Formation Control via Rotation Symmetry Constraints

We present a distributed formation control strategy for multi-agent systems based only on rotation symmetry constraints. We propose a potential function that enforces inter-agent rotational symmetries, with its gradient defining the control law driving the agents toward a desired symmetric and planar configuration. We show that only $(n-1)$ edges, the minimal connectivity requirement, are sufficient to implement the control strategy, where n is the number of agents. We further augment the design to address the maneuvering problem, enabling the formation to undergo coordinated translations, rotations, and scalings along a predefined virtual trajectory. Numerical simulations demonstrate the effectiveness and flexibility of the proposed method.