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 (1993). In this paper, we concentrate on how to find such coordinate transformations for multisteering, multitrailer 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