Pose stabilization of a bar tethered to two aerial vehicles

• Published in: Automatica (Oxford) 2020-02, Vol.112, p.108695, Article 108695
• Main Authors: Pereira, Pedro O., Dimarogonas, Dimos V.
• Format: Article
• Language: English
• ISSN: 0005-1098; 1873-2836; 1873-2836
• DOI: 10.1016/j.automatica.2019.108695

This work focuses on the modeling, control and analysis of a bar, tethered to two unmanned aerial vehicles, which is required to stabilize around a desired pose. We derive the equations of motion of the system, we close the loop by equipping each UAV with a PID control law, and finally we linearize the closed-loop vector field around some equilibrium points of interest. When requiring the bar to stay on the horizontal plane and under no normal stress, we verify that the bar’s motion is decomposable into three decoupled motions, namely a longitudinal, a lateral and a vertical: for a symmetric system, each of those motions is further decomposed into two decoupled sub-motions, one linear and one angular; for an asymmetric system, we provide relations on the UAVs’ gains that compensate for the system asymmetries and which decouple the linear sub-motions from the angular sub-motions. From this analysis, we provide conditions, based on the system’s physical parameters, that describe good and bad types of asymmetries. Finally, when requiring the bar to pitch or to be under normal stress, we verify that there is a coupling between the longitudinal and the vertical motions, and that a positive normal stress (tension) has a positive effect on the stability, while a negative normal stress (compression) has a negative effect on the stability.