Equilibria, Stability, and Sensitivity for the Aerial Suspended Beam Robotic System subject to Parameter Uncertainty

TL;DR

This paper analyzes how parametric uncertainties influence the stability and control of a cable-suspended beam manipulated by two aerial robots without explicit communication, highlighting robustness factors and sensitivity to model variations.

Contribution

It introduces a method to determine equilibrium configurations and stability under uncertainties, and studies the robustness of load attitude control with a novel sensitivity analysis.

Findings

Equilibrium configurations are identified under parametric uncertainties.

Stability analysis reveals the importance of internal forces for robustness.

Sensitivity of attitude error to parameter variations is formally characterized.

Abstract

This work studies how parametric uncertainties affect the cooperative manipulation of a cable-suspended beam-shaped load by means of two aerial robots not explicitly communicating with each other. In particular, the work sheds light on the impact of the uncertain knowledge of the model parameters available to an established communication-less force-based controller. First, we find the closed-loop equilibrium configurations in the presence of the aforementioned uncertainties, and then we study their stability. Hence, we show the fundamental role played in the robustness of the load attitude control by the internal force induced in the manipulated object by non-vertical cables. Furthermore, we formally study the sensitivity of the attitude error to such parametric variations, and we provide a method to act on the load position error in the presence of the uncertainties. Eventually, we validate the results through an extensive set of numerical tests in a realistic simulation environment including underactuated aerial vehicles and sagging-prone cables, and through hardware experiments.