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We revisit the static coverage control problem for placement of vehicles withsimple motion on the real line, under the assumption that the cost is apolynomial function of the locations of the vehicles. The main contribution ofthis paper is to demonstrate the use of tools from numerical algebraicgeometry, in particular, a numerical polynomial homotopy continuation methodthat guarantees to find all solutions of polynomial equations, in order tocharacterize the \emph{global minima} for the coverage control problem. Theresults are then compared against a classic distributed approach involving theuse of Lloyd descent, which is known to converge only to a local minimum undercertain technical conditions.

Optimal Configurations in Coverage Control with Polynomial Costs