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

{{HTDB paper
| authors = D. Tilbury, R. M. Murray and S. S. Sastry
| title = Trajectory generation for the N-trailer problem using Goursat normal form
| source = <i>IEEE T. Automatic Control</i>, 40: (5) 802-819
| year = 1995
| type = 
ERL memo
| funding = 
| url = http://www.cds.caltech.edu/~murray/preprints/tms93-erl.pdf
| abstract = 
In this paper, we develop 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. We use this technique to solve the problem of steering a mobile robot with n trailers, We 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, we 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.

| flags = 
| tag = tms93-erl
| id = 1993a
}}