This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time...This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time horizon of interest.To effectively implement this concept,the Hermite spline is adopted to interpolate the continuous controls and the system dynamics are integrated with corresponding control parameters in prior.As a result,the optimal control problem can be transcribed into a nonlinear programming problem which has no dynamic equality constraints and no intermediate states in its design variables.In addition,the paper proposes an efficient recursive Jacobian estimation technique and introduces a Jacobian transformation matrix to straightforwardly handle the general state constraints.Important properties of the present method are thoroughly investigated through its applications to the trajectory optimization for a soft lunar landing from a parking orbit,including the detailed analyses for the de-orbiting phase.The computed results are compared with those using the pseudo-spectral method to demonstrate an extreme outperformance of the proposed method in the aerospace applications over the traditional direct method.展开更多
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.NRF-2020R1A2C2011955)supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(No.2020R1A6A1A03046811)。
文摘This paper proposes a new direct method for an efficient trajectory optimization using the point that the dynamics of a deterministic system are uniquely determined by initial states and controls imposed over the time horizon of interest.To effectively implement this concept,the Hermite spline is adopted to interpolate the continuous controls and the system dynamics are integrated with corresponding control parameters in prior.As a result,the optimal control problem can be transcribed into a nonlinear programming problem which has no dynamic equality constraints and no intermediate states in its design variables.In addition,the paper proposes an efficient recursive Jacobian estimation technique and introduces a Jacobian transformation matrix to straightforwardly handle the general state constraints.Important properties of the present method are thoroughly investigated through its applications to the trajectory optimization for a soft lunar landing from a parking orbit,including the detailed analyses for the de-orbiting phase.The computed results are compared with those using the pseudo-spectral method to demonstrate an extreme outperformance of the proposed method in the aerospace applications over the traditional direct method.
