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Published December 1993 | Published
Book Section - Chapter Open

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


Shows how the machinery of exterior differential systems can be used to help solve nonholonomic motion planning problems. Since the Goursat normal form, for exterior differential systems is dual to chained form for vector fields, the authors solve the problem of steering a mobile robot with N trailers by converting the system into chained form, doing the path-planning in the chained form coordinates, and converting the path back into the original coordinates. Simulations of the N-trailer system parallel parking and backing into a loading dock are included.

Additional Information

© 1993 IEEE. The research of D. Tilbury and S. Sastry was supported in part by NSF under grant IRI-9014490. The work of R. Murray was supported in part by a grant from the Powell Foundation. D. Tilbury would also like to acknowledge an AT&:T Ph.D. Fellowship for partial support of this work. We 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, O. S1ardalen, H. Sussmann and G. Walsh. 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.

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August 20, 2023
August 20, 2023