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A Case Study in Approximate Linearization: The Acrobot Example 
Abstract 
The acrobot is a simple mechanical system … The acrobot is a simple mechanical system patterned after a gymnast
performing on a single parallel bar. By swinging her legs, a gymnast
is able to bring herself into an inverted position with her center of
mass above the part and is able to perform manuevers about this
configuration. This report studies the use of nonlinear control
techniques for designing a controller to operate in a neighborhood of
the manifold of inverted equilibrium points. The techniques described
here are of particular interest because the dynamic model of the
acrobot violates many of the necessary conditions required to apply
current methods in linear and nonlinear control theory.
<p>
The approach used in this report is to approximate the system in such
a way that the behavior of the system about the manifold of
equilibrium points is correctly captured. In particular, we construct
an approximating system which agrees with the linearization of the
original system on the equilibrium manifold and is full state
linearizable. For this class of approximations, controllers can be
constructed using recent techniques from differential geometric control
theory. We show that application of control laws derived in this
manner results in approximate trajectory tracking for the system under
certain restrictions on the class of desired trajectories. Simulation
results based on a simplified model of the acrobot are included. plified model of the acrobot are included. +


Authors  Richard M. Murray and John Hauser + 
Flags  NoRequest + 
ID  1991c + 
Source  ERL Technical Memo, May 1991 + 
Tag  mh91erl + 
Title  A Case Study in Approximate Linearization: The Acrobot Example + 
Type  Technical report + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:21:01 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/erlM9146.pdf + 
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A Case Study in Approximate Linearization: The Acrobot Example +  Title 
