Dynamics Modeling of Spacecraft Formation Flying and Evaluating the Models Accuracy under the Effects of Relative Distance, Eccentricity and Earth Gravitational Perturbation

Navabi, M.; Barati, M.

Dynamics Modeling of Spacecraft Formation Flying and Evaluating the Models Accuracy under the Effects of Relative Distance, Eccentricity and Earth Gravitational Perturbation

Authors

M. Navabi

M. Barati

Faculty of New Technologies Engineering, Shahid Beheshti University, Tehran, Iran

Abstract

Relative motion of satellites in a formation can be studied in several forms of dynamics models. In this paper, some of the most applicable models each implying particular assumptions, constraints and specifications are described in Cartesian and orbital element spaces. Despite the significant applications of models based on linear equations of motion in modeling orbital rendezvous and ducking maneuvers, it is shown that the modeling errors of these simplified models limits their application in long term missions such as formation flying. Nonlinear equations of relative motion are derived in addition to 6 other dynamical models to simulate a low earth two satellite formation with projected circular relative orbit. Models are evaluated under the effects of non-spherical earth perturbation, relative distance between the satellites, and the eccentricity of the chief orbit. Analyzing the results of simulations emphasizes the importance of accuracy of the system.

Keywords

spacecraft formation flying

relative motion

linear and nonlinear model

perturbations

Article Title Persian

مدل‌سازی دینامیکی پرواز آرایش‌مند فضاپیما و بررسی میزان دقت مدل‌ها تحت اثر فاصلة نسبی، خروج از مرکز و اغتشاش زمین غیرکروی

Authors Persian

محمد نوابی

محمد براتی

دانشکده فناوری های نوین، دانشگاه شهید بهشتی، تهران، ایران

Abstract Persian

حرکت نسبی ماهواره‌ها در پرواز آرایش‌مند توسط مدل‌های دینامیکی مختلفی قابل بررسی است. این مدل‌ها در دو فضای کارتزین و المان‌های مداری توصیف شده و هر یک دارای فرضیات، قیود و ویژگی‌های مختلف هستند. از جمله، مدل‌هایی بر پایة معادلات خطی حرکت نسبی که کاربرد فراوانی در مدل‌سازی ملاقات‌های مداری و مانورهای اتصال فضاپیماها داشته است، اما خطای موجود در این معادلات‌ محدودیت‌هایی برای استفادة آن در مأموریت‌های پرواز آرایش‌مند فضاپیما که حرکت نسبی بلندمدت دارد، ایجاد می‌کند. در این مقاله، علاوه بر استخراج معادلات غیرخطی حرکت نسبی، 6 مدل دیگر از مدل‌های قابل استفاده برای مدل‌سازی آرایش‌های پروازی ارائه می‌شوند. در ادامه با شبیه‌سازی یک مأموریت پرواز آرایش‌مند ارتفاع پایین شامل دو ماهواره با تصویر دایروی مدار نسبی بر روی زمین، اعتبارسنجی مدل‌ها از سه منظر اغتشاش غیرکروی‌بودن زمین، میزان فاصلة ماهواره‌ها در آرایش، و میزان بیضوی‌بودن مدار مرجع بررسی می‌‌شود. تحلیل نتایج شبیه‌سازی برای 7 مدل مذکور، اهمیت دقت مد‌‌ل‌سازی دینامیکی سیستم را بازگو می‌کند.

Keywords Persian

پرواز آرایش‌مند فضاپیما

حرکت نسبی

مدل خطی و غیرخطی

مدار نسبی

اغتشاشات

Krieger, G., Moreira, A., Fiedler, H., Hajnsek, I., Werner, M., Younis, M. and Zink, M., “TanDEM-X: a Satellite Formation for High-Resolution SAR Interferometry,” IEEE Transactions on Geoscience and Remote Sensing, 45, No. 11, 2007, pp. 3317 – 3341.
Fowler, W., and Bettadpur, S., and Tapley, B., “Mission Planning for The Twin GRACE Satellites,” AAS/AIAA Space Flight Mechanics Meeting, Paper AAS 00-164, Clearwater, Florida, 2000.
Dunn, C., and et. al., “The Instrument on NASA’s GRACE Mission: Augmentation of GPS to Achieve Unprecedented Gravity Field Measurements,” Proceedings of ION GPS, Portland, Oregon, 2002.
Beugnon, C., Calvel, B., Boulade, S. and Ankersen, F., “Design and Modeling of the Formation-Flying GNC System for the DARWIN Interferometer,” SPIE 5497, 2004.
Shahid, K. and Kumar, K. D., “Formation Control at the Sun–Earth L2 Libration Point Using Solar Radiation Pressure,” Journal of Spacecraft and Rockets, Vol. 47, No. 4, 2010, pp. 614-626.
Schaub, H. and Junkins, J. L., Analytical Mechanics of Space Systems, AIAA Education Series, 2003.
Clohessy, W. H. and Wiltshire, R. S., “Terminal Guidance System for Satellite Rendezvous,” Journal of the Aerospace Sciences, Vol. 27, No. 9, 1960, pp. 653-658.
Schaub, H. and Alfriend, K. T., “Hybrid Cartesian and Orbit Element Feedback Law for Formation Flying Spacecraft,” Journal of Guidance, Control and Dynamics, Vol. 25, No. 2, 2002, pp. 387–393.
Inalhan, G. and How, J. P., “Relative Dynamics & Control of Spacecraft Formations in Eccentric Orbits,” Journal of Guidance, Control, and Dynamics. Vol. 25, No. 1, 2002, pp. 48-59.
Alfriend, K. T., Rao Vadali, , Gurfil, P., How, J. and Breger, L., Spacecraft Formation Flying: Dynamics, Control and Navigation, Elsevier, 2010.
Vadali, S. R., Vaddi, S. S., and Alfriend, K. T., “A New Concept for Controlling Formation Flying Satellite Constellations,” Advances in the Astronautical Sciences, Vol. 108, No. 2, 2001, pp. 1631-1648.
Toledano, J. G. T. and Succar, L. E. S., “Bayesian Networks for Reliability Analysis of Complex Systems,” Computer Scince, Vol. 1484, No. 465, 1998, pp. 1-17.
Barlow, R. E, “Using Influence Diagrams,” Accelerated Life Testing and Experts’ Opinions in Reliability, 1988, pp.145-150.
Xie, M. and Wohlin, C., “An Additive Reliability Model for the Analysis of Modular Software Failure Data,” Proceedings of the Sixth Interrnational symposium on Software Reliability Engineering, 1996, pp. 188-193.
Krishnemurthy, S. and Mathur, A. P., “On the Estimation of Reliability of a Software System Using Reliabilities of Its Components,” Proceedings of the Ninth International Symposium on Software Reliability Engineering, 1997, pp.146.
Ghokale, S., Lyu, M. and Trivedi, K., “Reliability Simulation of Component Based Software Systems,” Proceedings of the International Symposium on Software Reliability Engineering,
Gran, B. A. and al, “Estimating Dependability of Programmable Systems Using BBNs,” Proceedings of the Safecomp, 2000, pp. 309-320.
Jensen, V., Bayesian Networks and Decision Graphs, Springer, New York, 2001.
Amasaki, S. and et. al, “A Bayesian Belief Network for Assessing Likelihood of Fault Content,” Proceedings of the 14^th International Symposium on Software Reliability Engineering, 2003, pp. 215-226.
Boudali, and Dugan J. B, “A Continuous-Time Bayesian Network Reliability Modeling and Analysis Framework,” IEEE Trans Reliability, 2006, Vol. 55, No.1, pp. 86-97.
Doguc, O. and Marquez, J. R., “A Generic Method for Estimating System Reliability Using Bayesian Network,” Reliability Engineering and System Safety, Vol. 94, No.2, 2009, pp. 542-550.
Abou Nassar, L. and et. al, “Spacecraft Structures and Launch Vehicles,” A Presentation in Department of Aerospace and Ocean Engineering, Virginia Tech University, 2004.
Stengel, R., “Launch Vehicle Design: Conﬁgurations and Structures, Space System Design”, One Course in Department of Mechanical and Aerospace, Princeton University, 2008.
Vesely, W. and Goldbrg, B, “Fault Tree Handbook,” United State Nuclear Regulatory Commission, 1981.
MIL-HDBK-217F Notice 2, “Reliability Prediction of Electronic Equipment,” 1995.
MIL-HDBK-H 108, “Sampling Procedures and Tables for Life and Reliability Testing (Based on Exponential Distribution),” 2002.
MIL-HDBK-338, “Electronic Reliability Design Handbook,” 1995.