The problem is studied of achieving a specified formation among a group of mobile autonomous agents by distributed control. If convergence to a point is feasible, then more general formations are achievable too, so the focus is on convergence to a point (the agreement problem). Three formation strategies are studied and convergence is proved under certain conditions. Also, motivated by the question of whether collisions occur, formation evolution is studied.

Two related problems are treated in continuous time. First, the state agreement problem is studied for coupled nonlinear differential equations. The vector fields can switch within a finite family. Associated to each vector field is a directed graph based in a natural way on the interaction structure of the subsystems. Generalizing the work of Moreau, under the assumption that the vector fields satisfy a certain sub-tangentiality condition, it is proved that asymptotic state agreement is achieved if and only if the dynamic interaction digraph has the property of being sufficiently connected over time. The proof uses nonsmooth analysis. Secondly, the rendezvous problem for kinematic point-mass mobile robots is studied when the robots' fields of view have a fixed radius. The circumcenter control law of Ando et al. [1] is shown to solve the problem. The rendezvous problem is a kind of state agreement problem, but the interaction structure is state dependent.

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