Comprehensive Unified Control Strategy and Global Stability Analysis for Underactuated Two-link Manipulators
欠驱动两杆机器人的统一控制策略和全局稳定性分析

This paper presents a unified treatment of the motion control of underactuated two-link manipulators, including Acrobot and Pendubot.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 the system and control the posture of the actuated link in the swing-up area.Next,a parameter in the WCLF is chosen to be a nonlinear function of the state so as to avoid any singularities.Then,another design parameter in the control law based on WCLF is adjusted based on the state to improve the control performance.The stability of the swing-up area is guaranteed by the use of a WCLF based on the largest invariant set theorem.And a non-smooth Lyapunov function(NSLF)is employed to guarantee stability after the manipulator leaves the swing-up area.Finally, the global stability of the control system is guaranteed by the combination of a weak-control Lyapunov function and a non-smooth Lyapunov function.