Advertisement

Acta Mechanica Sinica

, Volume 34, Issue 4, pp 754–768 | Cite as

Review of deployment technology for tethered satellite systems

  • B. S. Yu
  • H. Wen
  • D. P. Jin
Review Paper
  • 157 Downloads

Abstract

Tethered satellite systems (TSSs) have attracted significant attention due to their potential and valuable applications for scientific research. With the development of various launched on-orbit missions, the deployment of tethers is considered a crucial technology for operation of a TSS. Both past orbiting experiments and numerical results have shown that oscillations of the deployed tether due to the Coriolis force and environmental perturbations are inevitable and that the impact between the space tether and end-body at the end of the deployment process leads to complicated nonlinear phenomena. Hence, a set of suitable control methods plays a fundamental role in tether deployment. This review article summarizes previous work on aspects of the dynamics, control, and ground-based experiments of tether deployment. The relevant basic principles, analytical expressions, simulation cases, and experimental results are presented as well.

Keywords

Tethered satellite Deployment Dynamics Control Experiment 

Notes

Acknowledgements

This study was funded by the National Natural Science Foundation of China (11672125, 11732006), the Civil Aerospace Pre-research Project of China (D010305), the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics, MCMS-0116K01), the Fundamental Research Funds for the Central Universities (NS2016009), and in part by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

References

  1. 1.
    Wood, G.M., Siemers, P.M., Squires, R.K., et al.: Downward-deployed tethered platforms for high-enthalpy aerothermodynamic research. J. Spacec. Rocket. 27, 216–221 (1990)Google Scholar
  2. 2.
    Brown, K.G., Melfi, L.T., Upchurch, B.T., et al.: Downward-deployed tethered satellite systems, measurement techniques, and instrumentation: a review. J. Spacecr. Rocket. 29, 671–677 (1992)Google Scholar
  3. 3.
    Grassi, M., Cosmo, M.L.: Atmospheric research with the small expendable deployer system: preliminary analysis. J. Spacec. Rocket. 33, 70–78 (1996)Google Scholar
  4. 4.
    Cosmo, M.L., Lorenzini, E.C.: Tethers in Space Handbook, 3rd edn. NASA Marshall Space Flight Center, Washington (1997)Google Scholar
  5. 5.
    Kyroudis, G.A., Conway, B.A.: Advantages of tether release of satellites from elliptic orbits. J. Guidance Control Dyn. 11, 441–448 (1988)zbMATHGoogle Scholar
  6. 6.
    Landis, G.A.: Reactionless orbital propulsion using tether deployment. Acta Astronaut. 26, 307–312 (1992)Google Scholar
  7. 7.
    Kumar, K.D.: Payload deployment by reusable launch vehicle using tether. J. Spacecr. Rocket. 38, 291–294 (2001)Google Scholar
  8. 8.
    Wang, W., Baoyin, H.X., Li, J.F.: Orbital maneuvers of tethered satellite system of the dynamic release. J. Tsinghua Univ. (Science and Technology) 48, 1351–1354 (2008). (in Chinese)Google Scholar
  9. 9.
    Williams, P.: Tether capture and momentum exchange from hyperbolic orbits. J. Spacecr. Rocket. 47, 205–209 (2010)Google Scholar
  10. 10.
    Quadrelli, M.B., Backes, P., Wilkie, W.K., et al.: Investigation of phase transition-based tethered systems for small body sample capture. Acta Astronaut. 68, 947–973 (2011)Google Scholar
  11. 11.
    Huang, P.F., Wang, D.K., Meng, Z.J., et al.: Adaptive postcapture backstepping control for tumbling tethered space robot-target combination. J. Guidance Control Dyn. 39, 150–156 (2016)Google Scholar
  12. 12.
    Huang, P.F., Wang, D.K., Meng, Z.J., et al.: Impact dynamic modelling and adaptive target capturing control for tethered space robots with uncertainties. IEEE/ASME Trans. Mechatron. 21, 2260–2271 (2016)Google Scholar
  13. 13.
    Zhang, F., Huang, P.F.: Releasing dynamics and stability control of maneuverable tethered space net. IEEE/ASME Trans. Mechatron. 22, 983–993 (2017)Google Scholar
  14. 14.
    Sabath, D., Kast, W., Kowalczyk, M., et al.: Results of the parabolic flight tests of the rapunzel deployer. Acta Astronaut. 41, 841–845 (1997)Google Scholar
  15. 15.
    Andrés, Y., Zimmermann, F., Schöttle, U.M.: Optimization and control of the early deployment phase during a tether-assisted deorbit maneuver. In: Proceedings of the 22nd International Symposium on Space Technology and Science, Morioka, May 28-June 4 (2000)Google Scholar
  16. 16.
    Gläßel, H., Zimmermann, F., Brückner, S., et al.: Adaptive neural control of the deployment procedure for tether-assisted re-entry. Aerosp. Sci. Technol. 8, 73–81 (2004)zbMATHGoogle Scholar
  17. 17.
    Aslanov, V.S.: Swing principle for deployment of a tether-assisted return mission of a re-entry capsule. Acta Astronaut. 120, 154–158 (2016)Google Scholar
  18. 18.
    Aslanov, V.S., Ledkov, A.S.: Tether-assisted re-entry capsule deorbiting from an elliptical orbit. Acta Astronaut. 130, 180–186 (2017)Google Scholar
  19. 19.
    Sanmartín, J.R., Lorenzini, E.C., Martinez-Sanchez, M.: Electrodynamic tether applications and constraints. J. Spacecr. Rocket. 47, 442–456 (2010)Google Scholar
  20. 20.
    Carroll, J.A.: SEDS deployer design and flight performance. In: Proceedings of Space Programs and Technologies Conference and Exhibit, Huntsille, September 21–23 (1993)Google Scholar
  21. 21.
    Carroll, J.A., Oldson, J.C.: Tethers for small satellite applications. In: Proceedings of AIAA/USU Small Satellite Conference, Logan, September 18–21 (1995)Google Scholar
  22. 22.
    Barnds, W.J., Coffey, S., Davis, M.: Determination of TiPS libration using laser radar. In: Proceedings of the SPIE Conference on Laser Radar Technology and Applications III, Orlando, April 10–11 (1998)Google Scholar
  23. 23.
    Kruijff, M., van der Heide, E.J.: Qualification and in-flight demonstration of a European tether deployment system on YES2. Acta Astronaut. 64, 882–905 (2009)Google Scholar
  24. 24.
    Gates, S.S., Koss, S.M., Zedd, M.F.: Advanced tether experiment deployment failure. J. Spacecr. Rocket. 38, 60–68 (2001)Google Scholar
  25. 25.
    Hoyt, R., Slostad, J., Twiggs, R.: Mutli-application survivable tether experiment. In: Proceedings of the 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Huntsville, July 20–23 (2003)Google Scholar
  26. 26.
    Sasaki, S., Oyama, K.I., Kawashima, N., et al.: Results from a series of tethered rocket experiments. J. Spacecr. Rocket. 24, 444–453 (1987)Google Scholar
  27. 27.
    Kawashima, N., Sasaki, S., Oyama, K.I., et al.: Results from a tethered rocket experiment (CHARGE-2). Adv. Space Res. 8, 197–201 (1988)Google Scholar
  28. 28.
    Tyc, G., Han, R.P.S.: Attitude dynamics investigation of the OEDIPUS-A tethered rocket payload. J. Spacecr. Rocket. 32, 133–141 (1995)Google Scholar
  29. 29.
    Vigneron, F.R., Schultz, F., Jablonski, A.M., et al.: Tether deployment and trajectory modeling for the OEDIPUS missions. In: Proceedings of AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Boston, August 10–12 (1998)Google Scholar
  30. 30.
    Dobrowolny, M., Stone, N.H.: A technical overview of TSS-1: the first tethered-satellite system mission. Il Nuovo Cimento C. 17, 1–12 (1994)Google Scholar
  31. 31.
    Stone, N.H., Raitt, W.J., Wright, K.H.: The TSS-1R electrodynamic tether experiment: scientific and technological results. Adv. Space Res. 24, 1037–1045 (1999)Google Scholar
  32. 32.
    Fujii, H.A., Watanabe, T., Sahara, H., et al.: Space demonstration of bare electrodynamic tape-tether technology on the sounding rocket S520-25. In: Proceedings of AIAA Guidance, Navigation, and Control Conference, Portland, August 8–11 (2011)Google Scholar
  33. 33.
    Mankala, K.K., Agrawal, S.K.: Dynamic modeling of satellite tether systems using Newton’s Laws and Hamilton’s Principle. J. Vib. Acoust. 130, 014501 (2008)Google Scholar
  34. 34.
    Kong, X.R., Xu, D.F., Yang, Z.X., et al.: Modeling and simulation for free deployment of a space tether system. J. Vib. Shock 30, 37–42 (2011). (in Chinese)Google Scholar
  35. 35.
    Lee, T., Leok, M., McClamroch, Harris N.: High-fidelity numerical simulation of complex dynamics of tethered spacecraft. Acta Astronaut. 99, 215–230 (2014)Google Scholar
  36. 36.
    Carter, J.T., Greene, M.: Deployment and retrieval simulation of a single tether satellite system. In: Proceedings of the 20th Southeastern Symposium on System Theory, Charlotte, August 19–21 (1988)Google Scholar
  37. 37.
    Barkow, B., Steindl, A., Troger, H.: A targeting strategy for the deployment of a tethered satellite system. IMA J. Appl. Math. 70, 626–644 (2005)MathSciNetzbMATHGoogle Scholar
  38. 38.
    Mankala, K.K., Agrawal, S.K.: Dynamic modeling and simulation of satellite tethered systems. J. Vib. Acoust. 127, 144–156 (2005)Google Scholar
  39. 39.
    Steiner, W., Zemann, J., Steindl, A., et al.: Numerical study of large amplitude oscillations of a two-satellite continuous tether system with a varying length. Acta Astronaut. 35, 607–621 (1995)Google Scholar
  40. 40.
    Wiedermann, G., Schagerl, M., Steindl, A., et al.: Computation of force controlled deployment and retrieval of a tethered satellite system by the finite element method. In: Proceedings of European Conference on Computational Mechanics’99, Wünchen, August 31-September 3 (1999)Google Scholar
  41. 41.
    Yu, B.S., Wen, H., Jin, D.P.: Dynamics of tethered satellite with a time-varying number of degrees-of-freedom. Chin. J. Theor. Appl. Mech. 42, 926–932 (2010)MathSciNetGoogle Scholar
  42. 42.
    Yu, B.S.: Dynamics and control of flexible tethered satellite in complex space environment [PhD. Thesis]. Nanjing University of Aeronautics and Astronautics, Nanjing (2011) (in Chinese)Google Scholar
  43. 43.
    Williams, P.: Deployment/retrieval optimization for flexible tethered satellite systems. Nonlinear Dyn. 52, 159–179 (2008)zbMATHGoogle Scholar
  44. 44.
    Barkow, B., Steindl, A., Troger, H., et al.: Various methods of controlling the deployment of a tethered satellite. J. Vib. Control 9, 187–208 (2003)MathSciNetzbMATHGoogle Scholar
  45. 45.
    Modi, V.J., Geng, C.F., Misra, A.K., et al.: On the control of the space shuttle based tethered systems. Acta Astronaut. 9, 437–443 (1982)Google Scholar
  46. 46.
    Cui, N.G., Liu, D., Yang, D., et al.: The analysis on the motion stability of a tethered satellite system. In: Proceedings of AIAA/AAS Astrodynamics Conference, Scottsdale, August 1–3 (1994)Google Scholar
  47. 47.
    Chu, S.S., Wang, L.S.: Adiabatic invariance for tether deployment/retrieval problem. In: Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, December 7–10 (1999)Google Scholar
  48. 48.
    Misra, A.K.: Dynamics and control of tethered satellite systems. In: Proceedings of the 54th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law, Bremen, September 29-October 3 (2003)Google Scholar
  49. 49.
    Vadali, S.R., Kim, E.S.: Feedback control of tethered satellites using Lyapunov stability theory. J. Guidance Control Dyn. 14, 729–735 (1991)Google Scholar
  50. 50.
    Kokubun, K., Fujii, H.A.: Deployment/retrieval control of a tethered subsatellite under effect of tether elasticity. J. Guidance Control Dyn. 19, 84–90 (1996)zbMATHGoogle Scholar
  51. 51.
    Wang, W., Li, J.F., Baoyin, H.X.: The deployment and retrieval control of the tethered satellite based on the PSO algorithm. Aerosp. Control Appl. 35, 48–51 (2009). (in Chinese)Google Scholar
  52. 52.
    McKenzie, D.J.: The dynamics of tethers and space-webs [PhD. Thesis]. University of Glasgow, Glasgow (2010)Google Scholar
  53. 53.
    Malashin, A.A., Smirnov, N.N., Bryukvina, O.Y., et al.: Dynamic control of the space tethered system. J. Sound Vib. 389, 41–51 (2017)Google Scholar
  54. 54.
    Yu, B.S., Jin, D.P., Wen, H.: An analytical control law of length rate for tethered satellite system. Meccanica 52, 2035–2046 (2017)MathSciNetzbMATHGoogle Scholar
  55. 55.
    Kumar, K.D., Yasaka, T.: Rotating formation flying of three satellites using tethers. J. Spacec. Rocket. 41, 973–985 (2004)Google Scholar
  56. 56.
    Kumar, K.D., Patel, T.R.: Dynamics and control of multi-connected satellites aligned along local horizontal. Acta Mechan. 204, 175–191 (2009)zbMATHGoogle Scholar
  57. 57.
    Zhao, J., Cai, Z.Q., Qi, Z.H.: Dynamics of variable-length tethered formations near libration points. J. Guidance Control Dyn. 33, 1172–1183 (2010)Google Scholar
  58. 58.
    Cai, Z.Q., Li, X.F., Wu, Z.G.: Deployment and retrieval of a rotating triangular tethered satellite formation near libration points. Acta Astronaut. 98, 37–49 (2014)Google Scholar
  59. 59.
    Jung, W., Mazzoleni, A.P., Chung, J.: Nonlinear dynamic analysis of a three-body tethered satellite system with deploymen/retrieval. Nonlinear Dyn. 82, 1–18 (2015)Google Scholar
  60. 60.
    Vadali, S.R.: Feedback tether deployment and retrieval. J. Guidance Control Dyn. 14, 469–470 (1991)Google Scholar
  61. 61.
    Tang, J.L., Ren, G.X., Zhu, W.D., et al.: Dynamics of variable-length tethers with application to tethered satellite deployment. Commun. Nonlinear Sci. Numer. Simul. 16, 3411–3424 (2011)MathSciNetzbMATHGoogle Scholar
  62. 62.
    Kane, T.R., Levinson, D.A.: Deployment of a cable-supported payload from an orbiting spacecraft. J. Spacecr. Rocket. 14, 409–413 (1977)Google Scholar
  63. 63.
    Auzinger, W., Barkow, B., Hörmann, N., et al.: Dynamic Analysis of Tethered Systems Using Continuum Modelling for the Tether [Technical Report]. Vienna University of Technology, Vienna (2000)Google Scholar
  64. 64.
    Yu, B.S., Jin, D.P.: Deployment and retrieval of tethered satellite system under \(J_{2}\) perturbation and heating effect. Acta Astronaut. 67, 845–853 (2010)Google Scholar
  65. 65.
    Williams, P.: Optimal deployment/retrieval of tethered satellites. J. Spacecr. Rocket. 45, 324–343 (2008)Google Scholar
  66. 66.
    Wen, H., Jin, D.P., Hu, H.Y.: Optimal feedback control of the deployment of a tethered subsatellite subject to perturbations. Nonlinear Dyn. 51, 501–514 (2008)MathSciNetzbMATHGoogle Scholar
  67. 67.
    Sun, G.H., Zhu, Z.H.: Fractional-order tension control law for deployment of space tether system. J. Guidance Control Dyn. 37, 2057–2061 (2014)Google Scholar
  68. 68.
    Wen, H., Zhu, Z.H., Jin, D.P., et al.: Space tether deployment control with explicit tension constraint and saturation function. J. Guidance Control Dyn. 39, 915–920 (2016)Google Scholar
  69. 69.
    Wen, H., Zhu, Z.H., Jin, D.P., et al.: Constrained tension control of a tethered space-tug system with only length measurement. Acta Astronaut. 119, 110–117 (2016)Google Scholar
  70. 70.
    Mantri, P., Mazzoleni, A.P., Padgett, D.A.: Parametric study of deployment of tethered satellite systems. J. Spacecr. Rocket. 44, 412–424 (2007)Google Scholar
  71. 71.
    Mantri, P.: Deployment dynamics of space tether systems [PhD. Thesis]. North Carolina State University, Raleigh (2007)Google Scholar
  72. 72.
    Mantellato, R., Valmorbida, A., Lorenzini, E.C.: Thrust-aided librating deployment of tape tethers. J. Spacecr. Rocket. 52, 1395–1406 (2015)Google Scholar
  73. 73.
    Liu, Y.Y., Zhou, J.: Research on dynamics and developing method for short tethered satellite. J. Syst. Simul. 20, 5642–5645 (2008). (in Chinese)Google Scholar
  74. 74.
    Liu, Y.Y., Zhou, J.: Attitude dynamics and thrust control for short tethered sub-satellite in deployment. J. Aerosp. Eng. 229, 1407–1422 (2015)Google Scholar
  75. 75.
    Wen, H., Chen, H., Jin, D.P., et al.: Deployment and attitude control of tethered subsatellite with controllable arm. Chin. J. Theor. Appl. Mech. 44, 408–414 (2012). (in Chinese)MathSciNetGoogle Scholar
  76. 76.
    Nohmi, M., Yamamoto, T., Takagi, Y.: Microgravity experiment for attitude control of a tethered body by arm link motion. In: Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation, Harbin, August 5–8 (2007)Google Scholar
  77. 77.
    Wang, D., Huang, P.F., Cai, J., et al.: Coordinated control of tethered space robot using mobile tether attachment point in approaching phase. Adv. Space Res. 54, 1077–1091 (2014)Google Scholar
  78. 78.
    Yu, B.S., Jin, D.P., Pang, Z.J.: Coupling dynamics of spacecraft with deployment of a tether. Sci. Sin. Phys. Mech. Astronom. 44, 858–864 (2014). (in Chinese)Google Scholar
  79. 79.
    Yu, S.H.: Tethered satellite system analysis (1)—two-dimensional case and regular dynamics. Acta Astronaut. 47, 849–858 (2000)Google Scholar
  80. 80.
    Barkow, B.: A chaos control strategy for the deployment of a tethered satellite system [PhD. Thesis]. Vienna University of Technology, Vienna (2002)Google Scholar
  81. 81.
    Rajan, M., Anderson, T.J.: First integrals of motion in the deployment and retrieval of shuttle-tethered-subsatellite system. In: Proceedings of Astrodynamics Conference, Fluid Dynamics and Co-located Conferences, Williamsburg, August 15–17 (1986)Google Scholar
  82. 82.
    Kumar, K., Kumar, R., Misra, A.K.: Effects of deployment rates and librations on tethered payload raising. J. Guidance Control Dyn. 15, 1230–1235 (1992)Google Scholar
  83. 83.
    Peláez, J.: On the dynamics of the deployment of a tether from an orbiter—I. Basic equations. Acta Astronaut. 36, 113–122 (1995)Google Scholar
  84. 84.
    Peláez, J.: On the dynamics of the deployment of a tether from an orbiter—part II. Exponential deployment. Acta Astronaut. 36, 313–335 (1995)Google Scholar
  85. 85.
    Pascal, M., Djebli, A., El Bakkali, L.: Laws of deployment/retrieval in tether connected satellites systems. Acta Astronaut. 45, 61–73 (1999)Google Scholar
  86. 86.
    Pascal, M., Djebli, A., El Bakkali, L.: A new deployment/retrieval scheme for a tethered satellite system, intermediate between the conventional scheme and the crawler scheme. J. Appl. Math. Mech. 65, 689–696 (2001)MathSciNetzbMATHGoogle Scholar
  87. 87.
    Zakrzhevskii, A.E.: Method of deployment of a space tethered system aligned to the local vertical. J. Appl. Math. Mech. 63, 221–236 (2016)Google Scholar
  88. 88.
    Modi, V.J., Misra, A.K.: Deployment dynamics and control of tethered satellite systems. In: Proceedings of American Institute of Aeronautics and Astronautics/American Astronautical Society Astrodynamics Conference, Vancouve, August 7–9 (1978)Google Scholar
  89. 89.
    Gou, X.Y., Ma, X.R., Shao, C.X., et al.: Deploying of tethered subsatellite. J. Harbin Inst. Technol. 30, 11–14 (1998). (in Chinese)Google Scholar
  90. 90.
    Kumar, K.D., Yasaka, T.: Dynamics of rotating linear array tethered satellite system. J. Spacecr. Rocket. 42, 373–378 (2005)Google Scholar
  91. 91.
    Misra, A.K., Modi, V.J.: Deployment and retrieval of shuttle supported tethered satellites. J. Guidance Control Dyn. 5, 278–285 (1982)zbMATHGoogle Scholar
  92. 92.
    Banerjee, A.K.: Dynamics of tethered payloads with deployment rate control. J. Guidance Control Dyn. 13, 759–762 (1990)Google Scholar
  93. 93.
    Licata, R.: Tethered system deployment controls by feedback fuzzy logic. Acta Astronaut. 40, 619–634 (1997)Google Scholar
  94. 94.
    Williams, P., Trivailo, P.: Dynamics of circularly towed cable systems, part 2: transitional flight and deployment control. J. Guidance Control Dyn. 30, 766–779 (2007)Google Scholar
  95. 95.
    Yu, B.S., Jin, D.P., Wen, H.: Analytical deployment control law for a flexible tethered satellite system. Aerosp. Sci. Technol. 66, 294–303 (2017)Google Scholar
  96. 96.
    Ebner, S.G.: Deployment dynamics of rotating cable-connected space stations. J. Spacecr. Rocket. 7, 1274–1275 (1970)Google Scholar
  97. 97.
    Rupp, C.C.: A Tether Tension Control Law for Tethered Subsatellites Deployed Along Local Vertical [Technical Report]. Marsball Space Flight Center, Huntsville (1975)Google Scholar
  98. 98.
    Fujii, H., Ishijima, S.: Mission function control for deployment and retrieval of a subsatellite. J. Guidance Control Dyn. 12, 243–247 (1989)Google Scholar
  99. 99.
    Fujii, H., Uchiyama, K., Kokubun, K.: Mission function control of tethered subsatellite deployment/retrieval: in-plane and out-of-plane motion. J. Guidance Control Dyn. 14, 471–473 (1991)Google Scholar
  100. 100.
    Fujii, H.A., Anazawa, S.: Deployment/retrieval control of tethered subsatellite through an optimal path. J. Guidance Control Dyn. 17, 1929–1998 (1994)Google Scholar
  101. 101.
    Kim, E., Vadali, S.R.: Nonlinear feedback deployment and retrieval of tethered satellite systems. J. Guidance Control Dyn. 15, 28–34 (1992)Google Scholar
  102. 102.
    Zhong, R., Xu, S.J.: Simple tension control strategy for variable length tethered satellite system. Chin. Space Sci. Technol. 29, 66–73 (2009). (in Chinese)Google Scholar
  103. 103.
    Zabolotnov, Y.M.: Control of the deployment of a tethered orbital system with a small load into a vertical position. J. Appl. Math. Mech. 79, 28–34 (2015)MathSciNetGoogle Scholar
  104. 104.
    Kentaroh, K., Anazawa, S., Fujii, H.A.: Real-time optimal state feedback control for tethered subsatellite system. J. Guidance Control Dyn. 19, 972–974 (1996)zbMATHGoogle Scholar
  105. 105.
    Fujii, H.A.: Optimal trajectory analysis for deployment/retrieval of tethered subsatellite using riemannian metric. In: Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, Denver, August 14–17 (2000)Google Scholar
  106. 106.
    Fujii, H.A., Kojima, H.: Optimal trajectory analysis for deployment/retrieval of tethered subsatellite using metric. J. Guidance Control Dyn. 26, 177–179 (2002)Google Scholar
  107. 107.
    Steindl, A., Troger, H.: Optimal control of deployment of a tethered subsatellite. Nonlinear Dyn. 31, 257–274 (2003)MathSciNetzbMATHGoogle Scholar
  108. 108.
    Steindl, A.: Optimal control of the deployment (and retrieval) of a tethered satellite under small disturbances. Meccanica 49, 1879–1885 (2014)MathSciNetzbMATHGoogle Scholar
  109. 109.
    Steindl, A.: Optimal deployment of a tethered satellite using tension control. Int. Fed. Autom. Control Papersonline 48, 53–54 (2015)Google Scholar
  110. 110.
    Steindl, A.: Time optimal control for the deployment of a tethered satellite allowing for a massive tether. Meccanica 51, 2741–2751 (2016)MathSciNetGoogle Scholar
  111. 111.
    Williams, P., Trivailo, P.: On the optimal deployment and retrieval of tethered satellites. In: Proceedings of the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Tucson, July 10–13 (2005)Google Scholar
  112. 112.
    Williams, P.: Optimal deployment and offset control for a spinning flexible tethered formation. In: Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, Keystone, August 21–24 (2006)Google Scholar
  113. 113.
    Williams, P.: Optimal deployment/retrieval of a tethered formation spinning in the orbital plane. J. Spacecr. Rocket. 43, 638–650 (2006)Google Scholar
  114. 114.
    Wen, H.: Dynamic and Control for Deployment and Retrieval of Tethered Satellite Systems [PhD. Thesis]. Nanjing University of Aeronautics and Astronautics, Nanjing (2009). (in Chinese)Google Scholar
  115. 115.
    Wen, H., Jin, D.P., Hu, H.Y., et al.: Three-dimensional optimal deployment of a tethered subsatellite with an elastic tether. Int. J. Comput. Math. 85, 915–923 (2008)MathSciNetzbMATHGoogle Scholar
  116. 116.
    Wen, H., Zhu, Z.H., Jin, D.P., et al.: Tension control of space tether via online quasi-linearization iterations. Adv. Space Res. 57, 754–763 (2016)Google Scholar
  117. 117.
    Ma, Z.Q., Sun, G.H.: Adaptive sliding mode control of tethered satellite deployment with input limitation. Acta Astronaut. 127, 67–75 (2016)Google Scholar
  118. 118.
    Ma, Z.Q., Sun, G.H., Li, Z.K.: Dynamic adaptive saturated sliding mode control for deployment of tethered satellite system. Aerosp. Sci. Technol. 66, 355–365 (2017)Google Scholar
  119. 119.
    Ma, Z.Q., Sun, G.H.: Full-order sliding mode control for deployment_retrieval of space tether system. In: Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, Budapest, October 10–12 (2016)Google Scholar
  120. 120.
    Wang, C.Q., Wei, H.L., Li, A.J., et al.: Sliding mode variable structure control for the deployment of tethered satellite system. Control Theory Appl. 33, 70–76 (2016). (in Chinese)zbMATHGoogle Scholar
  121. 121.
    Kang, J.J., Zhu, Z.H., Wang, W., et al.: Fractional order sliding mode control for tethered satellite deployment with disturbances. Adv. Space Res. 59, 263–273 (2017)Google Scholar
  122. 122.
    Iki, K., Kawamoto, S., Yoshiki, M.: Numerical simulations of an electrodynamic tether deployment from a spool-type reel using thrusters. In: Proceedings of the 1st International Academy of Astronautics Conference on Dynamics and Control of Space Systems, Porto, March 19–21 (2012)Google Scholar
  123. 123.
    Iki, K., Kawamoto, S., Yoshiki, M.: Experiments and numerical simulations of an electrodynamical tether deployment from a spool-type reel using thrusters. Acta Astronaut. 94, 318–327 (2014)Google Scholar
  124. 124.
    Kumar, K., Pradeep, S.: Strategies for three dimensional deployment of tethered satellites. Mech. Res. Commun. 25, 543–550 (1998)MathSciNetzbMATHGoogle Scholar
  125. 125.
    Nakaya, K., Iai, M., Omagari, K., et al.: Formation deployment control for spinning tethered formation flying-simulations and ground experiments. In: Proceedings of AIAA Guidance, Navigation, and Control Conference and Exhibit, Providence, August 16–19 (2004)Google Scholar
  126. 126.
    Jin, D.P., Hu, H.Y.: Optimal control of a tethered subsatellite of three degrees of freedom. Nonlinear Dyn. 46, 161–178 (2006)MathSciNetzbMATHGoogle Scholar
  127. 127.
    Wen, H., Jin, D.P., Hu, H.Y.: Time-optimal deployment of a tethered subsatellite based on differential inclusion. Chin. J. Theor. Appl. Mech. 40, 135–140 (2008). (in Chinese)Google Scholar
  128. 128.
    Liu, Y.Y., Zhou, J., Chen, H.L.: Variable structure control for tethered satellite fast deployment and retrieval. Future Control Autom. 172, 157–164 (2012)Google Scholar
  129. 129.
    Netzer, E., Kane, T.R.: Deployment and retrieval optimization of a tethered satellite system. J. Guidance Control Dyn. 16, 1085–1091 (1993)Google Scholar
  130. 130.
    Wen, H., Jin, D.P., Hu, H.Y.: Three-dimensional deployment of electro-dynamic tether via tension and current control with constraints. Acta Astronaut. 129, 253–259 (2016)Google Scholar
  131. 131.
    Zhang, J., Zhu, Z.H., Sun, Z.W.: Reduction of libration angle in electrodynamic tether deployment by Lorentz force. J. Guidance Control Dyn. 40, 164–169 (2017)Google Scholar
  132. 132.
    Nakamura, Y., Hashimotot, H.: Ground test of tether deployment and retrieval along optimal path with a tether reeling mechanism designed for micro-class satellites. In: Proceedings of the 54th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law, Bremen, September 29-October 3 (2003)Google Scholar
  133. 133.
    Yamanaka, T., Iai, M., Fujiwara, K., et al.: Design and microgravity experiment of separation mechanism for tether deployment. In: Proceedings of the 56th International Astronautical Congress, Fukuoka, October 17–21 (2005)Google Scholar
  134. 134.
    van de Heijning, S., Zandbergen, B.: Design of an electro-dynamic tape-tether deployment system. In: Proceedings of the 56th International Astronautical Congress, Fukuoka, October 17–21 (2005)Google Scholar
  135. 135.
    van de Heijning, S., Zandbergen, B.: Testing of a tether deployment system using a cold gas thruster. In: Proceedings of the 56th International Astronautical Congress, Fukuoka, October 17–21 (2005)Google Scholar
  136. 136.
    Watanabe, T., Kikuchi, T., Kusagaya, T., et al.: Fundamental experiment of tape tether deployment system. In: Proceedings of the 56th International Astronautical Congress, Fukuoka, October 17–21 (2005)Google Scholar
  137. 137.
    Bindra, U., Zhu, Z.H.: Development of an air-bearing inclinable turntable for testing tether deployment. In: Proceedings of AIAA Guidance, Navigation, and Control Conference, San Diego, January 4–8 (2016)Google Scholar
  138. 138.
    Tortora, P., Tappi, M., Piraccini, G.: Analytical modeling of the dynamics of an unrolling space tether deployer. In: Proceedings of the 55th International Astronautical Congress, Vancouver, October 4–8 (2004)Google Scholar
  139. 139.
    Menon, C., Kruijff, M., Vavouliotis, A.: Design and testing of a space mechanism for tether deployment. J. Spacecr. Rocket. 44, 927–939 (2007)Google Scholar
  140. 140.
    Gloder, A., Pellegrina, L., Pezzato, M., et al.: An innovative space tether deployer with retrieval capability: design and test of STAR experiment. In: Proceedings of the 68th International Astronautical Congress, Adelaide, September 25–29 (2017)Google Scholar
  141. 141.
    Olivieri, L., Antonello, A., Bettiol, L., et al.: Microgravity tests in preparation of a tethered electromagnetic docking space demonstration. In: Proceedings of the 68th International Astronautical Congress, Adelaide, September 25–29 (2017)Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanics and Control of Mechanical StructuresNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations