Journal
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS
Volume 39, Issue 2, Pages 389-398Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMCB.2008.2005910
Keywords
Acrobot; LaSalle's invariance principle; nonsmooth Lyapunov function (NSLF); singularity; stabilization; underactuated manipulator; weak-control Lyapunov function (WCLF)
Categories
Funding
- National Science Foundation of China [60674044, 60425310]
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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.
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