In this paper, a trajectory generation algorithm within an integrated flight guidance and control system is presented. The approach uses clothoids to deal with the problem of curvature steps during the transition phase between straight line and arc flight. The algorithm is designed in interaction with a trajectory controller for 2 ^nd order error dynamics, which hence requires more trajectory information than a conventional approach. The presented test results were obtained via in-flight tests with an experimental CS 23 aircraft.

In practical scenarios, flight trajectories shall be smooth to comply with the required curvature behavior. The paper describes a trajectory generation method that is able to produce smooth control commands with an arbitrary order of smoothness. The system inputs are formulated analytically as trigonometric series in which the coefficients are to be determined by optimization. Effective implementations of the proposed method are presented. These include a numerical benchmark that shows how the order of the series shapes the results as well as the comparison with the optimal solution, and the UAV transition trajectory generation using a convex optimization framework integrated with the proposed design.

This study develops a chance–constrained open–loop optimal control (CC–OC) framework capable of handling rare event probabilities. Therefore, the framework uses the generalized polynomial chaos (gPC) method to calculate the probability of fulfilling rare event constraints under uncertainties. Here, the resulting chance constraint (CC) evaluation is based on the efficient sampling provided by the gPC expansion. The subset simulation (SubSim) method is used to estimate the actual probability of the rare event. Additionally, the discontinuous CC is approximated by a differentiable function that is iteratively sharpened using a homotopy strategy. Furthermore, the SubSim problem is also iteratively adapted using another homotopy strategy to improve the convergence of the Newton-type optimization algorithm. The applicability of the framework is shown in case studies regarding battery charging and discharging. The results show that the proposed method is indeed capable of incorporating very general CCs within an open–loop optimal control problem (OCP) at a low computational cost to calculate optimal results with rare failure probability CCs.

This study proposes a novel, nonlinear trajectory/path-following controller based on jerk-level error dynamics. Therefore, at first the nonlinear acceleration-based kinematic equations of motion of a dynamic system are differentiated with respect to time to obtain a representation connecting the translation jerk with the (specific) force derivative. Furthermore, the path deviation, i.e., the difference between the planned and the actual path, is formulated as nonlinear error dynamics based on the jerk error. Combining the derived equations of motion with the nonlinear error dynamics as well as employing nonlinear dynamic inversion, a control law can be derived that provides force derivative commands, which may be commanded to an inner loop for trajectory control. This command ensures an increased smoothness and faster reaction time compared to traditional approaches based on a force directly. Furthermore, the nonlinear parts in the error dynamic are feedforward components that improve the general performance due to their physical connection with the real dynamics. The validity and performance of the proposed trajectory/path-following controller are shown in an aircraft-related application example.