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arXiv · 1912.10539

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

Gerhard Freudenthaler·Thomas Meurer
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Abstract

A PDE-based control concept is developed to deploy a multi-agent system into desired formation profiles. The dynamic model is based on a coupled linear, time-variant parabolic distributed parameter system. By means of a particular coupling structure parameter information can be distributed within the agent continuum. Flatness-based motion planning and feedforward control are combined with a backstepping-based boundary controller to stabilise the distributed parameter system of the tracking error. The tracking controller utilises the required state information from a Luenberger-type state observer. By means of an exogenous system the relocation of formation profiles is achieved. The transfer of the control strategy to a finite-dimensional discrete multi-agent system is obtained by a suitable finite difference discretization of the continuum model, which in addition imposes a leader-follower communication topology. The results are evaluated both in simulation studies and in experiments for a swarm of mobile robots realizing the transition between different stable and unstable formation profiles.

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Gerhard Freudenthaler, Thomas Meurer. 2019-12-22. PDE-based multi-agent formation control using flatness and backstepping: analysis, design and robot experiments. https://doi.org/10.1016/j.automatica.2020.108897

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