Asymmetric Collaborative Bar Stabilization Tethered to Two Heterogeneous Aerial Vehicles

We consider a system composed of a bar tethered to two unmanned aerial vehicles (UAVs), where the cables behave as rigid links under tensile forces, and with the control objective of stabilizing the bar's pose around a desired pose. Each UAV is equipped with a PID control law, and we verify that the bar's motion is decomposable into three decoupled motions, namely a longitudinal, a lateral and a vertical. We then provide relations between the UAVs' gains, which, if satisfied, allows us to decompose each of those motions into two cascaded motions; the latter relations between the UAVs' gains are found so as to counteract the system asymmetries, such as the different cable lengths and the different UAVs' weights. Finally, we provide conditions, based on the system's physical parameters, that describe good and bad types of asymmetries. We present experiments that demonstrate the stabilization of the bar's pose.