Current browse context:
eess.SY
Change to browse by:
References & Citations
Electrical Engineering and Systems Science > Systems and Control
Title: Excessive Transverse Coordinates for Orbital Stabilization of (Underactuated) Mechanical Systems
(Submitted on 1 Oct 2019 (v1), last revised 3 May 2020 (this version, v2))
Abstract: Transverse linearization-based approaches have become among the most prominent methods for orbitally stabilizing feedback design in regards to (periodic) motions of underactuated mechanical systems. Yet, in an $n$-dimensional state-space, this requires knowledge of a set of $(n-1)$ independent transverse coordinates, which can be nontrivial to find and whose definitions might vary for different motions (trajectories). In this paper, we consider instead a generic set of $excessive$ transverse coordinates which are 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 transverse linearization, as well as state a sufficient condition for the existence of a feedback controller rendering the desired trajectory (locally) asymptotically orbitally stable. The presented approach is applied to stabilizing oscillations of the underactuated cart-pendulum system about its unstable upright position, in which a novel motion planning approach based on virtual constraints is utilized for trajectory generation.
Submission history
From: Christian Fredrik Sætre [view email][v1] Tue, 1 Oct 2019 16:45:39 GMT (719kb)
[v2] Sun, 3 May 2020 11:47:14 GMT (315kb)
Link back to: arXiv, form interface, contact.