Distributed Time-Varying Optimization-Based Protocols for Affine Formation Maneuver

In this work, an affine formation maneuver control problem is studied for second-order multiagent system. The agents’ task is to achieve affine formation maneuver through local interaction while minimizing the global time-varying cost functions. First, a distributed time-varying optimization problem with affine formation constraints is presented, where the solution trajectory is the affine transformation of the desired nominal configuration. Second, distributed time-varying optimization-based protocols are proposed. Using the proposed protocols, the agents’ states asymptotically converge to the optimal solution, and thus the desired affine formation and the collective maneuvers issues can be solved. Third, the asymptotic convergence is proved using Lyapunov arguments. Finally, the effectiveness of the protocols is demonstrated by numerical simulation and experimental examples.