A method for decentralized self-deployment of a mobile sensor network with given regular geometric patterns

This paper addresses a problem of cooperative formation control of a network of self-deployed autonomous mobile sensors. We propose a decentralized randomized algorithm for self-deployment of a mobile sensor network in an unknown bounded region with obstacles. Furthermore, we propose a decentralized randomized motion coordination control law for the mobile sensors s so that they form a desired geometric pattern on a square grid from any initial position. In particular, we consider self-deployment with desired shapes such as interiors of a circle, an ellipse, a rectangle and a ring. There are no predefined leaders in the group and only local information about the closest neighbours of each sensor is required for the control. We give mathematically rigorous proofs of convergence with probability 1 of the proposed algorithms. Their effectiveness is also illustrated via numerical simulations.