Control of mechanical and nonholonomic systems

Abstract

There is a large literature on nonholonomic motion planning, the construction in the nonholonomic setting of explicit open loop controls as discussed in Chapter 4 ; see, for example, Li and Canny [1993] and Murray and Sastry [1993] and the works cited therein as well as, for example, Sussmann and Liu [1991], Lafferiere and Sussman [1991], Lewis, Ostrowski, Murray, and Burdick [1994], Ostrowski, Desai, and Kumar [1997], Lewis and Murray [1999], Ostrowski [2000], Bullo, Leonard, and Lewis [2000], and Bullo, Lewis, and Lynch [2002]. It is not our intention in this book to give an exhaustive account of the details of this theory. We will instead illustrate some aspects of the theory illustrated by Brockett’s generalization of the Heisenberg system as well as systems in so-called chained form.