Spatially-distributed coverage optimization and control with limited-range interactions

Abstract

Abstract. This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing or communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.Mathematics Subject Classification. 37N35, 49J52, 68W15, 93D20.

Coordinated deployment of mobile sensing networks with limited-range interactions

“…This result is a consequence of Proposition 2.3; we refer the interested reader to [12] for a detailed proof. For particular choices of performance function, the corresponding multicenter function and its gradient have different features.…”

“…One can show (cf. [12]) that the Voronoi partition is optimal within the set of partitions of Q, that is, H e (P, W) ≤ H e (P, V(P )) for all P ∈ Q n . Moreover, the inequality is strict if f is strictly decreasing and the partitions V(P ) and W differ by a set of non-zero measure.…”

“…This latter algorithm has the advantage of being spatially distributed over G LD (r). We do not follow this path here, and instead refer the interested reader to [12] for a complete exposition, including a detailed characterization of the approximation properties of this procedure.…”

“…The numerical outcomes of the algorithms' implementation are reported in Section V. Finally, we discuss possible avenues of future research in Section VI. We refer the interested reader to the full journal version [12] of this work for a detailed discussion of the computational geometric and algorithmic aspects, and the proofs of all statements presented here.…”

Vehicle placement to intercept moving targets

“…Akin to similar results in Cortés et al (2004Cortés et al ( , 2005; Bullo et al (2009), the proof involves writing the gradient as a sum of two contributing terms. The first is the final expression, while the second is a number of boundary terms For τ ∈ [t, t + 1], move according to…”