Formation Control via Rotation Symmetry Constraints

This work introduces a distributed formation control strategy for multi-agent systems based solely on rotation symmetry constraints. We propose a potential function that enforces inter-agent $\mathbf{\text{rotational}}$ symmetries, whose gradient defines a control law that drives the agents toward a desired planar symmetric configuration. We show that only $n-1$ edges (the minimal connectivity requirement) are sufficient to implement the strategy, where $n$ is the number of agents. We further augment the design to address the $\mathbf{\text{maneuvering}}\mathbf{\text{problem}}$, enabling the formation to undergo coordinated translations, rotations, and scaling along a predefined virtual trajectory. Simulation examples are provided to validate the effectiveness of the proposed method.