Motion control algorithms for mechanical systems with symmetry
underactuated by one control

Sonia Martínez and Jorge Cortés
Acta Applicandae Mathematicae, 76 (3) (2003), 221-264

Abstract:

We treat underactuated mechanical control systems with symmetry taking the viewpoint of the affine connection formalism. We first review the appropriate notions and tests of controllability associated with these systems, including that of fiber controllability. Secondly, we present a series expansion describing the evolution of the trajectories of general mechanical control systems starting from non-zero velocity. This series is then used to investigate the behavior of the system under small-amplitude periodic forcing. On this basis, motion control algorithms are designed for systems with symmetry to solve the tasks of point-to-point reconfiguration, static interpolation and stabilization problems. Several examples are given and the performance of the algorithms is illustrated in the blimp system.

File: main.pdf

Bib-tex entry:

@article{SM-JC:03,
author = {S. Mart{/'/i}nez and J. Cort\'es},
title = {Motion control algorithms for mechanical systems with symmetry
underactuated by one control},
journal= {Acta Applicandae Mathematicae},
volume = 76,
number = 3,
year = 2003,
pages = {221--264}
}