Intrinsic and apparent singularities in differentially flat systems, and application to global motion planning

Yirmeyahu J. Kaminski, Jean Lévine, François Ollivier

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

In this paper, we study the singularities of differentially flat systems, in the perspective of providing global or semi-global motion planning solutions for such systems: flat outputs may fail to be globally defined, thus potentially preventing from planning trajectories leaving their domain of definition, the complement of which we call singular. Such singular subsets are classified into two types: apparent and intrinsic. A rigorous definition of these singularities is introduced in terms of atlas and local charts in the framework of the differential geometry of jets of infinite order and Lie–Bäcklund isomorphisms. We then give an inclusion result allowing to effectively compute all or part of the intrinsic singularities. Finally, we show how our results apply to the global motion planning of the celebrated example of non holonomic car.

Original languageEnglish
Pages (from-to)117-124
Number of pages8
JournalSystems and Control Letters
Volume113
DOIs
StatePublished - Mar 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

  • Apparent and intrinsic singularity
  • Atlas
  • Differential flatness
  • Global motion planning
  • Jets of infinite order
  • Lie–Bäcklund isomorphism
  • Local chart

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