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Excessive Transverse Coordinates for Orbital Stabilization of (Underactuated) Mechanical Systems

Abstract : The transverse linearization is a useful tool for the design of feedback controllers that orbitally stabilizes (periodic) motions of mechanical systems. Yet, in an n-dimensional state-space, this requires knowledge of a set of (n − 1) independent transverse coordinates, which at times can be difficult to find and whose definitions might vary for different motions (trajectories). Motivated by this, we present in this paper a generic choice of excessive transverse coordinates defined in terms of a particular parameterization of the motion and a projection operator recovering the "position" along the orbit. We present a constructive procedure for obtaining the corresponding excessive transverse linearization and state a sufficient condition for the existence of a feedback controller rendering the desired trajectory (locally) asymptotically orbitally stable. The approach is demonstrated through numerical simulation by stabilizing oscillations around the unstable upright position of the underactuated cart-pendulum system, in which a novel motion planning approach based on virtual constraints is utilized for trajectory generation.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-02441659
Contributor : Ahmed Chemori Connect in order to contact the contributor
Submitted on : Thursday, January 16, 2020 - 9:05:46 AM
Last modification on : Friday, August 5, 2022 - 3:03:30 PM
Long-term archiving on: : Friday, April 17, 2020 - 1:15:57 PM

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Christian Fredrik Saetre, Anton Shiriaev, Stepan Pchelkin, Ahmed Chemori. Excessive Transverse Coordinates for Orbital Stabilization of (Underactuated) Mechanical Systems. European Control Conference (ECC), May 2020, Saint Petersburg, Russia. ⟨lirmm-02441659⟩

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