# Control of an Omnidirectional UAV for Transportation and Manipulation Tasks
## 1 Introduction  
In recent years, the use of aerial robotic platforms, due to their nearly unlimited motion space, has become popular in many applications scenarios, e.g., inspection and maintenance services [1], data collection and exploration operations [2], and precision agriculture [3]. More and more frequently, aerial robots are involved in tasks requiring both autonomous flight and physical interaction capabilities, such as assembly of structures in remote environments, object grasping [4], and payload transportation [5, 6]. The most popular configuration of vertical take off and landing (VTOL) unmanned aerial vehicle (UAV) is that of a multi-rotor vehicle, i.e., an aerial vehicle equipped with four or more coplanar propellers, which offers the best trade-off between mobility, simplicity, and cost. The main drawback of classical multi-rotor vehicles is that they are underactuated systems, since thrusts generated by propellers are directed along parallel axes, orthogonal to the plane of the propellers [7]. Therefore, in order to change its position and/or counteract external disturbances, rotation of vehicle's body is required: thus, only four degrees of freedom (DOFs) are left to execute the task assigned to the UAV. This limitation may become severe in some applications that might benefit from availability of all six DOFs, e.g., manipulation tasks involving contact with the environment [8], and/or limit the disturbance counteraction capabilities of the system. To overcome this problem, in recent years, platforms with multi-directional thrust have been designed. One of the most common approaches is based on the use of tilted propellers, e.g., as in [9, 10]. The overactuated platforms require additional motors for tilting the propellers, and this has the negative effect of increasing the system weight and the complexity of the control for handling both vertical and lateral air flows. Such a problem can be overcame by adopting hexarotorswith tilted propellers, e.g., as in [11], where each rotor is mounted in a fixed configuration rotated about two axes. More efficient solutions are proposed in [12; 13]. More in detail, in [12], an additional motor is added in order to tilt all propellers at the same time, in such a way as to reduce the energy consumption and the total mass, allowing to drive the platform from a configuration energetically efficient, but underactuated to a fully actuated but less efficient one. In [13], an hexator with independently tiltable rotors is designed; the tilting angle of the rotors is computed online via a suitable control allocation scheme. This platform by exploiting its bi-directional thrusters can apply forces in any direction, while for the other platforms using uni-directional thrusters, the forces are usually limited in the upper hemisphere. An interesting analysis conducted in [14] proved that, for unidirectional thrusters, the minimum number of rotors in order to achieve omnidirectional forces is seven. Such analysis leads to the platform in [15], which is equipped with seven propellers, whose tilting angles are computed according to the optimization procedure in [14] and guarantee the omnidirectional property of the platform, while enforcing equal sharing of the desired forces between the propellers. The previous solutions, do not avoid internal wrenches caused by counteracting actuators and require redundant control inputs. In order to overcome this problem, in [16], a quadrotor vehicle is designed, with the tilting angle of the propellers simultaneously controlled by two additional actuators via a parallelogram mechanism. In this way, only six inputs are adopted to control six degrees of freedom (DOFs), and the thrust generated by all propellers is always aligned along the same direction, thus avoiding energy dissipation due to internal wrench. A similar configuration has been proposed in [17], where a new concept of omnidirectional aerial vehicle, named ODQuad, is designed in particular for transportation and manipulation tasks.