Robust formation tracking and collision avoidance for uncertain nonlinear multi-agent systems subjected to heterogeneous communication delays

In this paper, formation control problem for multiple uncertain nonlinear second-order agents in the presence of heterogeneous communication delays is addressed. A continuous repulsive vector is incorporated into agents’ velocity to ensure collision avoidance, whose time derivative is approximated via a finite-time robust integral of the sign of the error (RISE)-like observer. Using adaptive neural control scheme, unknown model dynamics, external disturbances, RISE estimation error, and the time-delays among agents are robustly addressed. The sufficient conditions on the stability of the overall system and collision avoidance are derived using Lyapunov–Krasovskii functionals and algebraic graph theory, and it is proven that the formation tracking error converges to a small neighborhood of zero. Numerical simulation results are also given to illustrate the effectiveness of our proposed methods.