Graph-based distributed control of non-holonomic vehicles endowed with local positioning information engaged in escorting missions

Abstract- Formation building and keeping among vehicles has been studied for many years, since 1987 with Reynolds' rules [1]. This paper presents a control algorithm, based on re-cent work in graph theory, able to reconfigure static formations of non-holonomic vehicles endowed solely with local positioning capabilities. The convergence of our approach is mathematically proven and applied to a realistic robotic platform. II. BACKGROUND A. The Consensus Problem The consensus problem [13] is a well-known and widely studied problem in the field of decentralized control. If we consider agents with a single integrator kinematic model Fig. 1. Closed loop control for the consensus algorithm