Control of nonholonomic systems using reference vector fields.

Abstract

This paper presents a control design methodology for n-dimensional nonholonomic systems. The main idea is that, given a nonholonomic system subject to κ Pfaffian constraints, one can define a smooth, N-dimensional reference vector field F, which is nonsingular everywhere except for a submanifold containing the origin. The dimension N ≤ n of F depends on the structure of the constraint equations, which induces a foliation of the configuration space. This foliation, together with the objective of having the system vector field aligned with F, suggests a choice of Lyapunov-like functions V. The proposed approach recasts the original nonholonomic control problem into a lower-dimensional output regulation problem, which although nontrivial, can more easily be tackled with existing design and analysis tools. The methodology applies to a wide class of nonholonomic systems, and its efficacy is demonstrated through numerical simulations for the cases of the unicycle and the n-dimensional chained systems, for n = 3, 4.

Bib

@inproceedings{DBLP:conf/cdc/PanagouTK11,
  author       = {Dimitra Panagou and
                  Herbert G. Tanner and
                  Kostas J. Kyriakopoulos},
  title        = {Control of nonholonomic systems using reference vector fields},
  booktitle    = {50th {IEEE} Conference on Decision and Control and European Control
                  Conference, 11th European Control Conference, {CDC/ECC} 2011, Orlando,
                  FL, USA, December 12-15, 2011},
  pages        = {2831--2836},
  publisher    = {{IEEE}},
  year         = {2011},
  url          = {https://doi.org/10.1109/CDC.2011.6160922},
  doi          = {10.1109/CDC.2011.6160922},
  timestamp    = {Wed, 24 Feb 2021 08:49:08 +0100},
  biburl       = {https://dblp.org/rec/conf/cdc/PanagouTK11.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}