Sub-Riemannian geometry on the group of motions of the plane

We will discuss the unique, up to local isometries, contact sub-Riemannian structure on the group SE(2) of proper motions of the plane (aka group of rototranslations). The following questions will be addressed:

• geodesics,
• 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.