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Trajectory generation for the N-trailer problem using Goursat normal form
| Content Provider | Semantic Scholar |
|---|---|
| Author | Tilbury, Dawn M. Murray, Richard M. Sastry, S. Shankar |
| Copyright Year | 1995 |
| 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. > |
| Starting Page | 802 |
| Ending Page | 819 |
| Page Count | 18 |
| File Format | PDF HTM / HTML |
| DOI | 10.1109/9.384215 |
| Volume Number | 40 |
| Alternate Webpage(s) | http://www-personal.engin.umich.edu/~tilbury/me662/caen/me662/caen/me662/caen/papers/n_trailers.ps.gz |
| Alternate Webpage(s) | http://robotics.eecs.berkeley.edu/papers/motion_planning/n_trailers_cdc.ps.gz |
| Alternate Webpage(s) | http://www-personal.engin.umich.edu/~tilbury/me662/caen/me662/caen/me662/caen/papers/cdc93.ps |
| Alternate Webpage(s) | https://doi.org/10.1109/9.384215 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
