Formation Matrix and Energy-based Control of Multi-Agent Systems

Martín Crespo; Sergio Junco; Matías Nacusse

Home/Archive/arXiv

arXiv · 2609.04158

Formation Matrix and Energy-based Control of Multi-Agent Systems

Martín Crespo·Sergio Junco·Matías Nacusse

View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper presents an energy-based controller for a multiagent robotic system designed to achieve and maintain a specific formation while moving on a plane and avoiding collisions between agents. The controller emulates a network of elementary spring-damper modules connecting pairs of agents. This network, with its de-energized states representing the desired formation, determines the system's dynamics, which is fully encapsulated by a bond graph model. The modeling is further enhanced through the introduction of a formation matrix, using a graph-theoretic approach, that describes both the distances and relative velocities among the agents of the arrangement. This matrix mathematically represents the interconnection and energy-exchange structure of the bond graph, allowing us to put it in correspondence with the control-by-interconnection CbI-scheme of the IDA-PBC theory, facilitating the solution of the formation control problem within the port-Hamiltonian system framework. Furthermore, the paper presents leader-following and position-based formation control systems based on the CbI scheme, including a stability analysis of the corresponding closed-loop systems. The theoretical findings are validated through numerical simulations across various scenarios.

Explore related subjects

eess.SY cs.RO cs.SY

Keep this discovery

BibTeX RIS

Martín Crespo, Sergio Junco, Matías Nacusse. 2026-09-03. Formation Matrix and Energy-based Control of Multi-Agent Systems. https://arxiv.org/abs/2609.04158

Cite the original work for its findings. Save a collection to share your selection of sources.

Discover connections

cs.RO subject cs.SY subject eess.SY subject

Connections use source metadata and explicit phrase matches, not verified experimental comparisons.

KEEP EXPLORING

Related papers

arXiv2026

Multi-Robot Bearing-based Pose Estimation via Angle Rigidity

This letter proposes a novel distributed pose estimator for multi-robot systems evolving on $\mathrm{SE}(3)$. The robots' positions are estimated in $\mathbb{R}^3$ using angles computed from body-frame bearings, without requiring orientation knowledge. The robots' orientations are then recovered in $\mathrm{SO}(3)$ from the estimated positions, together with bearing and bearing-rate measurements. The estimator accommodates directed sensing topologies and requires only infinitesimal angle rigidity (IAR), thereby relaxing the requirement, common in bearing-based approaches, that every robot acquire at least two bearings. Unlike existing angle-based schemes, the proposed method also estimates the robots' orientations. We prove local uniform exponential stability of the observer, assuming that a subset of robots executes persistently exciting motions. These theoretical results are corroborated through numerical simulations.

cs.RO↗

arXiv2026

On Global Regulatability of Robot Manipulators by Classical PID

A long-standing open problem in robot manipulator control is whether global regulation can be achieved by classical PID control. This paper provides an answer to this question for classical PID controllers with triple parameters (k_p,k_i,k_d) in R^3. We find and prove that for one-degree-of-freedom manipulators, the classical PID control guarantees global stability and asymptotic regulation under standard structural assumptions, and further derive explicit quantitative design conditions for the PID gains. However, for multi-degree-of-freedom cases, we can construct a robot manipulator satisfying the same structural assumptions for which no choice of PID gains (k_p,k_i,k_d) can achieve global asymptotic regulation. These results provide a fundamental understanding of the abovementioned open problem, revealing both the fundamental capability and intrinsic limitation of the classical PID control for robot manipulator dynamics.

cs.RO↗

arXiv2026

Provably Safe Decentralized Contingency MPC under State-Only Information and Limited Sensing for Nonlinear Multi-agent Systems

This paper considers decentralized contingency MPC for multi-agent control under a state-only information pattern, with particular focus on limited sensing and plug-and-play operation. The objective is to retain recursive feasibility, safety, and Lyapunov-type convergence while reducing conservatism in local interaction handling. The framework relies on agent-wise fallback regions (safe sets) in which a feasible contingency maneuver to a safe equilibrium is always available. A novel safe-set update mechanism is introduced that supports less conservative decentralized interaction while preserving the underlying guarantees. This, in turn, enables memory-free local interaction and finite sensing ranges without requiring agents to reconstruct the exact neighbor geometry. The resulting scheme remains fully decentralized and preserves the shared-first-input contingency MPC structure. Theoretical guarantees and simulation results illustrate the effectiveness of the approach in dense multi-agent scenarios.

math.OC↗