Smooth Sub-Optimal Trajectory Generation for Transition Maneuvers

Abstract

In this paper, a sub-optimal trajectory optimization method is developed to generate trajectories for transition phases connecting two steady flights. Both control histories as well as the time step length that specify the trajectory for a transition maneuver are calculated as a root of an underdetermined system. Here, the unknowns are computed by a series of Newton iterations for finding the root, where explicit closed-form expressions are utilized within the algorithm to ensure computational efficiency. Moreover, a line-search strategy is incorporated to enhance the robustness. The terminal hard output constraints are guaranteed by the root finding, and the terminal control constraints are realized by using a time-varying weighting matrix in the cost function. Numerical simulations investigate multiple scenarios of transition phases, which show the effectiveness of the proposed method.

Trajectory/Path-Following Controller Based on Nonlinear Jerk-Level Error Dynamics

“…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.…”