Affine formation control for heterogeneous multi-agent systems with directed interaction networks

In this paper, affine formation control problems of heterogeneous multi-agent systems with linear dynamics are studied. As a novel method, the affine formation control has the ability to handle various movement constraints based on the affine transformation. A proportional-integral (PI)-type control scheme is proposed to ensure the effective affine formation control of the leader-following group with directed interaction graphs and successfully eliminate the steady-state errors. Sufficient conditions for the selection of control parameters are given and proved. Considering that the followers are subjected to the external bounded time-varying disturbances, the designed protocol shows good robustness and can guarantee uniformly ultimate boundedness of affine formation errors. Numerical simulations are carried out to verify the theoretical results.