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Trajectory generation for the Ntrailer problem using Goursat normal form 
Abstract 
In this paper, we develop the machinery of … 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 socalled chainedform 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 Ntrailer system into chained form. Three methods for planning trajectories for chainedform systems using sinusoids, piecewise constants, and polynomials as inputs are presented.
The motion planning strategy is therefore to first convert the Ntrailer system into Goursat form, use this to find the chainedform coordinates, plan a path for the corresponding chainedform system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the Ntrailer system for parallel parking and backing into a loading dock using this strategy are included. ing dock using this strategy are included. +


Authors  D. Tilbury, R. M. Murray and S. S. Sastry + 
ID  1993a + 
Source  <i>IEEE T. Automatic Control</i>, 40: (5) 802819 + 
Tag  tms93erl + 
Title  Trajectory generation for the Ntrailer problem using Goursat normal form + 
Type  ERL memo + 
Categories  Papers 
Modification date This property is a special property in this wiki.

15 May 2016 06:20:58 + 
URL This property is a special property in this wiki.

http://www.cds.caltech.edu/~murray/preprints/tms93erl.pdf + 
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Trajectory generation for the Ntrailer problem using Goursat normal form +  Title 
