On the Trajectories and Coordination of Steered Particles with Time-Periodic Speed Profiles

Daniel T. Swain and Naomi Ehrich Leonard

Motivated by observations of fish and possibilities for mobile robotics, we study collective motion of networks of agents that move with periodically time-varying speed. Each agent is modeled as a particle with constant turning rate and time-periodic speed profile at steady state. Expressions are derived for the trajectories of such particles, emphasizing the variation from the constant-speed circular orbit. We show that trajectories remain bounded if the speed profile contains no frequency content at the turning rate. Steering and speed control laws are derived that stabilize a rich family of collective motion patterns of a many-particle system about a common center point, where headings and speed phases are coordinated.