Higher order approximations for chained form

The work presented in this paper is strongly inspired by the joint work of A. J. Krener and one of the authors [1] on normal forms and also by the work of R. Murray and S.S. Sastry [2] on the control of systems in chained form. Our interest of finding a normal form for a class of nonholonomic systems (two inputs) is motivated by the fact that the sufficient conditions in [2] for the existence of feedback and diffeomorphism transforming the dynamics into a chained form are not satisfied by many systems. Thus it is necessary to seek for an approximate chained form for feedback design. To the best of our knowledge. [3] is the first paper which deals with approximate chained form.