Angular Momentum Based Controller for Balancing an Inverted Double Pendulum

  • Morteza Azad
  • Roy Featherstone
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 544)


This paper presents a new control algorithm, based on angular momentum, for balancing a planar inverted double pendulum robot having one degree of underactuation. The robot may either pivot about a fixed point, or roll with a curved foot over a flat ground. The controller is able to stabilize the robot in any unstable balanced configuration, and to follow arbitrary motion trajectories without losing balance. The latter necessarily involves some tracking error. Several simulation results are presented.


Angular Momentum Contact Point Tracking Error Trajectory Tracking Revolute Joint 
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  1. M. D. Berkemeier and R. S. Fearing. Tracking fast inverted trajectories of the underactuated acrobot. IEEE Trans. Robotics and Automation, 15(4):740–750, August 1999.CrossRefGoogle Scholar
  2. J. W. Grizzle, C. H. Moog, and C. Chevallereau. Nonlinear control of mechanical systems with an unactuated cyclic variable. IEEE Trans. Automatic Control, 50(5):559–576, May 2005.MathSciNetCrossRefGoogle Scholar
  3. J. Hauser and R. M. Murray. Nonlinear controllers for nonintegrable systems: the acrobot example. In Proc. American Control Conf., pages 669–671, San Diego, CA, 23–25 May 1990.Google Scholar
  4. A. Inoue, M. Deng, S. Hara, and T. Henmi. Swing-up and stabilizing control system design for an acrobot. In Proc. IEEE Int. Conf. Networking, Sensing and Control, pages 559–561, London, UK, 15–17 April 2007.Google Scholar
  5. X. Lai, Y. Wu, J.She, and M. Wu. Control design and comprehensive stability analysis of acrobots based on lyapunov functions. J. Central South University of Technology, 12(1):210–216, 2005.CrossRefGoogle Scholar
  6. M. W. Spong. The swing up control problem for the acrobot. IEEE Control Systems, 15(1):49–55, 1995.CrossRefGoogle Scholar
  7. X. Xin and M. Kaneda. A new solution to the swing up control problem for the acrobot. In Proc. 40th SICE Annual Conf., pages 124–129, Nagoya, Japan, 25–27 July 2001.Google Scholar
  8. M. Yamakita, T. Yonemura, Y. Michitsuji, and Z. Luo. Stabilization of acrobot robot in upright position on a horizontal bar. In Proc. IEEE Int. Conf. Robotics and Automation, pages 3093–3098, Washington, DC, 11–15 May 2002.Google Scholar
  9. T. Yonemura and M. Yamakita. Swing up control problem of acrobot based on switched output functions. In Proc. SICE Annual Conf., pages 1909– 1914, Sapporo, 4–6 August 2004.Google Scholar

Copyright information

© CISM, Udine 2013

Authors and Affiliations

  • Morteza Azad
    • 1
  • Roy Featherstone
    • 1
  1. 1.School of EngineeringAustralian National UniversityCanberraAustralia

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