A Unified Approach for Finite-Time Global Stabilization of Affine, Rigid and Translational Formation

This paper studies the multi-agent control problem for affine, rigid, and translational formation, with the aim of developing a unified distributed control strategy for global and finite-time convergence. Global stabilization of rigid formation in arbitrary dimensional spaces still remains open and challenging. This paper provides a general solution to it based on the sliding mode control idea. The control law design consists of two parts: the main control force regulates the trajectories of all agents to reach a sliding surface defined by an affine formation space in finite time and remain in it thereafter; the extra control force governs certain chosen leader agents towards the desired formation in the sliding surface. The paper then presents in detail two approaches for designing the extra control force, one based on distance constraints and the other based on relative position constraints. For the first time, the proposed sliding mode formation control laws solve the open problem of (almost) global and finite-time stabilization of affine, rigid and translational formations in any dimensional space.