A unified framework for constrained linearization of 2D/3D sensor networks with arbitrary shapes

In this paper, we study the problem of linearizing sensor networks, i.e., computing a constrained space filling curve (SFC), with the constraint on a pair of given starting location and destination. Our work is motivated by the fact that in application scenarios such as motion planing of a mobile robot for data collection or battery recharging, a mobile robot often starts from a pre-required location (referred to as Entrance) and quits at another pre-required location (referred to as Exit) before visiting all sensors. We thus propose a unified framework, which is novel, simple yet efficient, for the constrained linearization of 2D or 3D surface/volume sensor networks merely using connectivity information. Specifically, we first compute a shortest path between the Entrance and the Exit to initialize the constrained SFC; then, in each round we simultaneously deform the edges on the constrained SFC until most of sensors are visited, and a coarse constrained SFC, possibly missing some sensors (e.g., due to network irregularity), is thus derived. We then propose to connect the unvisited sensors into the constrained SFC, and the network is linearized such that all nodes are orderly traversed by the SFC from the Entrance to the Exit. Extensive simulations on 2D/3D sensor networks show the efficiency of our work.