Direct method for rapid prototyping of near-optimal aircraft trajectories

A direct method for a real-time generation of near-optimal spatial trajectories of short-term maneuvers onboard a flying vehicle with predetermined thrust history is introduced. The paper starts with a survey about the founders of the direct methods of calculus of variations and their followers in flight mechanics, both in Russia and in the United States. It then describes a new direct method based on three cues: high-order polynomials from the virtual are as a reference function for aircraft's coordinates, a preset history of one of the controls (thrust), and a few optimization parameters. The trajectory optimization problem is transformed into a nonlinear programming problem and then solved numerically using an appropriate algorithm in accelerated scale of time. A series of examples Is presented. Calculated near-optimal trajectory is compared with real Right data, and with the solution obtained by Pontryagin's maximum principle. Fast convergence of the numerical algorithm, which has been already implemented and tested onboard a real aircraft, is illustrated.