欠驱动两杆机器人的统一控制策略和全局稳定性分析

针对包括 Acrobot 和 Pendubot 在内的欠驱动两杆机器人, 提出了一种统一的运动控制策略. 欠驱动两杆机器人的整个运动空间分为两个区域: 摇起区和平衡区, 并对这两个区域分别设计控制律. 首先, 在摇起区, 应用一种基于弱控制 Lyapunov 函数 (Weak-control Lyapunov function, WCLF) 的控制方法, 来增加系统能量和控制驱动杆的姿势. 其次, 为了避免奇异值的出现, 选择弱控制 Lyapunov 函数中的一个参数为系统状态空间的非线性函数. 然后, 通过系统状态调节基于弱控制 Lyapunov 函数的控制律中的另一个设计参数, 来改进系统控制效果. 使用弱控制 Lyapunov 设计的摇起区控制律, 可基于最大不变集原理保证其稳定性; 而机器人离开摇起区后, 利用非光滑 Lyapunov 函数 (Non-smooth Lyapunov function, NSLF) 来保证其稳定. 最后, 结合 WCLF 和 NSLF 保证了控制系统的全局稳定.

Comprehensive Unified Control Strategy and Global Stability Analysis for Underactuated Two-link Manipulators

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.