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Trajectory Real-time Optimization Based on Variable Node Inverse Dynamics in the Virtual Domain
Received date: 2013-01-25
Revised date: 2013-08-15
Online published: 2013-12-23
To solve the problem of low utilization rate in inverse dynamics in the virtual domain (IDVD) trajectory optimization caused by node distribution in equal distances, a real time variable node IDVD trajectory optimization algorithm is presented in this paper. Based on the variable upper limit integral of the overload on the virtual arc the algorithm transcribes fixed node and fixed step IDVD to variable node and variable step IDVD by performing optimization twice. A comparison with two examples using IDVD in the interception of ballistic missile trajectory at the ascent phase shows that, if the number of nodes is equal, the variable node IDVD reaches lower standard deviations of error of about 20% at the x axis, y axis, z axis respectivlely, and cuts the optimization time by 20% approximately. Results show that the variable node IDVD is able to distribute nodes adaptively according to the size of the curvature of the virtual arc, which improves the utilization rate of nodes, enhances trajectory calculation accuracy and reduces online optimization time.
YAN Liang , LI Yuan , ZHAO Jiguang , DU Xiaoping . Trajectory Real-time Optimization Based on Variable Node Inverse Dynamics in the Virtual Domain[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2013 , 34(12) : 2794 -2803 . DOI: 10.7527/S1000-6893.2013.0360
[1] Ocampo C A, Mathur R. Variational model for optimization of finite-burn escape trajectories using a direct method. Journal of Guidance, Control, and Dynamics, 2012, 35(2): 598-608.
[2] Liu T, Nachtsheim P R. Shooting method for solution of boundary-layer flows with massive blowing. AIAA Journal, 1973, 11(11): 1584-1586.
[3] Matausek M R. Direct shooting method, linearization, and nonlinear algebraic equations. Journal of Optimization Theory and Applications, 1974, 14(2): 199-212.
[4] Blank D. A direct shooting algorithm and the application of parametric optimization for constrained optimal control problems. Haifa: Department of Aeronautical Engineering, Israel Institute of Technology, 1978.
[5] Lenz S M, Bock H G, Schlder J P, et al. Multiple shooting method for initial satellite orbit determination. Journal of Guidance, Control, and Dynamics, 2010, 33(5): 1334-1346.
[6] Maurer H, Gillessen W. Application of multiple shooting to the numerical solution of optimal control problems with bounded state variables. Computing, 1975, 15(2): 105-126.
[7] Rentrop P. Numerical solution of the singular Ginzburg-Landau equations by multiple shooting. Computing, 1976, 16(1-2): 61-67.
[8] Subbarao K, Shippey B M. Hybrid genetic algorithm collocation method for trajectory optimization. Journal of Guidance, Control, and Dynamics, 2009, 32(4): 1396-1403.
[9] Benson D A, Huntington G T, Thorvaldsen T P, et al. Direct trajectory optimization and costate estimation via an orthogonal collocation method. Journal of Guidance, Control, and Dynamics, 2006, 29(6): 1435-1440.
[10] Dwivedi P N, Bhattacharya A, Padhi R. Suboptimal midcourse guidance of interceptors for high-speed targets with alignment angle constraint. Journal of Guidance, Control, and Dynamics, 2011, 34(3): 860-877.
[11] Seywald H. Trajectory optimization based on differential inclusion (revised). Journal of Guidance, Control, and Dynamics, 1994, 17(3): 480-487.
[12] Fahroo F, Ross I M. Second look at approximating differential inclusions. Journal of Guidance, Control, and Dynamics, 2001, 24(1): 131-133.
[13] Lu P. Inverse dynamics approach to trajectory optimization for an aerospace plane. Journal of Guidance, Control, and Dynamics, 1993, 16(4): 726-732.
[14] von Stryk O, Bulirsch R. Direct and indirect methods for trajectory optimization. Annals of Operations Research, 1992, 37(1-4): 357-373.
[15] Yakimenko O A. Direct method for rapid prototyping of near-optimal aircraft trajectories. Journal of Guidance, Control, and Dynamics, 2000, 23(5): 865-875.
[16] Basset G, Xu Y, Yakimenko O A. Computing short-time aircraft maneuvers using direct methods. Journal of Computer and Systems Sciences International, 2010, 49(3): 481-513.
[17] Benson D A, Huntington G T, Thorvaldsen T P, et al. Direct trajectory optimization and costate estimation via an orthogonal collocation method. Journal of Guidance, Control, and Dynamics, 2006, 29(6): 1435-1440.
[18] Fahroo F, Ross I M. Costate estimation by a Legendre pseudospectral method. Journal of Guidance, Control, and Dynamics, 2001, 24(2): 270-277.
[19] Fahroo F, Ross I M. Direct trajectory optimization by a Chebyshev pseudospectral method. Journal of Guidance, Control, and Dynamics, 2002, 25(1): 160-166.
[20] Ross I M, Fahroo F. Pseudospectral knotting methods for solving optimal control problems. Journal of Guidance, Control, and Dynamics, 2004, 27(3): 397-405.
[21] Boyarko G A, Romano M, Yakimenko O A. Time-optimal reorientation of a spacecraft using an inverse dynamics optimization method. Journal of Guidance, Control, and Dynamics, 2011, 34(4): 1197-1208.
[22] Yakimenko O A. Shortcut-time spatial trajectories on-board optimization and their cognitive head-up display visualization for pilot's control actions during manoeuvring support. International Congress on Instrumentation in Aerospace Simulation Facilities, 1997: 246-256.
[23] Lukacs J A I, Yakimenko O A. Trajectory-shaping guidance for interception of ballistic missiles during the boost phase. Journal of Guidance, Control, and Dynamics, 2008, 31(5): 1524-1531.
[24] Paris S W, Riehl J P, Sjauw W K. Enhanced procedures for direct trajectory optimization using nonlinear programming and implicit integration. AIAA-2006-6309, 2006.
[25] Lu Z L. Ballistic missile interception from UCAV. Monterey: Naval Postgraduate School, 2011.
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