Direct Method for Rapid Prototyping of Near-Optimal Aircraft Trajectories

Abstract

A direct method for a real-time generation of near-optimal spatial trajectories of short-term maneuvers 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 obtainedby Pontryagin's maximumprinciple. Fast convergence of the numerical algorithm,which has been already implemented and tested onboard a real aircraft, is illustrated. Nomenclature a ik= polynomial coef cients g = acceleration due to gravity J = cost function j = quantity pertaining to the j th time node m = aircraft mass N = number of nodes n = polynomial order n = relative revolutions of engine's rotor n x , n z = tangential and normal projections of load factor, respectively Sh = penalty function T,T = total thrust and relative thrust (fraction of maximum thrust), respectively CONCEPT of the onboard pilot's support system (PSS; electronic copilot or pilot associate) assumes the presenceof a sub-

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