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Trajectory generation for the N-trailer problem using Goursat normal form

Tilbury, Dawn and Murray, Richard M. and Sastry, S. Shankar (1995) Trajectory generation for the N-trailer problem using Goursat normal form. IEEE Transactions on Automatic Control, 40 (5). pp. 802-819. ISSN 0018-9286. http://resolver.caltech.edu/CaltechAUTHORS:TILieeetac95

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Abstract

Develops the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. The authors use this technique to solve the problem of steering a mobile robot with n trailers. The authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, the authors are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained-form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented. The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included.


Item Type:Article
Additional Information:© Copyright 1995 IEEE. Reprinted with permission. Manuscript received March 5, 1993; revised June 21, 1994. The work was supported in part by NSF Grant IRI-9014490 and a grant from the Powell Foundation. D. Tilbury would also like to acknowledge an AT&T Ph.D. Fellowship for financial support of this work. The authors would like to thank several people who have helped us in understanding this problem over the past few years: R. Brockett, L. Bushnell, J. Canny, R. Gardner, G. Giralt, G. Lafferiere, J.-P. Laumond, Z. Li, B. Mirtich, R. Montgomery, D. Normand-Cyrot, W. Sluis, W. Shadwick, H. Sussmann and G. Walsh. They are also indebted to O. Sørdalen for furnishing us with his transformation of the N-trailer system into chained-form coordinates. D. Tilbury and S. Sastry would like to thank S. Mitter for his hospitality at LIDS and CICS at MIT where some of this research was done in the fall of 1992.
Subject Keywords:mobile robots; path planning; polynomials; state feedback
Record Number:CaltechAUTHORS:TILieeetac95
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:TILieeetac95
Alternative URL:http://dx.doi.org/10.1109/9.384215
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7332
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:31 Jan 2007
Last Modified:26 Dec 2012 09:31

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