Analysis of the energy‐based swing‐up control of the Acrobot
Analysis of the energy‐based swing‐up control of the Acrobot
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DOI：
10.1002/rnc.1184
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发表时间：
2007-11
影响因子：
3.9
通讯作者：
Xin Xin-Xin;M. Kaneda
中科院分区：
文献类型：
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作者：
Xin Xin-Xin;M. Kaneda
本文解决了基于能量的两连杆欠驱动机器人Acrobot的摆动控制问题，该机器人在两个连杆的连接处有一个驱动器。根据基于能量的控制方法，给出了该控制律不存在任何奇点的充分必要条件，并对Acrobot的能量收敛性和运动收敛性进行了完整的分析。具体而言，对于Acrobot的任何初始状态，本文清楚地说明了如何选择控制参数，使Acrobot最终将被摆动到直立平衡点的任意小邻域，或保持在包含有限个平衡点的集合中。此外，本文还证明了这些平衡点是不稳定的。进一步，对控制参数施加更强的条件，则平衡集只包含向下的平衡点，该平衡点被证明是双曲的和不稳定的。这证明了除了一组勒贝格测度为零外，在所有初始条件下，Acrobot最终都会进入任何稳定控制器的吸引池。版权所有©2007 John Wiley & Sons， Ltd
This paper addresses the energy‐based swing‐up control problem for the Acrobot, a two‐link underactuated robot with a single actuator at the joint of the two links. In line with the energy‐based control approach, this paper presents a necessary and sufficient condition for non‐existence of any singular point in the derived control law, and provides a complete analysis of the convergence of the energy and the motion of the Acrobot. Specifically, for any initial state of the Acrobot, this paper shows clearly how to choose control parameters such that the Acrobot will eventually either be swung up to any arbitrarily small neighbourhood of the upright equilibrium point, or remain in a set containing a finite number of equilibrium points. Moreover, this paper shows that these equilibrium points are unstable. Furthermore, imposing a stronger condition on a control parameter yields that the equilibrium set contains only the downward equilibrium point, which is shown to be hyperbolic and unstable. This proves that the Acrobot will eventually enter the basin of attraction of any stabilizing controller for all initial conditions with the exception of a set of Lebesgue measure zero. Copyright © 2007 John Wiley & Sons, Ltd.