Cooperative transportation using rotorcraft: Swing state estimation and control

A cooperative transportation scenario is examined wherein two rotorcraft jointly carry a suspended payload. The equations of motion are first derived using the Lagrangian approach, under the assumption that the coupled slung–load system is represented by three point masses connected via two massless, rigid cables. The system is identified as underactuated, with a remaining degree of freedom corresponding to the swinging motion of the payload. An observation model is then formulated, enabling direct estimation of the oscillation angle from a minimal set of measurements, specifically the positions of both rotorcraft and their accelerations in the local horizontal plane. Data fusion is achieved through the application of a Fading Gaussian Deterministic Filter, the theoretical foundations of which were recently investigated by one of the authors. The proposed methodology is numerically validated in a high–fidelity simulation environment, where the multirotors are modeled as rigid bodies, accounting for viscous–elastic cable dynamics, aerodynamic disturbances, and rotor forces and moments computed via Blade Element Theory. The estimated swing angle and its rate are demonstrated to serve as effective feedback variables for payload stabilization. To this end, a control strategy is introduced to achieve simultaneous minimal–swing formation–keeping and trajectory–tracking maneuvers, offering improved flight characteristics and reduced overall energy consumption.