Abstract
The number of actuators of an underactuated robot is less than its degree of freedom. In other words, underactuated robots can be designed with fewer actuators than fully actuated ones. Although an underactuated robot is more complex than a fully actuated robot, it has many advantages, such as energy, material, and space saving. Therefore, it has high research value in both control theory and practical applications. Swing-up is a mechanism with two links, which mimics a gymnast performing a horizontal bar movement. Over the past few decades, many sufficiently robust control techniques have been developed for a fully actuated robot but almost none of them can be directly applicable to an underactuated robot system. The reason is that such control techniques require certain assumptions that are valid only for fully actuated robot systems but not for underactuated ones. In this paper, a control system design method for underactuated robots based on operator theory and an isomorphism scheme is first proposed. Bezout identity is designed using isomorphism. The effectiveness of the design method is confirmed by simulation. The simulation results show that the performances, such as robust stability and response time, of an underactuated robot control system are improved.
Highlights
According to the relationship between degree of freedom (DOF) of a robot and the number of independent control inputs, robots can be devided into three types: fully actuated, redundantly actuated, and underactuated ones [1]
Many sufficiently robust control techniques have been developed for a fully actuated robot but they are not directly applicable to an underactuated robot system. [4] concerns the energy-based swing-up control for a remotely driven acrobot (RDA), which is a 2-link planar robot with the first link being underactuated and the second link being remotely driven by an actuator mounted at a fixed base through a belt
A control system design method based on operator theory and an isomorphism scheme is proposed to improve the performance of an underactuated robot with instability and uncertainties
Summary
According to the relationship between degree of freedom (DOF) of a robot and the number of independent control inputs, robots can be devided into three types: fully actuated, redundantly actuated, and underactuated ones [1]. An energy-based control law for swinging up the acrobot is proposed in [5]. The control law is designed and the convergence analysis is carried out based on Lyapunov stability theory. The proposed method for swinging up and stabilizing underactuated two-link robots in [12] does not need to switch control laws when the system is near to the desired equilibrium point, and as the system approach to this equilibrium, the nonlinear control law becomes an LQR controller. A control system design method based on operator theory and an isomorphism scheme is proposed to improve the performance of an underactuated robot with instability and uncertainties. Operator theory is employed for guaranteeing the robust stability, while an isomorphism scheme is used to avoid the existence of differential controller in operator-based control systems.
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