Monitoring environmental boundaries with a robotic sensor network

In this paper we propose and analyze an algorithm to monitor an environmental boundary with mobile sensors. 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 known results on approximation of convex bodies. The algorithm is provably convergent for static boundaries and also for slowly-moving boundaries because of certain input-to-state stability properties.