Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2501.01817

Distributed Framework Construction for Affine Formation Control

Huiming Li·Hao Chen·Xiangke Wang·Zhongkui Li·Lincheng Shen
View original source ↗Read source document ↗Export metadata ↓

Abstract

In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the formation or link/agent failures emerge. Motivated by this observation, we investigate the problem of constructing affine frameworks in three scenarios, including vertex addition, edge deletion and vertex deletion. Our approach starts from the original affine formation and uses geometric methods to locally adjust the structure of the weighted graph to describe the topology, so that the modified framework maintains the universal rigidity and affine localizability. Notably, the developed strategies only utilize local measurements and exhibit distributed characteristics, laying the foundation for applications in multi-agent systems. To demonstrate the compatibility with affine formation control proposals, we present a case study on affine formation tracking in a multi-UAV formation, demonstrating the effectiveness of our algorithms in constructing eligible frameworks in aforementioned scenarios. Moreover, a comparative simulation is also conducted to highlight the low time complexity of our distributed algorithm relative to the centralized optimization-based method.

Explore related subjects

eess.SYcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Huiming Li, Hao Chen, Xiangke Wang, Zhongkui Li, Lincheng Shen. 2025-06-04. Distributed Framework Construction for Affine Formation Control. https://arxiv.org/abs/2501.01817

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

KEEP EXPLORING

Related papers

arXiv2026

Ensuring Stability of Non-Minimal Modes in Input-Output Data-Driven Representation

Many recent data-driven control approaches for linear time-invariant systems are based on output trajectory prediction using input-output data matrices. The system dynamics described by this predictor, which we refer to as the input-output data-driven representation, yields non-unique autoregressive with exogenous inputs (ARX) models having possibly unstable non-minimal modes. In this note, we show that the stability of these non-minimal modes is ensured by a certain choice of ARX model, which coincides with the minimum-norm least-squares predictor using the Moore-Penrose inverse of the data matrix. This stability guarantee holds regardless of the underlying system's stability. Moreover, the stability persists under sufficiently small noise in data when a suitably truncated Moore-Penrose inverse is used. Consequently, the ARX model need not be reduced to the true system order in order to avoid unstable additional modes.

eess.SY↗
arXiv2026

Optimization-Based Formation Flight on Libration Point Orbits

A model predictive control (MPC) framework is developed for station-keeping in spacecraft formation flight along libration point orbits. At each control period, the MPC policy solves a multi-vehicle optimal control problem (MVOCP) that tracks a reference trajectory, while enforcing path constraints on the relative motion of the formation. The control policy makes use of a limited set of control nodes consistent with operational constraints that allow only a small number of maneuver opportunities per revolution. To promote recursive feasibility, path constraints are progressively tightened across the prediction horizon. An isoperimetric reformulation of the constraints is used to prevent inter-sample violations. The resulting MVOCP is a nonconvex program, which is solved via sequential convex programming. The proposed approach is evaluated in a high-fidelity ephemeris model under uncertainties for a formation along the near-rectilinear halo orbit (NRHO), and subject to path constraints on inter-spacecraft separation and relative Sun phase angle. The results demonstrate maintenance of a spacecraft formation that satisfies the path constraints with realistic cumulative propellant consumption.

eess.SY↗
arXiv2026

Certificates Synthesis for A Class of Observational Properties in Stochastic Systems: A Unified Approach

In this paper, we investigate the probabilistic formal verification of stochastic dynamical systems over continuous state spaces. Motivated by problems in state estimation and information-flow security, we introduce the notion of observational properties, which characterize the inferences an external observer can draw from system outputs. These properties are formulated as probabilistic hyperproperties based on HyperLTL over finite traces, yielding a unified framework that subsumes several existing notions studied separately in the literature. We reduce the verification problem to reachability analysis over an augmented structure that integrates the system dynamics with an automaton representation of the specification. Building on this construction, we develop stochastic barrier certificates that provide probabilistic guarantees for property satisfaction while avoiding explicit state-space discretization. The effectiveness of the proposed framework is demonstrated through a case study.

eess.SY↗