Free-floating robotic systems

  • Olav Egeland
  • Kristin Y. Pettersen
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 230)


This chapter reviews selected topics related to kinematics, dynamics and control of free-floating robotic systems. Free-floating robots do not have a fixed base, and this fact must be accounted for when developing kinematic and dynamic models. Moreover, the configuration of the base is given by the Special Euclidean Group SE(3), and hence there exist no minimum set of generalized coordinates that are globally defined. Jacobian based methods for kinematic solutions will be reviewed, and equations of motion will be presented and discussed. In terms of control, there are several interesting aspects that will be discussed. One problem is coordination of motion of vehicle and manipulator, another is in the case of underactuation where nonholonomic phenomena may occur, and possibly smooth stabilizability may be precluded due to Brockett's result.


Autonomous Underwater Vehicle Nonholonomic System Virtual Displacement Space Robot IEEE Trans Robot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Alexander H L, Cannon R H Jr 1987 Experiments on the control of a satellite manipulator. In: Proc 1987 American Control Conf. Seattle, WAGoogle Scholar
  2. [2]
    Bremer H 1988 Über eine Zetralgleichung in der Dynamik. Z Angew Math Mech. 68:307–311Google Scholar
  3. [3]
    Brockett R W 1983 Asymptotic stability and feedback stabilization. In: Brockett R W, Millmann R S, Sussman H J (eds) Differential Geometric Control Theory. Birkhäuser, Boston, MA, pp 181–208Google Scholar
  4. [4]
    Coron J-M, Kerai E-Y 1996 Explicit feedbacks stabilizing the attitude of a rigid spacecraft with two control torques. Automatica. 32:669–677Google Scholar
  5. [5]
    Coron J-M, Rosier L 1994 A relation between continuous time-varying and discontinuous feedback stabilization. J Math Syst Estim Contr. 4:67–84Google Scholar
  6. [6]
    Egeland O 1987 Task-space tracking with redundant manipulators. IEEE J Robot Automat. 3:471–475Google Scholar
  7. [7]
    Egeland O, Godhavn J-M 1994 Passivity-based attitude control of a rigid spacecraft. IEEE Trans Automat Contr. 39: 842–846Google Scholar
  8. [8]
    Egeland O, Sagli J R 1993 Coordination of motion in a spacecraft/manipulator system. Int J Robot Res. 12:366–379Google Scholar
  9. [9]
    Goldstein H 1980 Classical mechanics. (2nd ed) Addison Wesley, Reading, MAGoogle Scholar
  10. [10]
    Hermes H 1967 Discontinuous vector fields and feedback control. In: Hale J K, LaSalle J P (eds) Differential Equations and Dynamical Systems. Academic Press, New York, pp 155–165Google Scholar
  11. [11]
    Hermes H 1991 Nilpotent and high-order approximation of vector field systems. SIAM Res. 33:238–264Google Scholar
  12. [12]
    Hughes P C 1986 Spacecraft Attitude Dynamics. Wiley, New YorkGoogle Scholar
  13. [13]
    Kawski M 1990 Homogeneous stabilizing feedback laws. Contr Theo Adv Tech. 6:497–516Google Scholar
  14. [14]
    Khalil H K 1996 Nonlinear systems. (2nd ed) Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  15. [15]
    Longman R W, Lindberg R E, Zedd M F 1987 Satellite-mounted robot manipulators — New kinematics and reaction moment compensation. Int J Robot Res. 6(3):87–103Google Scholar
  16. [16]
    M'Closkey R T, Murray R M 1993 Nonholonomic systems and exponential convergence: Some analysis tools. In: Proc 32nd IEEE Conf Decision Contr. San Antonio, TX, pp 943–948Google Scholar
  17. [17]
    M'Closkey R T, Murray R M 1997 Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. IEEE Trans Automat Contr. 42:614–628Google Scholar
  18. [18]
    Morin P, Samson C 1995 Time-varying exponential stabilization of the attitude of a rigid spacecraft with two controls. In: Proc 34th IEEE Conf Decision Contr. New Orleans, LA, pp 3988–3993Google Scholar
  19. [19]
    Morin P, Samson C 1996 Time-varying exponential stabilization of chained form systems based on a backstepping technique. In: Proc 35th IEEE Conf Decision Contr. Kobe, Japan, pp 1449–1454Google Scholar
  20. [20]
    Morin P, Samson C 1997 Time-varying exponential stabilization of a rigid spacecraft with two control torques. IEEE Trans Automat Contr. 42:528–534Google Scholar
  21. [21]
    Mukherjee R, Chen D 1992 Stabilization of free-flying under-actuated mechanisms in space. In: Proc 1992 Amer Contr Conf. Chicago, IL, pp 2016–2021Google Scholar
  22. [22]
    Mukherjee R, Nakamura Y 1992 Formulation and efficient computation of inverse dynamics of space robots. IEEE Trans Robot Automat. 8: 400–406Google Scholar
  23. [23]
    Murray R M, Li Z, Sastry S S 1994 A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton, FLGoogle Scholar
  24. [24]
    Nakamura Y, Mukherjee R 1991 Nonholonomic path planning of space robots via a bidirectional approach. IEEE Trans Robot Automat. 7:500–514Google Scholar
  25. [25]
    Olver P J 1993 Applications of Lie Groups to Differential Equations. (2nd ed) Springer-Verlag, New YorkGoogle Scholar
  26. [26]
    Oriolo G, Nakamura Y 1991 Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators. In: Proc 30th IEEE Conf Decision Contr. Brighton, UK, pp 2398–2403Google Scholar
  27. [27]
    Papadopoulos E, Dubowsky S 1991 On the nature of control algorithms for free-floating space manipulators. IEEE Trans Robot Automat. 7:750–758Google Scholar
  28. [28]
    Pettersen K Y, Egeland O 1996 Position and attitude control of an underactuated autonomous underwater vehicle. In: Proc 35th IEEE Conf Decision Contr. Kobe, Japan, pp 987–991Google Scholar
  29. [29]
    Pettersen K Y, Egeland O 1997 Robust control of an underactuated surface vessel with thruster dynamics. In: Proc 1997 Amer Contr Conf. Albuquerque, New MexicoGoogle Scholar
  30. [30]
    Pomet J-B, Samson C 1993 Time-varying exponential stabilization of nonholonomic systems in power form. Tech Rep 2126, INRIAGoogle Scholar
  31. [31]
    Rosenberg R M 1977 Analytical Dynamics of Discrete Systems. Plenum Press, New YorkGoogle Scholar
  32. [32]
    Rui C, Kolmanovsky I, McClamroch N H 1996 Feedback reconfiguration of underactuated multibody spacecraft. In: Proc 35th IEEE Conf Decision Contr. Kobe, Japan, pp 489–494Google Scholar
  33. [33]
    Samson C 1991 Velocity and torque feedback control of a nonholonomic cart. In: Canudas de Wit C (ed) Advanced Robot Control. Springer-Verlag, London, UK, pp 125–151Google Scholar
  34. [34]
    Samson C, Le Borgne M, Espiau B 1991 Robot Control: The Task Function Approach. Clarendon Press, Oxford, UKGoogle Scholar
  35. [35]
    Sciavicco L, Siciliano B 1996 Modeling and Control of Robot Manipulators. McGraw-Hill, New YorkGoogle Scholar
  36. [36]
    Sontag E, Sussmann H 1980 Remarks on continuous feedback. In: Proc 19th IEEE Conf Decision Contr. Albuquerque, NM, pp 916–921Google Scholar
  37. [37]
    Umetani Y, Yoshida K 1987 Continuous path control of space manipulators. Acta Astronaut. 15:981–986Google Scholar
  38. [38]
    Vafa Z, Dubowsky S. 1987 On the dynamics of manipulators in space using the virtual manipulator approach. In: Proc 1987 IEEE Int Conf Robot Automat. Raleigh, NC, pp 579–585Google Scholar
  39. [39]
    Wen J T-Y, Kreutz-Delgado K 1991 The attitude control problem. IEEE Trans Automat Contr. 36:1148–1162Google Scholar

Copyright information

© Springer-Verlag London Limited 1998

Authors and Affiliations

  • Olav Egeland
    • 1
  • Kristin Y. Pettersen
    • 1
  1. 1.Department of Engineering CyberneticsNorwegian University of Science and TechnologyNorway

Personalised recommendations