Formation Control and Stability Analysis of Spacecraft: An Energy Concept–Based Approach

  • Zhijie Gao
  • Fuchun Sun
  • Tieding Guo
  • Haibo Min
  • Dongfang Yang
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 213)


In this paper, the spacecraft formation control and its stability problems are studied on the basis of the energy concept. The formation systems are viewed as a multi-mass point system with both generalized elastic deformation and rigid body movement, and certain potential fields interact with each other within the formation. Consequently, the stability of formation and coordination and the controller design problems are studied from the perspectives of energy. The symmetry in formation motion is studied, and the definition of formation stability and its corresponding criteria are presented based upon the notion of relative equilibrium. Then, the artificial potential method is explored to design the formation control law, and the stability of which is followed by utilizing the former criterions. The effectiveness of the proposed formation control approach is also demonstrated by numerical results.


Formation control Energy concept Stability analysis Spacecraft 



This work was financially supported by the Tsinghua Self-innovation Project (Grant No: 20111081111) and the National Natural Science Foundation of China (Grant Nos: 2009CB724000, 2012CB821206, 61202332, 61203354).


  1. 1.
    Daniel PS, Fred YH, Scott RP (2004) A survey of spacecraft formation flying guidance and control (Part II ). In: Proceeding of the 2004 American control conference. Massachusetts, BostonGoogle Scholar
  2. 2.
    Robert GL, Matthias R (1997) Gauge fields in the separation of rotations and internal motions in the n-body problem. Rev Mod Phys 69(1)Google Scholar
  3. 3.
    Jerrod EM (1992) Lectures on mechanics. Cambridge University Press, New YorkGoogle Scholar
  4. 4.
    Naomi EL, Edward F (2001) Virtual, artificial potentials and coordinated control of groups. In: Proceeding 40th IEEE conference on decision and controlGoogle Scholar
  5. 5.
    Zhang F (204) Geometric cooperative control of formations, PhD Thesis, University of Maryland, USGoogle Scholar
  6. 6.
    Edward AF (2005) Cooperative vehicle control, Feature tracking and ocean sampling, PhD Thesis, Princeton UniversityGoogle Scholar
  7. 7.
    Anthony MB, Dong EC, Naomi EL, Jerrold EM (2001) Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping. IEEE Trans Autom Control 46(10):2253–2270Google Scholar
  8. 8.
    Malta G (2006) Theoretical mechanics. Higher Education Press, BeijingGoogle Scholar
  9. 9.
    Willems JC (1991) Paradigms and puzzles in the theory of dynamical systems. IEEE Trans Autom Control 36(3):259–294MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Ortega R, van-der-Schaft AJ, Mareels I, Maschke B (2001) Putting energy back in control. IEEE Control Syst Mag 21(2):18–33Google Scholar
  11. 11.
    Slotine JJ (1988) Putting physics in control—The example of robotics. IEEE Control Syst Mag 8(6):12–18CrossRefGoogle Scholar
  12. 12.
    Wang Z (1992) Stability of motion and its application. High Education Press, BeijingGoogle Scholar
  13. 13.
    Lin H (2001) Stability theory. Peking University Press, BeijingGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Zhijie Gao
    • 1
  • Fuchun Sun
    • 1
  • Tieding Guo
    • 1
  • Haibo Min
    • 1
  • Dongfang Yang
    • 2
  1. 1.Tsinghua UniversityBeijingChina
  2. 2.Hi-Tech institute of Xi’anXi’anChina

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