This paper presents a Lyapunov design for thestabilization of collective motion in a planar kinematic modelof N particles moving at constant speed. We derive a control lawthat achieves asymptotic stability of the splay state formation,characterized by uniform rotation of N evenly spaced particleson a circle. In designing the control law, the particle headingsare treated as a system of coupled phase oscillators. Thecoupling function which exponentially stabilizes the splay stateof particle phases is combined with a decentralized beaconcontrol law that stabilizes circular motion of the particles in thesplay state formation around the center of mass of the group.
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