Extended Goursat Normal Forms With Applications To Nonholonomic Motion Planning

. The theme of this paper is the generalization of Goursat normal forms for Pfaffian systems with co-dimension greater than two. There are necessary and sufficient conditions for the existence of coordinates that transform a Pfaffian system with co-dimension greater than two into an extended Goursat normal form, which is the dual of the multiple-chain, single-generator chained form mentioned in our earlier work. In this paper, we concentrate on how to find such coordinate transformations for multi-steering, multi-trailer mobile robot systems so that we can use available steering and stabilization algorithms for nonholonomic motion planning. We present a methodology for constructing a coordinate transformation and apply it to the example of a five-axle, two-steering mobile robot. 1. Introduction We are interested in motion planning for nonholonomic systems with nonintegrable velocity constraints. The constraints can be written as ff i = 0, where the ff i are one-forms on the config..