Direct Method for Rapid Prototyping of Near-Optimal Aircraft Trajectories

Adirect method for a real-time generationof near-optimal spatial trajectories of short-termmaneuvers onboard a ying 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 ight 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 arc 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 ight data, and with the solution obtainedbyPontryagin’smaximumprinciple.Fast convergenceof the numerical algorithm,whichhasbeen already implemented and tested onboard a real aircraft, is illustrated. Nomenclature aik = polynomial coef cients g = accelerationdue to gravity J = cost function j = quantity pertaining to the j th time node