Trajectory Generation for the N-Trailer Problem Using Goursat Normal Form. Murray, R., M. IEEE Transactions on Automatic Control, 40(5):802-819, 1995. Paper abstract bibtex 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
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title = {Trajectory Generation for the N-Trailer Problem Using Goursat Normal Form},
type = {article},
year = {1995},
identifiers = {[object Object]},
pages = {802-819},
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notes = {N-trailer problem. No prototype.},
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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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