Leader–Follower Affine Formation Control of Second-Order Nonlinear Uncertain Multi-Agent Systems

This brief proposes two leader-follower affine formation control algorithms for a class of second-order uncertain multi-agent systems. The model of each agent is described by the second-order dynamics with nonlinear uncertainties. Due to the high robustness, flexibility and maneuverability, the affine formation approaches based on the stress matrix are adopted to achieve a target formation, in which the formation control laws are designed for followers to keep a desired formation configuration with respect to leaders. First, considering that the velocities of leaders are constant, we design an estimator to compensate for the uncertainties and propose a PI-like affine formation control law to guarantee that the followers can achieve the target formation. Then, for the case that the velocities of leaders are time-varying, we propose another control algorithm with variable gains for followers under which a time-varying formation configuration can be maintained. Finally, the corresponding simulations of a realistic example are carried out to validate the effectiveness of the proposed affine formation control algorithms.