Affine transformation based formation maneuvering for discrete-time directed networked systems

For the tracking control problems of affine formation maneuvers with discrete leader-following multi-agent systems, various distributed control schemes based on the directed graphs are designed in this paper. Consider the single and double-integrator models, different types of formation maneuvers can be achieved subject to the states of leaders with the novel characteristic of affine localizability. Meanwhile, the properties of affine transformation and signed Laplacian are introduced, which simplify the structures of controllers with distinct constraints to a great extent. Moreover, the convergence analysis of proposed protocols is proven. Static, constant and time-varying target formations can be tracked successfully. In the end, corresponding numerical simulations are carried out to certify the validity of theoretical results.