Six-Degree-of-Freedom Aircraft Landing Trajectory Planning with Runway Alignment

This paper presents a numerical optimization algorithm for generating approach and landing trajectories for a six-degree-of-freedom (6-DoF) aircraft. We improve on the existing research on aircraft landing trajectory generation by formulating the trajectory optimization problem with additional real-world operational constraints, including 6-DoF aircraft dynamics, runway alignment, constant wind field, and obstacle avoidance, to obtain a continuous-time nonconvex optimal control problem. Particularly, the runway alignment constraint enforces the trajectory of the aircraft to be aligned with the runway only during the final approach phase. This is a novel feature that is essential for preventing an approach that is either too steep or too shallow. The proposed method models the runway alignment constraint through a multi-phase trajectory planning scheme, imposing alignment conditions exclusively during the final approach phase. We compare this formulation with the existing state-triggered constraint formulation for runway alignment. To solve the formulated problem, we design a novel sequential convex programming algorithm called xPTR that extends the penalized trust-region (PTR) algorithm by incorporating an extrapolation step to expedite convergence. We validate the proposed method through extensive numerical simulations, including a Monte Carlo study, to evaluate the robustness of the algorithm to varying initial conditions.