Vision-Based Distributed Formation Control Without an External Positioning System

Abstract

In this paper, we present a fully distributed solution to drive a team of robots to reach a desired formation in the absence of an external positioning system that localizes them. Our solution addresses two fundamental problems that appear in this context. First, we propose a 3-D distributed control law, designed at a kinematic level, that uses two simultaneous consensus controllers: one to control the relative orientations between robots, and another for the relative positions. The convergence to the desired configuration is shown by comparing the system with time-varying orientations against the equivalent approach with fixed orientations, showing that their difference vanishes as time goes to infinity. Second, in order to apply this controller to a group of aerial robots, we combine this idea with a novel sensor fusion algorithm to estimate the relative pose of the robots by using onboard cameras and information from the inertial measurement unit. The algorithm removes the influence of roll and pitch from the camera images and estimates the relative pose between robots by using a structure from the motion approach. Simulation results, as well as hardware experiments with a team of three quadrotors, demonstrate the effectiveness of the controller and the vision system working together.