Seminar talk, 14 April 2021
Speaker: Yuri Sachkov
Title: Sub-Riemannian geometry on the group of motions of the plane
We will discuss the unique, up to local isometries, contact sub-Riemannian struc ture on the group SE(2) of proper motions of the plane (aka group of rototransla tions). The following questions will be addressed:
- their local and global optimality,
- cut time, cut locus, and spheres,
- infinite geodesics,
- bicycle transform and relation of geodesics with Euler elasticae,
- group of isometries and homogeneous geodesics,
- applications to imaging and robotics.
Joint work with Andrei Ardentov.