Based on the practical scenario where collisions in formation control may lead to agent damage, this paper investigates the integrated problem of distance-based formation control and collision avoidance for multi-agent systems governed by port-Hamiltonian dynamics. A foundational step involves constructing a signed incidence matrix, which, by design, corresponds to a directed acyclic graph and possesses the full column rank property. To overcome the prevalent issue of local minima in traditional artificial potential fields, a novel design utilizing attraction-only potentials is introduced, with collision avoidance rigorously enforced by safety barriers. This framework leads to a unified controller that concurrently manages velocity tracking, target formation acquisition, and inter-agent safety. The stability of the resulting closed-loop system is guaranteed through LaSalle's invariance principle. Numerical simulations demonstrate the validity and effectiveness of the proposed control strategy.
@article{arxiv.2605.18502,
title = {The distance-based formation controller design for multi-agent systems in port-Hamiltonian form},
author = {Jingyi Zhao and Yongxin Wu and Héctor García de Marina and Yuhu Wu and Yann Le Gorrec},
journal= {arXiv preprint arXiv:2605.18502},
year = {2026}
}