Comprehensive unified control strategy for underactuated two-link manipulators

  • Authors:

  • Xu-Zhi Lai;Jin-Hua She;Simon X. Yang;Min Wu

  • Affiliations:

  • School of Information Science and Engineering, Central South University, Changsha, China;School of Computer Science, Tokyo University of Technology, Tokyo, Japan;Advanced Robotics and Intelligent Systems Laboratory, School of Engineering, University of Guelph, Guelph, ON, Canada;School of Information Science and Engineering, Central South University, Changsha, China

  • Venue:
  • IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
  • Year:
  • 2009

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Abstract

This paper presents a unified treatment of the motion control of underactuated two-link manipulators, including acrobots and pendubots. The motion space is divided into two areas: swing-up and attractive; and control laws are designed for each. First, a control law based on a weak-control Lyapunov function (WCLF) is employed to increase the energy of and control the posture of the actuated link in the swing-up area. Next, one parameter of the WCLF is chosen to be a nonlinear function of the state to avoid singularities. Then, another parameter of the control law is adjusted based on the state to improve the control performance. Finally, an optimal control law is designed for the attractive area. Stability is guaranteed in the swing-up area by the use of a WCLF based on LaSalle's invariance principle. Moreover, the global stability of the control system is guaranteed by integrating the WCLF and a nonsmooth Lyapunov function.