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

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.

Manipulation of Elasto-Flexible Cables with Single or Multiple UAVs

This work considers a large class of systems composed of multiple quadrotors manipulating deformable and extensible cables. The cable is described via a discretized representation, which decomposes it into linear springs interconnected through lumped-mass passive spherical joints. Sets of flat outputs are found for the systems. Numerical simulations support the findings by showing cable manipulation relying on flatness-based trajectories. Eventually, we present an experimental validation of the effectiveness of the proposed discretized cable model for a two-robot example. Moreover, a closed-loop controller based on the identified model and using cable-output feedback is experimentally tested.

Aerial Robots Carrying Flexible Cables: Dynamic Shape Optimal Control via Spectral Method Model

In this work, we present a model-based optimal boundary control design for an aerial robotic system composed of a quadrotor carrying a flexible cable. The whole system is modeled by partial differential equations (PDEs) combined with boundary conditions described by ordinary differential equations (ODEs). The proper orthogonal decomposition (POD) method is adopted to project the original infinite-dimensional system on a subspace spanned by orthogonal basis functions. Based on the reduced order model, nonlinear model predictive control (NMPC) is implemented online to realize shape trajectory tracking of the flexible cable in an optimal predictive fashion. The proposed reduced modeling and optimal control paradigms are numerically verified against an accurate high-dimensional FDM-based model in different scenarios and the controller's superior performance is shown compared to an optimally tuned PID controller.