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In this brief, we propose and analyze an algorithm to monitor an environmental boundary with mobile agents. The objective is to optimally approximate the boundary with a polygon. The mobile sensors rely only on sensed local information to position some interpolation points and define an approximating polygon. We design an algorithm that distributes the vertices of the approximating polygon uniformly along the boundary. The notion of uniform placement relies on a metric inspired by approximation theory for convex bodies. The algorithm is provably convergent for static boundaries and efficient for slowly-moving boundaries because of certain input-to-state stability properties.
Susca et al. (Fri,) studied this question.