Groups of unmanned aerial vehicles (UAVs) are increasingly utilized in transportation task as the combined strength allows to increase the maximum payload. However, the resulting mechanical coupling of the UAVs imposes new challenges in terms of tracking control. Thus, we design a geometric trajectory tracking controller for the cooperative task of four quadrotor UAVs carrying and transporting a rigid body, which is attached to the quadrotors via inflexible elastic cables. The elasticity of the cables together with techniques of singular perturbation allows a reduction in the model to that of a similar model with inelastic cables. In this reduced model, we design a controller such that the position and attitude of the load exponentially converge to a given desired trajectory. We then show that this result leads to a uniformly converging tracking error for the original elastic model under some assumptions. Furthermore, under the presence of unstructured disturbances on the system, we show that the error is ultimately bounded with an arbitrarily small bound. Finally, a simulation illustrates the theoretical results.

The project that gave rise to these results received the support of a fellowship from ”la Caixa” Foundation (ID 100010434). The fellowship codes are LCF/BQ/PI19/11690016 and LCF/BQ/DI19/11730028. The authors also acknowledge financial support from the Spanish Ministry of Science and Innovation, under grants PID2019- 106715GB-C21. All the results of the paper are original and have not been presented nor submitted to a conference. The authors also acknowledge Manuela Gamonal from ICMAT, Spain, for the help provided with the numerical simulations.

Peer reviewed