\(\def\xx{\mathbf{x}}\def\Real{\mathbb{R}} \)

We consider the problem of flock control: what are the natural constraints on the steering agents in reconfiguring an ensemble of agents?

Our basic setup is following: the agents are modeled as points \(\xx=(x_1,\ldots,x_n), x_k\in X, k=1,\ldots, N\), with \(X\) some terrain (for simplicity, we constrain ourselves here to Euclidean plane, but in general it can be some reasonably tame subset of a manifold). *Quasi-static behavior* is assumed, under which the system, for each value of the controlling parameters quickly settles into (locally minimizing) the equilibrium whose basin of attraction contains current position.…