Using Quaternions to Avoid Singularities in UAV-UGV Multi Robot Systems

Abstract

To control a formation composed by a ground unmanned vehicle (UGV) and an unmanned aerial vehicle (UAV) based on the virtual structure paradigm, the focus of this thesis, involves to relate the variables describing the formation, referred to as formation variables, to the positions of the robots, referred to as robots variables. Such relationship generates transformations from the formation space to the robots space, and vice-versa. An important issue that arises when adopting such a formulation is that there may be relative positions of the vehicles which characterize formation singularities. The characterization of such a formation based on spherical coordinates (distance and relative orientations) presents a singularity point when the UAV is just above the UGV, preparing to land on it, for instance. This thesis focuses exactly in such situation, dealing with the landing of UAV on the UGV, which emulates a static or moving base station for the UAV. In such case, the 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. To deal with this issue this thesis proposes a singularity-free representation of the formation, based on unit quaternions, and a formation controller, based on this formulation, to guide the formation in trajectory-tracking tasks. Besides the theoretical development, the text 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.