A survey of multi-agent formation control

This article considers the design of a formation control for multivehicle systems that uses only local information. The control is derived from a potential function based on an undirected infinitesimally rigid graph that specifies the target formation. A potential function is obtained from the graph, from which a gradient control is derived. Under this controller the target formation becomes a manifold of equilibria for the multivehicle system. It is shown that infinitesimal rigidity is a sufficient condition for local asymptotical stability of the equilibrium manifold. A complete study of the stability of the regular polygon formation is presented and results for directed graphs are presented as well. Finally, the controller is validated experimentally.

Stabilisation of infinitesimally rigid formations of multi-robot networks

Abstract Suppose a finite configuration of labeled
points p = (p1,. . . ,pn) in Ed is given along with
certain pairs of those points determined by a graph G such that the
coordinates of the points of p are generic, i.e., algebraically
independent over the integers. If another corresponding configuration
q = (q1,. . . ,qn) in Ed is given such that the
corresponding edges of G for p and q have the same
length, we provide a sufficient condition to ensure that p and
q are congruent in Ed. This condition, together with recent 
results of Jackson and Jordán, give necessary and sufficient conditions for 
a graph being generically globally rigid in the plane.

On Generic Global Rigidity.

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consist of an incomplete set of distances and the output is a set of points in Euclidean space realizing those given distances. We survey the theory of Euclidean distance geometry and its most important applications, with special emphasis on molecular conformation problems.

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Euclidean Distance Geometry and Applications

Suppose a finite configuration of labeled points p = (p1,. . . ,pn) in Ed is given along with certain pairs of those points determined by a graph G such that the coordinates of the points of p are generic, i.e., algebraically independent over the integers. If another corresponding configuration q = (q1,. . . ,qn) in Ed is given such that the corresponding edges of G for p and q have the same length, we provide a sufficient condition to ensure that p and q are congruent in Ed. This condition, together with recent results of Jackson and Jordan, give necessary and sufficient conditions for a graph being generically globally rigid in the plane.

L Asimow

Papers

The rigidity of graphs, II

Best approximation by gauges on a Banach space

Decomposability and dual optimization in Banach spaces