Control Design for Collaborative Aerial Transportation of Flexible Payload

The task of collaborative transportation of large in size cargo is associated with difficulties, both in the group organization of aircraft control, and in ensuring the safety of cargo and route optimality. However, this method of transportation is becoming more popular and is already being used in commercial services. Usually the loads are assumed to be rigid or are limited to a simplified description of elastic vibrations using approximating polynomials is being used. This paper consider the task of constructing a physically interpretable and simple for control algorithm design linear mathematical model of a system that describes the behavior of two aerial vehicles transporting a flexible inhomogeneous load. For this purpose, two classical models describing elastic vibrations were used - Euler-Bernoulli and Timoshenko. They make it possible to obtain intuitive and physically interpretable relations describing the dynamics of body deflection. The method is based on the use of a design model in the form of a beam or rod, which is typical for the problem under consideration. The proposed mathematical formulation constructing method allows one to simultaneously take into account the uniformity of the elastic load and describe the dynamics of motion in the easiest way. Regulator built on the basis of solutions of a linear matrix inequalities system which can achieve conveniently specified desired characteristics, ensure robustness, which is important for a system with uncertain parameters, and minimize the consumed power is proposed.