{
  "id": "1306.6005",
  "version": "v2",
  "published": "2013-06-25T15:39:42.000Z",
  "updated": "2015-01-20T05:50:17.000Z",
  "title": "Lagrange-Poincaré reduction for optimal control of underactuated mechanical systems",
  "authors": [
    "Leonardo Colombo"
  ],
  "comment": "This paper has been withdrawn by the author due to a crucial error",
  "categories": [
    "math-ph",
    "math.MP",
    "math.OC"
  ],
  "abstract": "We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the higher-order Lagrange-Poincar\\'e equations of classical mechanical systems with higher-order constraints are obtained from classical Lagrangian reduction. Higher-order Lagrange-Poincar\\'e operator is introduced to characterize higher-order Lagrange-Poincar\\'e equations. Interesting applications are derived as, for instance, the optimal control of an underactuated Elroy's Beanie and a snakeboard seens as an optimization problem with higher-order constraints.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-25T15:39:42.000Z",
      "comment": "First version, 34 pp, comments welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-20T05:50:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "underactuated mechanical systems",
      "optimal control",
      "higher-order constraints",
      "regular lagrangian constrained systems",
      "characterize higher-order lagrange-poincare equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.6005C"
    }
  }
}