Controlling Multiple Robots through Multiple 1D Homographies

We present a method for visual control of a set of robots moving on the ground plane. The goal of the control task is for the team to reach a desired geometric configuration. Each robot carries an omnidirectional camera and can communicate with a number of the other robots. The approach relies on the computation of the planar motion between two views, by means of 1D homographies. This knowledge, obtained by each robot from its own images and the visual information received from neighboring robots, allows it to define a desired position on the plane. Then, we propose a novel control scheme based on computing a particular 2D transformation to drive each robot towards its goal position. A contribution of this work is the use of 1D homography in a multirobot control framework. This tool allows to deal with purely angular visual information, which is precise and requires no calibration. The approach we present is completely distributed. Each robot uses only information from its formation neighbors and the global centroid to obtain its motion commands. These individual behaviors naturally result in the complete team of robots reaching the desired global configuration.