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Analysis of the energy‐based swing‐up control of the Acrobot
Author(s) -
Xin X.,
Kaneda M.
Publication year - 2007
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1184
Subject(s) - control theory (sociology) , underactuation , equilibrium point , controller (irrigation) , mathematics , control (management) , point (geometry) , swing , computer science , engineering , mathematical analysis , artificial intelligence , agronomy , mechanical engineering , geometry , biology , differential equation
Abstract 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.