Robust Formation Control of Nonlinear Agents with Distance Constraints

This paper studies robustness of the distance-based formation control problem for a set of nonlinear agents with additive uncertainties. Directed graph theory is used to model the desired formation topology, and the task of controlling an edge is given to only one of its incident agents. We proposed a distributed, robust control method for the distance-based formation control of uncertain nonlinear agents. We designed a distributed optimal controller for the nominal system. We then modified the nominal controller for the uncertain system by adding an integral sliding mode control (ISMC). A rigorous Lyapunov stability analysis is carried out to show the asymptotic convergence of each agent to its desired formation. Then, using the stability theory of cascaded interconnected systems, and the concept of mathematical induction, the stability of the overall formation is proven. Simulations results illustrate the effectiveness of the proposed method in two- and three-dimensional spaces.