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A PDE-based control concept is developed to deploy a multi-agent system intodesired formation profiles. The dynamic model is based on a coupled linear,time-variant parabolic distributed parameter system. By means of a particularcoupling structure parameter information can be distributed within the agentcontinuum. Flatness-based motion planning and feedforward control are combinedwith a backstepping-based boundary controller to stabilise the distributedparameter system of the tracking error. The tracking controller utilises therequired state information from a Luenberger-type state observer. By means ofan exogenous system the relocation of formation profiles is achieved. Thetransfer of the control strategy to a finite-dimensional discrete multi-agentsystem is obtained by a suitable finite difference discretization of thecontinuum model, which in addition imposes a leader-follower communicationtopology. The results are evaluated both in simulation studies and inexperiments for a swarm of mobile robots realizing the transition betweendifferent stable and unstable formation profiles.

PDE-based multi-agent formation control using flatness and backstepping: analysis, design and robot experiments