Algorithm of ISS Optimal Propellant Maneuver with Path Constraints in ISS Structure Loads

Authors: Atroshenkov S.N., Platonov V.N., Gubarev F.V., Saratov A.A. Published: 02.08.2017
Published in issue: #4(115)/2017  
DOI: 10.18698/0236-3933-2017-4-118-138

Category: Aviation, Rocket and Space Engineering | Chapter: Dynamics, Ballistics, Flying Vehicle Motion Control  
Keywords: elastic oscillations of ISS structure, critical interfaces, limit loads, ISS thrusters, Optimal Propellant Maneuver (ОРМ), optimization algorithms

The Integrated Guidance, Navigation and Control (GN&C) system of ISS is composed of the Russian segment (RS) GN&C system (SUDN) and American segment (AS) GN&C. The ISS flight schedule prescribes regular ISS large-angle maneuvers, which might be executed with two different methods, both of which utilize RS thrusters and ensure allowed structural loads in ISS critical interfaces. In the first method maneuver is performed under RS control around Euler axis; specific constraints, developed by NASA and known as "Pulse-Train", are imposed on command signals to ensure ISS structural integrity. Maneuver of the second type is conducted under AS control, and RS thrusters are activated via the procedure of CMG momentum desaturation. The maneuver trajectory is computed on the Earth as the solution of Optimal Propellant Maneuver (OPM) problem of rigid body rotation under the influence of gravitation and atmospheric forces and with smooth control. In this paper we present new ISS OPM algorithm, developed for RS GN&C, which solves optimal control problem of flexible body rotation under the influence of external forces and with pulse-like control signals. Specific path constraints on allowed structural loads in ISS critical interfaces are also taken into account. Reduced flexible model of ISS and optimal control problem formulation are developed by Rocket and Space Corporation Energia (RSCE). Modeling of elastic body dynamics and optimization problem solution are conducted by DATADVANCE and then verified by RSCE specialists using their own algorithms. Findings of the research show that in all relevant cases the proposed algorithm is twice fuel-efficient compared to existing methods and makes it possible to lower the required number of thrusters firings by order of magnitude.


[1] Chernous’ko F.L., Akulenko L.D., Sokolov B.N. Upravlenie kolebaniyami [Oscillations control]. Moscow, Nauka Publ., 1980. 383 p.

[2] Akulenko L.D., Chernous’ko F.L. The averaging method in optimal control problems. USSR Computational Mathematics and Mathematical Physics, 1975, vol. 15, no. 4, pp. 54-67.

[3] Bedrossian N., Bhatt S., Kang W., Ross M. Zero-propellant maneuver guidance. IEEE Control Systems, 2009, vol. 29, no. 5, pp. 53-73. DOI: 10.1109/MCS.2009.934089 Available at: http://ieeexplore.ieee.org/document/5256357

[4] Bhatt S. Optimal reorientation of spacecraft using only control moment gyroscopes. Master Thesis. Dept of Computational & Applied Mathematics, Rice Univ. 2007. 110 p.

[5] Bhatt S., Bedrossian N., Nguyen L. Optimal propellant maneuver flight demonstrations on ISS. AIAA Guidance, Navigation, and Control (GNC) Conf., 2013. DOI: 10.2514/6.2013-5027 Available at: https://arc.aiaa.org/doi/10.2514/6.2013-5027

[6] Jiann-Woei Jang. Multivariable flex model reduction. AAS/AIAA Astrodynamics Specialists Conference, 2003. 11 p.

[7] Antoulos A.C. Approximation of large-scale dynamics system. SIAM, 2009. 463 p.

[8] Hartl R.F., Sethi S.P., Vickson R.G. A survey of the maximum principles for optimal control problems with state constraints. SIAM Review, 1995, vol. 37, no. 2, pp. 181-218.

[9] Betts J.T. Survey of numerical methods for trajectory optimization. Journal of Guidance, Control, and Dynamics, 1998, vol. 21, no. 2, pp. 193-207. DOI: 10.2514/2.4231 Available at: https://arc.aiaa.org/doi/abs/10.2514/2.4231

[10] Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical recipes: the art of scientific computing (3d edition). Cambridge University Press, 2007. 1235 p.

[11] Celledoni E., Marthinsen H., Owren B. An introduction to Lie group integrators - basics, new developments and applications. Journal of Computational Physics, 2014, vol. 257-B, pp. 1040-1061.

[12] Betsch P., Siebert R. Rigid body dynamics in terms of quaternions: Hamiltonian formulation and conserving numerical integration. Int. J. Numer. Meth. Engng., 2009, vol. 79, no. 4, pp. 444-473. DOI: 10.1002/nme.2586 Available at: http://onlinelibrary.wiley.com/doi/10.1002/nme.2586/abstract

[13] Vilmart G. Rigid body dynamics. In: Encyclopedia of applied and computational mathematics. Springer, 2013, pp. 1268-1276.

[14] Forest E., Ruth R.D. Fourth-order symplectic integration. Physica D: Nonlinear Phenomena, 1990, vol. 43, no. 1, pp. 105-117.

[15] Yoshida H. Construction of higher order symplectic integrators. Physics Letters A, 1990, vol. 150, no. 5-7, pp. 262-268.

[16] Moser J., Veselov A.P. Discrete versions of some classical integrable systems and factorization of matrix polynomials. Comm. Math. Phys., 1991, vol. 139, no. 2, pp. 217-243. Available at: https://projecteuclid.org/euclid.cmp/1104203302

[17] Hairer E., Vilmart G. Preprocessed discrete Moser - Veselov algorithm for the full dynamics of a rigid body. Journal of Physics A: Mathematical and General, vol. 39, no. 42, pp. 13225.

[18] Giles M.B., Pierce N.A. An introduction to the adjoint approach to design. Flow, Turbulence and Combustion, 2000, vol. 65, no. 3, pp. 393-415.