Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Boundary Control of Pdes: A Course on Backstepping Designs
Boundary Control of Pdes: A Course on Backstepping Designs
Brief paper: Finite-time multi-agent deployment: A nonlinear PDE motion planning approach
Automatica (Journal of IFAC)
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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.