@article{
 title = {Trajectory Generation for the N-Trailer Problem Using Goursat Normal Form},
 type = {article},
 year = {1995},
 identifiers = {[object Object]},
 pages = {802-819},
 volume = {40},
 id = {19040a58-cd30-3527-aa6b-d8c5502aeb5a},
 created = {2017-11-10T18:50:22.658Z},
 file_attached = {true},
 profile_id = {0a17cdee-f944-3536-b518-2cfd7a0b3313},
 group_id = {1fc87704-3c7f-3e0e-ab3b-7af8b79238c4},
 last_modified = {2017-11-10T18:50:22.784Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 notes = {N-trailer problem. No prototype.},
 private_publication = {false},
 abstract = {Develops the machinery of exterior differential forms, more\nparticularly the Goursat normal form for a Pfaffian system, for solving\nnonholonomic motion planning problems, i.e., motion planning for systems\nwith nonintegrable velocity constraints. The authors use this technique\nto solve the problem of steering a mobile robot with n trailers. The\nauthors present an algorithm for finding a family of transformations\nwhich will convert the system of rolling constraints on the wheels of\nthe robot with n trailers into the Goursat canonical form. Two of these\ntransformations are studied in detail. The Goursat normal form for\nexterior differential systems is dual to the so-called chained-form for\nvector fields that has been studied previously. Consequently, the\nauthors are able to give the state feedback law and change of\ncoordinates to convert the N-trailer system into chained-form. Three\nmethods for planning trajectories for chained-form systems using\nsinusoids, piecewise constants, and polynomials as inputs are presented.\nThe motion planning strategy is therefore to first convert the N-trailer\nsystem into Goursat form, use this to find the chained-form coordinates,\nplan a path for the corresponding chained-form system, and then\ntransform the resulting trajectory back into the original coordinates.\nSimulations and frames of movie animations of the N-trailer system for\nparallel parking and backing into a loading dock using this strategy are\nincluded},
 bibtype = {article},
 author = {Murray, Richard M.},
 journal = {IEEE Transactions on Automatic Control},
 number = {5}
}

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No prototype.},\n private_publication = {false},\n abstract = {Develops the machinery of exterior differential forms, more\\nparticularly the Goursat normal form for a Pfaffian system, for solving\\nnonholonomic motion planning problems, i.e., motion planning for systems\\nwith nonintegrable velocity constraints. The authors use this technique\\nto solve the problem of steering a mobile robot with n trailers. The\\nauthors present an algorithm for finding a family of transformations\\nwhich will convert the system of rolling constraints on the wheels of\\nthe robot with n trailers into the Goursat canonical form. Two of these\\ntransformations are studied in detail. The Goursat normal form for\\nexterior differential systems is dual to the so-called chained-form for\\nvector fields that has been studied previously. Consequently, the\\nauthors are able to give the state feedback law and change of\\ncoordinates to convert the N-trailer system into chained-form. 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