Coordinated Patterns of Unit Speed Particles on a Closed Curve

Fumin Zhang and Naomi Ehrich Leonard

We present methods to stabilize a class of motion patterns for unit speed particles in the plane. From their initial positions within a compact set in the plane, all particles converge to travel along a closed curve. The relative distance between each pair of particles along the curve is measured using the relative arc-length between the particles. These distances are controlled to converge to constant values.