A constructive generalised Goursat normal form
نویسندگان
چکیده
منابع مشابه
A Constructive Generalised Goursat Normal Form
We provide necessary and sufficient conditions on the derived type of a vector field distribution V in order that it be locally equivalent to a partial prolongation of the contact distribution C (1) q , on the 1 order jet bundle of maps from R to R, q ≥ 1. This result fully generalises the classical Goursat normal form. Our proof is constructive: it is proven that if V is locally equivalent to ...
متن کاملTrajectory Generation for the N - trailer problem using Goursat Normal Form *
In this paper, we show how ihe machinery of ederior differential sysiemr can k wed i o help soltie nonholonomic motion planning problems. Since the Gorrsat normal form for ezterior differential systems is dual i o chained form for vectorfields, we solve the problem of steering a mobile robot with n trailers by convcriing ihe system int.0 chained form, doing ihe paih-planning in the chained form...
متن کاملTrajectory Generation for the N-trailer Problem Using Goursat Normal Form
In this paper, we develop the machinery of exterior diierential forms, more particularly the Goursat normal form for a Pfaaan system, for solving nonholonomic motion planning problems, i.e. planning problems with non-integrable velocity constraints. We apply this technique to solving the problem of steering a mobile robot with n trailers. We present an algorithm for nding a family of transforma...
متن کاملOn Goursat Normal Forms, Prolongations, and Control Systems
In this paper, the method of exterior diflerential systems for analyzing nonlinear systems is presented. Conditions are given for converting Pfafian systems into Goursat normal f o r m , and for converting control systems into Brunovsky form. All of the existing results on feedback linearization for control systems can be restated in the language of Pfafian systems, and in addition, new conditi...
متن کاملEfficient Construction of Contact Coordinates for PartialProlongations
Let V be a vector field distribution on manifold M . We give an efficient algorithm for the construction of local coordinates on M such that V may be locally expressed as some partial prolongation of the contact distribution C (1) q , on the 1 st order jet bundle of maps from R to R, q ≥ 1. It is proven that if V is locally equivalent to a partial prolongation of C (1) q then the explicit const...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2006
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2005.12.001