Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Archives of Control Sciences

The Journal of Polish Academy of Sciences

4 Issues per year

IMPACT FACTOR 2016: 0.705

CiteScore 2016: 3.11

SCImago Journal Rank (SJR) 2015: 0.359
Source Normalized Impact per Paper (SNIP) 2015: 0.934

Open Access
See all formats and pricing
In This Section

Tracking control of an underactuated rigid body with a coupling input force

Sebastian Korczak
  • Department of Mechanics, Faculty of Automotive and Construction Machinery Engineering, Warsaw University of Technology
  • Email:
Published Online: 2014-10-08 | DOI: https://doi.org/10.2478/acsc-2014-0019


This paper presents a set of basic problems concerning the control of an underactuated dynamic system. Exemplary system of a planar rigid body with a coupling input force is described. Lie brackets method is used to show accessibility of the system. A tracking problem is solved with computed torque algorithm. The coupling force makes the convergence to zero of all state variables errors impossible. After numerical simulation, stability of the system is mentioned

Keywords: underactuated system; tracking; coupling force; computed torque


  • [1] A.P. AGUIAR and J.P. HESPANHA: Position tracking of underactuated vehicles. Proc. American Control Conf., 3 (2003), 1988-1993.

  • [2] M.D. BERKEMEIER and R.S. FEARING: Tracking fast inverted trajectories of the underactuated acrobot. IEEE Trans. on Robotics and Automation, 15(4), (1999), 740-750.

  • [3] F. BULLO, N.E. LEONARD and A.D. LEWIS: Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups. IEEE Trans. on Automatic Control, 45(8), (2000), 1437-1454. [Web of Science]

  • [4] J. K. HENDRICK and A. GIRARD: Control of nonlinear dynamic systems: theory and applications ME237 (coursebook). Berkley University of California, http://www.me.berkeley.edu/ME237/,2010.

  • [5] R. HERMANN and A. KRENER: Nonlinear controllability and observability. IEEE Trans. on Automatic Control, 22(5), (1977), 728-740.

  • [6] Z. JIN, S. WAYDO, E. B. WILDANGER, M. LAMMERS, H. SCHOLZE, P. FOLEY, D. HELD, and R. M. MURRAY: MVWT-II: the second generation caltech multivehicle wireless testbed. Proc. American Control Conf., 6 (2004), 5321-5326.

  • [7] S. KORCZAK: http://myinventions.pl/underactuated.

  • [8] A.D. LEWIS: A brief on controllability of nonlinear systems. Mathematics & Statistics Control Seminar, Queen’s University. Conference notes. http://www.mast.queensu.ca/andrew/notes/, 2002.

  • [9] T. NARIKIYO, J. SAHASHI and K. MISAO: Control of a class of underactuated mechanical systems. Nonlinear Analysis: Hybrid Systems, 2(2), (2008), 231-241.

  • [10] F. REPOULIAS and E. PAPADOPOULOS: Planar trajectory planning and tracking control design for underactuated AUVs. Ocean Engineering, 34(11-12), (2007), 1650-1667. [Crossref] [Web of Science]

  • [11] M. REYHANOGLU: Exponential stabilization of an underactuated autonomous surface vessel. Automatica, 33(12), (1997), 2249-2254. [Crossref]

  • [12] H.J. SUSSMANN: A general theorem on local controllability. SIAM J. on Control and Optimization, 25(1), (1987), 158-194.

  • [13] A. ZELEI, L.L. KOVACS and G. STEPAN: Computed torque control of an underactuated service robot platform modeled by natural coordinates. Communications in Nonlinear Science and Numerical Simulation, 16(5), (2011), 2205-2217

About the article

Received: 2013-05-20

Revised: 2014-04-07

Published Online: 2014-10-08

Published in Print: 2014-09-01

Citation Information: Archives of Control Sciences, ISSN (Online) 2300-2611, DOI: https://doi.org/10.2478/acsc-2014-0019. Export Citation

© Archives of Control Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Comments (0)

Please log in or register to comment.
Log in