Normal Forms of a Free-Floating Space Robot

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


This paper is devoted to the dynamics of a free-floating space robot consisting of a mobile base (a spacecraft) and an on-board manipulator. Lagrangian equations of motion are derived. Special attention is paid to the equation resulting from the conservation of the angular momentum. This equation is represented in the form of a control system driven by joint velocities of the on-board manipulator. The main result of this paper consists in showing that this control system can be transformed by feedback to the chained form. Explicit form of the feedback transformations has been found for the case when the on-board manipulator is mounted at an arbitrary point of the base, and compared with the previously studied case of mounting point fixed at the center of mass of the base.


Space robot Dynamics Feedback Chained form 


  1. 1.
    Jakubczyk, B.: Equivalence and invariants of nonlinear control systems. In: Sussmann, H.J. (ed.) Nonlinear Controllability and Optimal Control. M. Dekker, New York (1998)zbMATHGoogle Scholar
  2. 2.
    Krener, A.J.: Feedback Linearization of Nonlinear Systems. In: Baillieul, J., Samad, T. (eds.) Encyclopedia of Systems and Control. Springer, London (2013)Google Scholar
  3. 3.
    Murray, R.M., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)zbMATHGoogle Scholar
  4. 4.
    Jiang, Z.P., Nijmeijer, H.: A recursive technique for tracking control of nonholonomic systems in chained form. IEEE Trans. Autom. Control 44, 265–279 (1999)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Papadopoulos, E., Tortopidis, I., Nanos, K.: Smooth planning for free-floating space robots using polynomials. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain , pp. 4283–4288 (2005)Google Scholar
  6. 6.
    Tortopidis, I., Papadopoulos, E.: On point-to-point motion planning for underactuated space manipulator systems. Rob. Auton. Syst. 55, 122–131 (2007)CrossRefGoogle Scholar
  7. 7.
    Rybus, T., et al.: Application of a planar air-bearing microgravity simulator for demonstration of operations required for an orbital capture with a manipulator. Acta Astronautica 155, 211–229 (2019)CrossRefGoogle Scholar
  8. 8.
    Tchoń, K., Respondek, W., Ratajczak, J.: Normal forms and configuration singularities of a space manipulator. J. Intell. Rob. Syst. 93, 621–634 (2019)CrossRefGoogle Scholar
  9. 9.
    Tchoń, K. Ratajczak, J. Jakubiak, J.: Normal forms of robotic systems with affine Pfaffian constraints: a case study. In: Lenarcic, J., Parenti-Castelli, V. (eds) Advances in Robot Kinematics 2018, pp. 250–257. Springer, Heidelberg (2019)Google Scholar
  10. 10.
    Krzykała, A.: Modeling and Control of Free-Floating Space Robots. Wroclaw University of Science and Technology, Wroclaw (2019). Diploma project, (in Polish)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Wroclaw University of Science and TechnologyWroclawPoland

Personalised recommendations