Distributed Self-Deployment for Forming a Desired Geometric Shape

This chapter considers a case of the so-called flocking problem for a group of mobile robots. In flocking problems, the control objective is to cooperatively drive mobile robots from random initial locations to a formation of a desired geometric shape. The decentralized randomized control algorithm to navigate a network of autonomous mobile robotic sensors has been modified so that they collectively form a desired geometric pattern on a square grid starting from any initial deployment. In particular, a self-deployment with desired shapes such as interiors of a circle, an ellipse, a rectangle, a ring, and a regular hexagon is considered. It also proposes a randomized algorithm for self-deployment of a robotic sensor network in an unknown bounded region with obstacles. For the proposed distributed randomized algorithms, convergence with probability 1 is proved.