Rapidly convergent leader-enabled multi-agent deployment into planar curves

We introduce an approach for stable deployment of agents into planar curves (1-D formations in 2-D space) parameterized by the agent index. Stability is ensured by leader feedback, which is designed in a manner similar to boundary control of PDEs. By discretizing the model and the PDE controllers with respect to the continuous agent index, we obtain control laws for the discrete follower agents and the leader agent. The class of PDEs that motivates our design is the reaction-advection-diffusion class (broader than the standard heat equation, which is stable and does not necessitate leader feedback), which allows a much broader family of deployment profiles. Many of these profiles, however, are open-loop unstable. We stabilize them with leader feedback.