Coordinated Patterns on Smooth Curves

Fumin Zhang and Naomi Ehrich Leonard

We show methods that control cooperative Newtonian particles to generate patterns on smooth curves. The spacing between neighboring particles is measured by the relative arc-length and the distance between a particle and the desired curve is measured using an orbit function. The orbit value and the relative arc-length are then used as feedback to control the motion of each particle to a pattern on the desired curve asymptotically. Possible applications of the methods to underwater mobile sensor networks are discussed.