Using Quaternions to Solve Singularity Problems for a UAV-UGV Formation

To control a formation of a ground robot and an aerial one based on the paradigm of virtual structures involves relating the variables that describe the formation, called formation variables, with the positions of the robots, called robot variables. This relationship generates what is called transformations from the formation space to the robots space and vice versa. An important issue that arises when such a formulation is used is that there may be relative positions between the vehicles that characterize singularities. The characterization of this formation based on spherical coordinates (distance and relative orientations) creates a singularity point when the aerial vehicle is above the ground vehicle, for example trying to land on it. This work considers exactly this situation, and proposes a solution in which there is no singularity, based on the use of unit quaternions. A description of the formation based on unit quaternions is presented and a suitable controller for such a formulation is proposed. Experimental results are also presented, using the proposed formulation and controller, which validate the proposal.