Geometric Control of two Quadrotors Carrying a Rigid Rod with Elastic Cables

TL;DR

This paper develops a geometric trajectory tracking controller for two quadrotors transporting a rigid rod with elastic cables, effectively managing elasticity and disturbances to ensure precise movement.

Contribution

Introduces a novel control scheme that accounts for cable elasticity using singular perturbation, enabling exponential trajectory tracking of the transported load.

Findings

Controller achieves exponential tracking of the rod's trajectory.

Elastic cable effects are effectively managed through model reduction.

System maintains bounded errors under disturbances.

Abstract

This paper presents the design of a geometric trajectory tracking controller for the cooperative task of two quadrotor UAVs (unmanned aerial vehicles) carrying and transporting a rigid bar, which is attached to the quadrotors via inflexible elastic cables. The elasticity of the cables together with techniques of singular perturbation allows a reduction in the model to that of a similar model with inelastic cables. In this reduced model, we design a controller such that the rod exponentially tracks a given desired trajectory for its position and attitude, under some assumptions on initial error. We then show that exponential tracking in the reduced model corresponds to exponential tracking of the original elastic model. We also show that the previously defined control scheme provides uniform ultimate boundedness in the presence of unstructured bounded disturbances.