Initial Guess Generation for Aircraft Landing Trajectory Optimization

Abstract

We present a semi-analytic framework for the generation of initial guesses for the numerical solution of the landing trajectory optimization problem of an aircraft. Our approach consists of the following tasks: First, we introduce a geometric framework for the generation of length-suboptimal, curvature-constrained, threedimensional curves, which satisfy the following requirements: 1) the projection of the curves on the horizontal plane correspond to Dubins-like paths, and 2) an aircraft traveling along these curves is descending continuously until it reaches its final destination. Subsequently, we generate a time-parametrization of the geometric path such that the control inputs required to traverse the geometric path do not exceed the control limits of the aircraft. The resulting time-parameterized path along with the control input time histories is subsequently fed as an initial guess into a numerical optimal control solver, such as the one introduced in Ref. [1]. Simulation results demonstrate the advantages of employing the proposed initial guess generation scheme in terms of convergence of the numerical landing trajectory generation.

Robust aircraft trajectory planning under uncertain convective environments with optimal control and rapidly developing thunderstorms

“…A large number of practical optimal control problems feature optimal trajectories that may display features at different timescales. For example, in a simple optimal cruise problem, the optimal solution is often composed by an initial phase at either maximum or minimum throttle until an efficient velocity is reached, a central "singular arc" phase where the aircraft slowly decelerates as the optimal velocity is adjusted to the changing mass of the aircraft, and a final acceleration or deceleration phase to match the terminal velocity (or the minimum allowed velocity, if no final condition is imposed on the velocity) [94,95]. This presents a challenge for most direct methods, since choosing a large step size that is efficient for the long central phase leads to inaccuracies in the initial and final phases, and choosing a small step size for accurate representation of the solution at the endpoints is computationally uneconomical for the central singular arc phase, leading to an oversized NLP.…”

“…Several researchers have also studied the aircraft trajectory optimization problem with direct methods. Efficient and reliable landing procedures using optimal control are developed in [95]. As the performance of direct methods is highly dependent on the initial guess, a method for generating initial guess trajectories for the same problem is introduced in [157].…”

“…Efficient and reliable landing procedures using optimal control are developed in [95]. As the performance of direct methods is highly dependent on the initial guess, a method for generating initial guess trajectories for the same problem is introduced in [157]. In [158,159], a complete trajectory is optimized using hybrid optimal control and Mixed-Integer Nonlinear Programming (MINLP), and a similar approach is employed in [160] in order to include contrail avoidance in the objective function.…”

A Machine Learning Enhanced Algorithm for the Optimal Landing Problem

“…We start from the indirect method, utilizing the PMP to transform the original optimal landing problem into a TPBVP. One critical issue of the TPBVP solver is to find good initial guesses (Tsiotras, Bakolas, and Zhao, 2011;Nakamura-Zimmerer et al, 2021a). To overcome this difficulty, we design a DNN-based algorithm to provide an initial guess of the optimal landing time and a space-marching scheme to provide an initial guess of the solution.…”

Optimizing Steady Turns for Gliding Trajectories

“…Steady-state trajectories allow fast guaranteed solutions that can be easily understood and followed by a pilot. The solutions can also be used to construct an initial estimate for an optimizer that can refine the proposed solution [12].…”