Construction of the best ellipsoidal approximation of the attraction domain in stabilization problem for a wheeled robot

2011 ◽  
Vol 72 (3) ◽  
pp. 512-528 ◽  
Author(s):  
A. V. Pesterev
Keyword(s):  
Attraction Domain ◽  
Stabilization Problem ◽  
Ellipsoidal Approximation ◽  
Wheeled Robot

Ellipsoidal Approximations of Invariant Sets in Stabilization Problem for a Wheeled Robot Following a Curvilinear Path

2009 ◽  
Author(s):  
Alexander V. Pesterev ◽  
Lev B. Rapoport
Keyword(s):  
Basic Result ◽  
Invariant Sets ◽  
Linear Matrix ◽  
Practical Implementation ◽  
Stabilization Problem ◽  
Invariant Ellipsoid ◽  
Target Trajectory ◽  
Wheeled Robot ◽  
Maximal Deviation ◽  
Target Path

A stabilization problem for a wheeled robot following a curvilinear target path is studied. In [1], a method for constructing invariant ellipsoids—quadratic approximations of the attraction domains for the target trajectory under a given control law—was developed. A basic result of that study is a theorem by means of which construction of the invariant ellipsoids reduces to solving a system of linear matrix inequalities (LMIs) and checking a scalar inequality. This paper is a sequel to work [1] and is devoted to practical implementation of the results obtained in that paper. It is discussed how to select the parameters in terms of which the theorem is formulated. An algorithm is developed that, for a given value of maximal deviation from the target trajectory, constructs an invariant ellipsoid of as large volume as possible.

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