is preserved: at each instant it is a closed curve, but not necessarily a polygon, with robots occupying some places on it. In order to provide a constructive solution, it is assumed that the region bounded by the polygon is star-shaped.