cs.ROFeb 19, 2026

Nonlinear Predictive Control of the Continuum and Hybrid Dynamics of a Suspended Deformable Cable for Aerial Pick and Place

Authors: Antonio Rapuano, Yaolei Shen, Federico Califano, Chiara Gabellieri, Antonio Franchi

Organizations: Department of Computer, Control and Management Engineering, Sapienza University of Rome, 00185 Rome, Italy. · Robotics and Mechatronics Department, Electrical Engineering, Mathematics, and Computer Science (EEMCS) Faculty, University of Twente, 7500 AE Enschede, The Netherlands.

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Abstract

This paper presents a framework for aerial manipulation of an extensible cable that combines a high-fidelity model based on partial differential equations (PDEs) with a reduced-order representation suitable for real-time control. The PDEs are discretised using a finite-difference method, and proper orthogonal decomposition is employed to extract a reduced-order model (ROM) that retains the dominant deformation modes while significantly reducing computational complexity. Based on this ROM, a nonlinear model predictive control scheme is formulated, capable of stabilizing cable oscillations and handling hybrid transitions such as payload attachment and detachment. Simulation results confirm the stability, efficiency, and robustness of the ROM, as well as the effectiveness of the controller in regulating cable dynamics under a range of operating conditions. Additional simulations illustrate the application of the ROM for trajectory planning in constrained environments, demonstrating the versatility of the proposed approach. Overall, the framework enables real-time, dynamics-aware control of unmanned aerial vehicles (UAVs) carrying suspended flexible cables.

Figures & tables

Fig. 1 : A UAV transports a slung payload through a narrow opening by exploiting the deformation of the cable.
Fig. 2 : Extensible string in R3\mathbb{R}^{3} .
Fig. 3 : Decomposition of the string position map on which the proposed model-order reduction method is based.
Fig. 4 : Aerial system composed of a quadrotor with a flexible cable and a payload attached to the distal end.
SymbolValue [SI units]SymbolValue [SI units]
mbm_{\textnormal{b}}0.30.3LL11
mpm_{\textnormal{p}}0.10.1ρc\rho_{\textnormal{c}}1.27\times103 1.27\text{\times}{10}^{3}\text{\,}
bpb_{\textnormal{p}}1.29\times10−2 1.29\text{\times}{10}^{-2}\text{\,}AA7.85\times10−5 7.85\text{\times}{10}^{-5}\text{\,}
bcb_{\textnormal{c}}1.29\times10−2 1.29\text{\times}{10}^{-2}\text{\,}EE1\times105 1\text{\times}{10}^{5}\text{\,}
TABLE I : Physical and geometrical parameters of the aerial system.
Fig. 5 : Relative energy content of each independent mode found via POD (logarithmic scale).
Fig. 6 : Spatial representation of the 33 modes with the highest energy content, i.e. the largest singular values.
Fig. 7 : Time characteristics across model variants.
Fig. 8 : Accuracy of the ROMs with respect to the FDM model across different orders.
Fig. 9 : Side-view time-lapses of the proposed Hybrid NMPC in experimental validation. The transparency indicates time evolution (opaque is current).
TABLE II : Cable-tip RMS tracking errors and average MPC iteration wall time in the online trajectory tracking scenario.
MetricHiLQRHiLQR-RTIUnit
ϵrms(r,r^)\epsilon^{\mathrm{rms}}(\bm{r},\hat{\bm{r}})0.153– m\text{\,}\mathrm{m}
ϵrms(rt,r^t)\epsilon^{\mathrm{rms}}(\bm{r}_{t},\hat{\bm{r}}_{t})0.941– m s−1\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}
hwh_{\textnormal{w}}42.8– ms\text{\,}\mathrm{ms}
TABLE III : RMS whole-cable tracking errors and average MPC iteration wall time in the obstacle avoidance experiment.

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