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

TL;DR

This paper presents a PDE-based control framework for multi-agent formation control, combining flatness, backstepping, and observer techniques, validated through simulations and robot experiments.

Contribution

It introduces a novel PDE-based control approach integrating flatness and backstepping for multi-agent formation, including experimental validation.

Findings

Successful formation transitions in robot swarms

Effective PDE-based control in simulations and experiments

Stable and unstable formation profile management

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.