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

arXiv: https://arxiv.org/abs/1912.10539 · HTML: https://mlsanity.com/paper/1912.10539/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2019.

## Built on by (most cited first, 1 of 1)

- [Data/moment-driven approaches for fast predictive control of collective dynamics](https://mlsanity.com/paper/2402.15611/) (2024)

## Abstract (arXiv)

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.