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We design an adaptive controller for a quadrotor UAV transporting a point-mass payload connected by a flexible cable modeled as serially-connected rigid links. The mass of the payload is uncertain. The objective is to transport the payload to a desired position while aligning the links along the vertical direction from an arbitrary initial condition. A fixed-gain nonlinear proportional-derivative controller is presented to achieve the desired performance for a nominal payload mass, and a retrospective cost adaptive controller is used to compensate for the payload mass uncertainty.
Dai et al. (2014) studied this question.