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

Carsten Collon; Joachim Rudolph; Frank Woittennek

doi:10.3934/proc.2011.2011.312

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2011, Volume 2011: 312-321. Doi: 10.3934/proc.2011.2011.312 open access

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

1.
Saarland University, Chair of Systems Theory and Control Engineering
2.
TU Dresden, Institut für Regelungs- und Steuerungstheorie

Received: June 30, 2010

Revised: January 31, 2011

Published: August 2017

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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.

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Mathematics Subject Classification: Primary: 93C10, 34C14; Secondary: 93C95.

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