Singularity-Free Quaternion Representation to Control a UGV-UAV Formation Performing Trajectory-Tracking Tasks

A formation composed by a ground unmanned vehicle (UGV) and an unmanned aerial vehicle (UAV) is considered here. The UAV should land on the UGV, which emulates a static or moving base station for the UAV. In such case, issues related to formation singularities may occur. An example of singularity is the fact that the UAV is not guaranteed to be laterally aligned with the UGV, thus not allowing to precisely get the current state of the formation when starting the landing maneuver. Focusing on this specific situation, this paper proposes a singularity-free representation of the formation, based on quaternions, and a formation controller, based on this formulation, to guide the formation in trajectory-tracking tasks. Besides the theoretical development, the paper also provides results of experiments run using a formation composed by a Pioneer 3-DX UGV and a Bebop 2 UAV, which validate the proposed formulation and controller.