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

TL;DR

This paper develops a spectral method-based optimal control framework for aerial robots with flexible cables, enabling precise shape and position tracking through reduced order modeling and predictive control.

Contribution

It introduces a POD-based reduced order model combined with nonlinear model predictive control for flexible cable dynamics in aerial robots, validated through simulations and experiments.

Findings

POD-based model effectively captures cable dynamics.

NMPC achieves accurate shape and position tracking.

Outperforms traditional PID control in experiments.

Abstract

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 finite low-dimensional space spanned by orthogonal basis functions. Based on such a reduced order model, nonlinear model predictive control (NMPC) is implemented online to realize both position and shape trajectory tracking of the flexible cable in an optimal predictive fashion. The proposed POD-based reduced modeling and optimal control paradigms are verified in simulation using an accurate high-dimensional FDM-based model and experimentally using a real quadrotor and a cable. The results show the viability of the POD-based predictive control approach (allowing closing the control loop on the full system state) and its superior performance compared to an optimally tuned PID controller (allowing closing the control loop on the quadrotor state only).