trajectory tracking for systems with nonminimum phase characteristics, such as aircraft [8]. See [9; 10] for a comparison of different path-following algorithms for fixed-wing UAVs, in two and three dimensions, respectively. For a recent survey with a focus on quadrotor UAVs, see [11]. Guidance and control systems for unmanned vehicles can be integrated, or separated [12]. For integrated guidance and control (IGC) systems, the guidance system and inner-loop autopilot are designed simultaneously, taking cross-coupling effects into account. On the other hand, in separated guidance and control (SGC), inner and outer loops are designed separately, with modularity and cross-platform use in mind [13]. Examples of separate guidance algorithms for fixed-wing UAVs include nonlinear guidance laws [14; 15], vector-field path following [16; 17] and a guidance law based on nested saturations [18]. In [19], path following is achieved by using an existing commercial inner-loop autopilot but augmented with an \(\mathcal{L}_{1}\) adaptive controller to deal with modeling uncertainty and environmental disturbances. While most guidance algorithms use only kinematic models, an integrated approach is presented in [20] that uses a simple model of the aerodynamic forces acting on the aircraft. Common to all the mentioned approaches, both IGC and SGC, is the reliance on attitude control in the inner-most loop. The rotational dynamics is not considered but rather assumed to be stabilized by some low-level controller. This motivates further research on attitude controllers, specifically tailored towards fixed-wing UAVs. Several different attitude representations have been employed for fixed-wing UAV path following, including Euler angles [21], rotation matrices [22] and unit quaternions [23]. Minimal representations such as Euler angles are often used because of their intuitive interpretation but suffer from \"gimbal-lock\" singularities [24]. Unit quaternions [25] are singularity-free, but provide a double cover of SO(3), the space of 3-D rotations. This might lead to unwinding, where the UAV unnecessarily makes a full rotation, even when arbitrarily close to the target attitude [26; 27]. Rotation matrices, on the other hand, provide a global and unique representation. This has led to a significant research effort into so-called geometric attitude control, where singularity-free controllers are designed directly on SO(3), using rotation matrices, that avoid the unwinding phenomenon and often controls the system along geodesics, i.e., paths of minimum length in rotation space [28; 29; 30; 31; 32; 33]. These advantages are desirable when the controlled vehicle is subject to large angle rotations, e.g., a fixed-wing UAV recovering from large attitude errors resulting from severe wind gusts [34]. Fixed-wing UAVs use one of two main mechanisms for turning: bank-to-turn, where a lateral acceleration is generated by reorienting the lift-force by rolling/banking the UAV, or skid-to-turn, where turning is achieved by generating a sideslip angle, which in turn generates a lateral force that turns the vehicle [35]. In [36], these methods are combined to reduce lateral distortion of camera images gathered by a fixed-wing UAV. In general, bank-to-turn is often preferred over skid-to-turn because for most aircraft the lift force is of orders of magnitude greater than thrust forces [37]. Thus, the course angle, yaw angle, and turn rate of aircraft are not controlled directly, but rather through banked-turn maneuvers. For aircraft in coordinated turns, i.e., with zero sideslip angle, the coordinated-turn equation provides a simple relationship between roll angle and resulting turn rate, and is for this  
Figure 1: Skywalker X8 fixed-wing UAV (Image courtesy of NTNU UAV-Lab). reason often used in autopilot design [1; 38; 39; 40; 41; 42], including those used in state-of-the-art open-source autopilots [43; 44].