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.

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Abstract-The reachability problem has received significant attention in the hybrid control literature with many questions still left unanswered. In this paper we solve the general problem of reaching a set of facets of an n-dimensional simplex in finite time, for a system evolving with linear affine dynamics. Necessary and sufficient conditions are presented in the form of inequalities on the vertices of the simplex, and a linear affine controller is constructed that solves the reachability problem.

This paper studies a theoretical problem of whether continuous state feedback and affine feedback are equivalent from the point of view of making an affine system defined on a simplex reach a prespecified facet in finite time. We show that the two classes of feedbacks are equivalent. As a byproduct, new necessary and sufficient conditions for solvability based more directly on the problem data are obtained.