## 1 Introduction  
Trajectory control as well as path-following are important topics in the research and industrial communities among others in, e.g., the fields of mobile robotics [2] and autonomous driving [3]. Research in these areas is mainly concerned with both a high availability of the path generation as well as a high integrity, stability, and accuracy of the trajectory/path-following controller. Especially,the importance of stable trajectory/path-following control is central as it ensures the safety of, e.g., the vehicle's and robot's operation. As a consequence of the increased onboard computation power and the emergence of small aerial vehicles, which should operate in close proximity to, e.g., housing, high accurate path control became of paramount importance in the context of aviation in the previous years as well. An overview on often used algorithms is given in [4; 5]: The variety of the applied algorithms ranges from simple geometric approaches to linear and decoupled control law design as well as sophisticated nonlinear control techniques, such as dynamic inversion and backstepping, and even optimal control-based approaches like model predictive control. Especially, nonlinear control techniques have shown their viability in application as they are able to exploit the full physical capabilities and available control authority of an aircraft, thus ensuring a high availability, integrity, and accuracy of the controller command. Additionally, they provide good interaction with the necessary inner-loop controllers as they can consider their dynamic behavior. Examples comprise backstepping control approaches [6], (nonlinear) adaptive control [7], and nonlinear dynamic inversion [8; 9; 10]. Considering the application to aircraft trajectory/path-following, the approach presented in [8; 10] has proven to be viable due to its modularity and independence of the dynamic model. Additionally, it allows for an independent control of the rigid-body/rotational dynamics in an inner loop by a stabilizing controller. Still, a drawback of the methodology is the fact that it is based on acceleration-level aircraft dynamics and kinematics, and thus produces force commands that the inner loop must directly follow. While this is theoretically possible, the inner-loop dynamics and actuators do not allow for direct changes of forces. Thus, this study proposes an enhancement of the existing trajectory/path-following approach by using jerk instead of acceleration-based dynamics and kinematics. In doing so, the command to the inner loop is a force derivative instead of the force, which allows for consideration of actuator dynamics [11; 12] and also yields smoother force commands by construction. A further advantage of the jerk-based control for manned application is that studies suggest an increased passenger comfort by controlling the jerk [13]. In addition, jerk is also a major contributor to the efficiency and this therefore often a minimization objective in robot manipulator path planning [14]. The general idea of the control approach of the paper is depicted in Figure 1: The desired trajectory is generated by a suitable method, e.g., geometric approaches [15; 16], (robust) optimal control [17; 18; 19; 20], or shortest path methods [21]. As the aircraft is generally never able to follow the path exactly, either due to imperfect planning or disturbances (e.g, wind or model errors), a deviation between the aircraft reference point \(R\) and the trajectory foot point \(F\) arises. This point is either specified by a \"virtual\" aircraft that the actual aircraft \"chases\" (this is said to be \"trajectory control\" in this study) [5] or by the orthogonal projection of the aircraft reference point on the trajectory (this is said to be \"path-following control\" in this study), which may be calculated by the methods proposed in [15; 22]. The trajectory/path-following controller then uses these deviations as well as their derivatives (velocity and acceleration) to calculate a suitable control command to reduce them.