Non-linear model predictive control (nMPC) is a powerful approach to control complex robots (such as humanoids, quadrupeds, or unmanned aerial manipulators (UAMs)) as it brings important advantages over other existing techniques. The full-body dynamics, along with the prediction capability of the optimal control problem (OCP) solved at the core of the controller, allows to actuate the robot in line with its dynamics. This fact enhances the robot capabilities and allows, e.g., to perform intricate maneuvers at high dynamics while optimizing the amount of energy used. Despite the many similarities between humanoids or quadrupeds and UAMs, full-body torque-level nMPC has rarely been applied to UAMs. This paper provides a thorough description of how to use such techniques in the field of aerial manipulation. We give a detailed explanation of the different parts involved in the OCP, from the UAM dynamical model to the residuals in the cost function. We develop and compare three different nMPC controllers: Weighted MPC, Rail MPC, and Carrot MPC, which differ on the structure of their OCPs and on how these are updated at every time step. To validate the proposed framework, we present a wide variety of simulated case studies. First, we evaluate the trajectory generation problem, i.e., optimal control problems solved offline, involving different kinds of motions (e.g., aggressive maneuvers or contact locomotion) for different types of UAMs. Then, we assess the performance of the three nMPC controllers, i.e., closed-loop controllers solved online, through a variety of realistic simulations. For the benefit of the community, we have made available the source code related to this work.
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