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Dynamic equations of aerial robots are complicated due to both high instability of the platform and the presence of aerodynamic effects which are not merely to model. By attaching a small-scale robot manipulator to such an aerial system, it is straightforward to recognize that the dynamic coupling between the modeling terms becomes relevant. Representing in a proper way the dynamic model of the whole system is then crucial to develop suitable control laws. A literature review about aerial manipulation is published by Fabio Ruggiero here.

The dynamic model of vertical take-off and landing (VToL) unmanned aerial vehicles (UAVs) with an attached robotic arm is derived here and here in a symbolic matrix form through the Euler-Lagrangian formalism. Cartesian impedance control for UAVs equipped with a robotic arm has been developed by Fabio Ruggiero. A dynamic relationship between generalized external forces acting on the structure and the system motion, which is specified regarding Cartesian space coordinates, is provided here. Through a suitable choice of such variables and with respect to a given task, thanks to the added degrees of freedom given by the robot arm attached to the UAV, it is possible to exploit the redundancy of the system so as to perform some useful subtasks as here.

However, since most robotic arms placed on the UAVs are often small-size manipulators made up by servomotors, it is often not possible to directly control the joint torques. Hence, Fabio Ruggiero developed a method here and here to control separately the aerial vehicle and the robotic manipulator. The latter can be moved through standard position-based and/or kinematic controller, while the former has to both compensate the movements of the arm and translate towards the desired position in the Cartesian space. Therefore, an estimator of generalized external forces (forces plus moments) acting on the aerial vehicle and based on the mechanical momentum of the system has been developed. The estimation is fed back to the aerial vehicle controller to take into account and compensate the robotic manipulator’s movements. The overall controller design is made up by an inner and an outer loop which are shaped as mechanical impedances, whose stiffness and damping are programmable through the control gains, giving in this way some passivity properties to the entire scheme as here. The overall architecture has been tested on both a UAV with unknown payload and external forces here, and a UAV equipped with a 6-DOF small-size servo robotic arm here.

In case of a dual-arm aerial manipulator, novel image-based visual-impedance controllers are developed here, allowing physical interaction of the platform equipped with a camera and a force/torque sensor. Visual information is employed both to coordinate the camera motion in an eye-in-hand configuration with the assigned task executed by the other robot arm, and to define the elastic wrench component of the proposed hybrid impedance equations directly in the image plane.