Unified Treatment of Motion Control of Underactuated two-link manipulators

This paper presents a comprehensive unified control strategy for 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 and control the posture of the actuated link in the swing-up area. Next, one of the parameters of the WCLF is chosen to be a nonlinear function of the state so as to avoid any singularities. Then, another parameter in the control law is adjusted based on the state to improve the control performance. Stability is guaranteed in the swing-up area by the use of a WCLF based on the LaSalle invariant theorem. Finally, the global stability of the control system is guaranteed by the use of a non-smooth Lyapunov function integrated with a minimum-switching strategy. Simulation results for a pendubot and an acrobot show this control scheme to be very effective