A linear approach to formation control under directed and switching topologies

The paper studies the formation control problem for distributed robot systems. It is assumed each robot only has access to local sensing information (i.e. the relative positions and IDs of its neighbors). Taking into consideration physical sensing constraints (e.g. limited sensing range) and the motion of the robots over time, it may be noted that the sensing graph for the system is directed and time-varying. This presents a challenging situation for formation control. As an initiative attempt to study this challenging situation, we suppose the sensing graph switches among a family of graphs with certain connectivity properties, under which a switching linear control law is then proposed. We show that for arbitrary dwell times or average dwell times, the proposed control law with properly designed control parameters can ensure global convergence to a desired formation shape. The proposed formation control law can be implemented in a distributed manner while the design of certain control parameters requires some global information.