Multi-agent deployment to a family of planar Arcs

We introduce an approach for stable deployment of agents into planar arc formations, including full circles and spirals. These deployments correspond to the equilibrium profiles of a nonlinear PDE model. The model incorporates the follower agents' control laws, which employ a spatial internal model principle, enabling them to achieve a family of arc deployments while utilizing only local information. Anchor agents are used to manipulate the geometry of the group, but are not required for stability. We obtain control laws for the discrete agents by spatially discretizing the PDE model with respect to the continuous agent index.