Coordinated Patterns on Smooth Curves

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