Scalable Formation Control of Multi-robot Chain Networks Using a PDE Abstraction

This work investigates the application of boundary control of the wave equation to achieve leader-induced formation control of a multi-robot network with a chain topology. In contrast to previous related work on controlling formations of single integrator agents, we consider a model for double integrator agents. For trajectory planning, we use the flatness based method for assigning trajectories to leader agents so that the agents’ trajectories and control inputs are computed in a decentralized way. We show how the approximation greatly simplifies the planning problem and the resulting synthesized controls are bounded and independent of the number of agents in the network. We validate our formation control approach with simulations of 100 and 1000 agents that converge to configurations on three different type of target curves.

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