Coordinated Patterns of Unit Speed Particles on a Closed Curve

Fumin Zhang and Naomi Ehrich Leonard

Systems and Control Letters, Vol. 56, pages 397-407, 2007.
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.

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