Path following for a Class of Underactuated Systems Using Global Parameterization

Adeel Akhtar, Sajid Saleem, Steven L. Waslander

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A large number of both aerial and underwater mobile robots fall in the category of underactuated systems that are defined on a manifold, which is not isomorphic to Euclidean space. Traditional approaches to designing controllers for such systems include geometric approaches and local coordinate-based representations. In this paper, we propose a global parameterization of the special orthogonal group, denoted by $ \mathsf {SO}(3)$ , to design path-following controllers for underactuated systems. In particular, we present a nine-dimensional representation of $ \mathsf {SO}(3)$ that leads to controllers achieving path-invariance for a large class of both closed and non-closed embedded curves. On the one hand, this over-parameterization leads to a simple set of differential equations and provides a global non-ambiguous representation of systems as compared to other local or minimal parametric approaches. On the other hand, this over-parameterization also leads to uncontrolled internal dynamics, which we prove to be bounded and stable. The proposed controller, when applied to a quadrotor system, is capable of recovering the system from challenging situations such as initial upside-down orientation and also capable of performing multiple flips.
Original languageEnglish (US)
Pages (from-to)34737-34749
Number of pages13
JournalIEEE Access
StatePublished - Jan 1 2020
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-10-11

ASJC Scopus subject areas

  • General Engineering
  • General Computer Science
  • General Materials Science


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