Global stabilization of rigid formations via sliding mode control

This paper studies the rigid formation control problem of multi-agent systems, for which finding a local interaction law ensuring global convergence towards a desired formation is the main challenge. A sliding mode control law is proposed in this paper, which steers all the agents to a desired rigid formation in any dimensional space for arbitrarily initial configuration. The main idea is to firstly make the trajectories of all the agents reach a sliding surface in finite time and secondly govern the agents towards the desired rigid formation while confining the motion in the sliding surface. Thus, the difficulty in achieving global convergence towards a desired formation is reduced to a much lower dimensional state space with much less number of agents being controlled to satisfy inter-agent distance constraints. Simulation results are provided to illustrate the effectiveness of our proposed control schemes.