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Invariant feedback design for control systems with lie symmetries - A kinematic car example

Pages: 312 - 321, Issue Special, September 2011

 Abstract        Full Text (206.5K)              

Carsten Collon - Saarland University, Chair of Systems Theory and Control Engineering, Germany (email)
Joachim Rudolph - Saarland University, Chair of Systems Theory and Control Engineering, Germany (email)
Frank Woittennek - TU Dresden, Institut für Regelungs- und Steuerungstheorie, Germany (email)

Abstract: Invariant tracking control design for control systems in state representation with classical Lie point symmetry is considered. The relevance of the invariance aspect is motivated by an exemplary control design for the kinematic car. Introducing the perpendicular distance between the position of the rear axle midpoint and the reference trajectory in combination with the contouring error as tracking error, an invariant feedback w.r.t. the action of $SE$(2) is derived. Generally, the use of compatible tracking errors allows the application of well-known feedback design approaches yielding an error dynamics that is invariant w.r.t. the group action. A normalization procedure allowing the construction of invariant tracking errors is recalled for which a geometric interpretation is presented.

Keywords:  Symmetries, nonlinear control, output tracking, invariant
Mathematics Subject Classification:  Primary: 93C10, 34C14; Secondary: 93C95

Received: July 2010;      Revised: February 2011;      Published: October 2011.