# Control of an Omnidirectional UAV for Transportation and Manipulation Tasks
## 1 Introduction
The ODQuad is a quadrotor with the capability of providing multi-directional thrusts by rotating the frame on which the four rotors are mounted through two actuated rotational joints realizing a two-axis (roll and pitch) gimbal mechanism. For classical underactuated multi-rotors, several controllers have been proposed, mostly based on linear approaches [18; 19], often requiring model linearization about a set of equilibrium conditions. Such controllers allow to achieve satisfactory performance near the design conditions and in lowering conditions, but performance degradation is usually observed when the aircraft moves away from these conditions. To overcome these drawbacks, nonlinear controllers have been designed, including model predictive control [20], backstepping and sliding mode techniques [21; 22], adaptive control [23], impedance control [24; 25], and geometric control [26]. More recently, data-based control approaches have been designed for achieving high-performance trajectory tracking with UAVs: in detail, in [27], an innovative iterative learning control algorithm is proposed based on an estimation of repetitive disturbances to improve the learning performance. Regarding the omnidirectional aerial platforms, the most common control approach is feedback linearization, aimed at decoupling the six DOFs that can be controlled separately. Such approaches are model-based; the nonlinear dynamical effects are compensated, and then the thrust is derived from the inversion of the control allocation matrix. Some examples of feedback linearization approaches can be found in [11; 16; 28]. One of the main issues occurring in feedback linearization is that the actuator saturation can destabilize the system. Solutions to this drawback have been proposed. In [29], the six inputs of a coplanar hexarotor are mapped in a four dimensional task output (i.e., the total thrust and the three moment components) via a weighted pseudoinverse. In [30], for constant position and attitude references, input saturation is avoided by resorting to an approach based on the explicit reference governor, which provides constraint handling capabilities by suitably manipulating the derivative of the applied reference [31]. In [32], a general geometric tracking controller for time-varying references is proposed, which also takes into account the bounds on the lateral control force. The aim of this paper is to present a novel motion control scheme for the ODQuad vehicle [17] and to test it both in free-space motion and in the presence of external disturbances, such as the contact with an object during a task of manipulation and transportation. More in detail, a model-based feedback linearization controller is proposed that computes the reference signals using a hierarchical two-loop scheme: the outer loop is a position controller aimed at computing the global thrust force and the reference values for the pitch and roll angles of the gimbal mechanism; then, in the inner loop, an attitude and gimbal controller, on the basis of these references, computes the moments acting on the quadrotor and the joint torques. A preliminary version of such a scheme has been introduced in [17]; here, two contribution are added: (i) the stability analysis of the system, based on Lyapunov arguments; and (ii) the extension to the case of contact with an object with the compensation of the interaction wrench performed via an online estimator. Finally, in order to prove the effectiveness of the approach, simulation case studies have been developed, in which the controller is tested in a non-ideal context by considering model uncertainties and sensor noise. It is worth pointing out that, although the ODQuad is conceived to perform tasks both in free space and involving interaction with the environment, the aim of this paper is to design and validate the first building block of the whole control architecture, namely the motion control.