Dynamic Modeling, Parameter Identification and Numerical Analysis of Flexible Cables in Flexibly Connected Dual-AUV Systems

This research presents a dynamic modeling framework and parameter identification methods for describing the highly nonlinear behaviors of flexibly connected dual-AUV systems. The modeling framework is established based on the lumped mass method, integrating axial elasticity, bending stiffness, added mass and hydrodynamic forces, thereby accurately capturing the time-varying response of the forces and cable configurations. To address the difficulty of directly measuring material-related and hydrodynamic coefficients, this research proposes a parameter identification method that combines the physical model with experimental data. High-precision inversion of the equivalent Youngs modulus and hydrodynamic coefficients is performed through tension experiments under multiple configurations, effectively demonstrating that the identified model maintains predictive consistency in various operational conditions. Further numerical analysis indicates that the dynamic properties of flexible cable exhibit significant nonlinear characteristics, which are highly dependent on material property variations and AUV motion conditions. This nonlinear dynamic behavior results in two typical response states, slack and taut, which are jointly determined by boundary conditions and hydrodynamic effects, significantly affecting the cable configuration and endpoint loads. In this research, the dynamics of flexible cables under complex boundary conditions is revealed, providing a theoretical foundation for the design, optimization and further control research of similar systems.

💡 Research Summary

This paper presents a comprehensive dynamic modeling and parameter identification framework for a novel underwater system in which two autonomous underwater vehicles (AUVs) are flexibly connected by a tether. The authors begin by highlighting the limitations of conventional single‑platform tow systems, which suffer from restricted cable length, strong flow disturbances, and formation instability. By introducing a “flexibly connected dual‑AUV” architecture, the system gains two moving boundaries that can be actively adjusted to maintain formation stability, enabling longer deployments and multi‑sensor configurations.

To capture the highly nonlinear behavior of the tether, the authors adopt a lumped‑mass approach: the cable is discretized into (N_c) mass points linked by (N_c-1) mass‑less spring elements. Each mass point incorporates axial elasticity (Young’s modulus (E)), bending stiffness ((EI)), buoyancy, added mass, and hydrodynamic forces (normal and tangential drag coefficients (C_n) and (C_t)). The model explicitly includes the time‑varying positions and velocities of both AUVs as boundary conditions, which are expressed in an Earth‑fixed inertial frame and transformed to local frames attached to each mass point. The AUV dynamics themselves are modeled as six‑degree‑of‑freedom rigid bodies with mass, Coriolis, and hydrodynamic damping matrices, driven by propulsion thrust and the tether forces/moments.

A major contribution lies in the parameter identification methodology. Because material‑related coefficients (equivalent Young’s modulus) and hydrodynamic coefficients cannot be measured directly on the composite cable, the authors conduct a series of tension experiments in a water tank under multiple configurations (different inter‑AUV distances, relative velocities, and cable orientations). They formulate a fitness function that minimizes the squared error between measured and simulated tensions across all experiments. A Genetic Algorithm (GA) is employed to search the feasible parameter space under physical constraints (e.g., positivity, realistic bounds). The GA simultaneously identifies the equivalent Young’s modulus, normal and tangential drag coefficients, added‑mass factor, and other relevant parameters. Validation shows that the identified set reproduces tension histories with (R^2 > 0.95) even for conditions not used in the calibration, confirming the robustness of the approach.

Numerical simulations using the identified parameters reveal two characteristic response regimes: a “slack” state and a “taut” state. In the slack regime, the cable exhibits low tension, curvature‑dominated bending, and its dynamics are heavily influenced by hydrodynamic drag. When the relative motion of the AUVs exceeds a critical combination of speed and separation, the cable abruptly transitions to the taut regime, becoming nearly straight, with a rapid surge in tension and a markedly asymmetric load distribution on the two AUVs. This transition is governed by the competition among inertial forces, gravity, buoyancy, and hydrodynamic drag, and is highly sensitive to the identified material and fluid parameters. Sensitivity analyses demonstrate that the Young’s modulus primarily controls the critical distance and peak tension, while the drag coefficients dominate the cable shape and displacement in the slack regime.

The authors discuss model limitations, including the small‑strain assumption ((\varepsilon \ll 1)), constant drag coefficients, and numerical stiffness inherent in explicit time‑integration of highly coupled equations. They suggest future work to incorporate nonlinear material models, flow‑dependent drag, and real‑time control strategies that exploit the slack‑taut transition for adaptive load management.

In summary, the paper delivers (1) a unified, physics‑based dynamic model that integrates cable elasticity, added mass, buoyancy, and hydrodynamic forces with moving AUV boundaries; (2) a practical, experiment‑driven parameter identification scheme that simultaneously recovers material and fluid coefficients; and (3) a detailed analysis of the nonlinear slack‑to‑taut transition, providing valuable insights for the design, optimization, and control of flexible‑cable‑based multi‑AUV systems.