New methods to color the vertices of a graph
Communications of the ACM
Control of Minimally Persistent Formations in the Plane
SIAM Journal on Control and Optimization
MAC protocols for wireless sensor networks: a survey
IEEE Communications Magazine
Scaling the size of a formation using relative position feedback
Automatica (Journal of IFAC)
Consensus of sampled-data multi-agent networking systems via model predictive control
Automatica (Journal of IFAC)
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This paper proposes algorithms to coordinate a formation of mobile agents when the agents are not able to measure the relative positions of their neighbors, but only the distances to their respective neighbors. In this sense, less information is available to agents than is normally assumed in formation stabilization or station keeping problems. To control the shape of the formation, the solution advanced in the paper involves subsets of non-neighbor agents cyclically localizing the relative positions of their respective neighbor agents while these are held stationary, and then moving to reduce the value of a cost function which is nonnegative and assumes the zero value precisely when the formation has correct distances. The movement schedule is obtained by a novel vertex-coloring algorithm whose computation time is linear in the number of agents when implemented on the graphs of minimally rigid formations. Since in some formations, it may be that an agent is never allowed to be stationary (e.g. it is a fixed-wing aircraft), or because formations may be required to move as a whole in a certain direction, the results are extended to allow for cyclic localization of agents in this case. The tool used is the Cayley-Menger determinant.