Steering nonholonomic systems in chained form

Abstract

The authors introduce a nilpotent form, called a chained form, for nonholonomic control systems. For the case of a nonholonomic system with two inputs, they give constructive conditions for the existence of a feedback transformation which puts the system into chained form, and show how to steer the system between arbitrary states. Examples are presented for steering a car and a car with a trailer attached: other examples can be found in the areas of space robotics and multifingered robot hands. The present results also have applications in the area of nilpotentization of distributions of vector fields on R/sup n/.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>