Abstract
An underactuated horizontal spring-coupled two-link manipulator (UHSTM) is a nonlinear system that has one actuator and two degrees of freedom (DOF). This paper analyzes the nonlinear dynamics and develops a new global stabilization control method for this 2-DOF underactuated system. First, a set of suitable state variables are constructed to change the UHSTM system into a cascade nonlinear system. Second, a Lyapunov function is constructed based on the structural characteristics of the cascade system. A control law is designed to ensure the closed-loop control system to be Lyapunov stable. After that, the global asymptotical stability conditions are derived from the analysis of the closed-loop control system. Finally, numerical examples demonstrate the validity of the theoretical analysis results.
Highlights
With the improvement of industrial automation, the manipulators have been widely used in many areas of engineering [1,2,3,4]
The damage of actuators is an inevitable problem caused by the wearing of devices and the influence of the surrounding environment. e failure of actuators results in that the manipulator becomes an underactuated mechanical system [5,6,7], in which the system has less number of actuators than degrees of freedom (DOF)
It is meaningful to study the control of this kind of mechanical system [8,9,10,11]. This problem is challenging due to the complex inherent nonlinear dynamics and nonholonomic constraints possessed by this kind of system [12]
Summary
With the improvement of industrial automation, the manipulators have been widely used in many areas of engineering [1,2,3,4]. It is meaningful to study the control of this kind of mechanical system [8,9,10,11] This problem is challenging due to the complex inherent nonlinear dynamics and nonholonomic constraints possessed by this kind of system [12]. In [26], a spring was added around the passive joint of the UHTM, and an underactuated horizontal spring-coupled two-link manipulator (UHSTM) was constructed (see Figure 1). E UHSTM uses the spring to create a source of potential energy It makes the control of the underactuated horizontal manipulator be easy to solve. Numerical examples verified the effectiveness of the presented theoretical results
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