# Nonholonomic Behavior in Robotic Systems

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In this chapter, we study the effect of nonholonomic constraints on the behavior of robotic systems. These constraints arise in systems such as multifingered robot hands and wheeled mobile robots, where rolling contact is involved, as well as in systems where angular momentum is conserved. We discuss the problem of determining when constraints on the velocities of the configuration variables of a robotic system are integrable, and illustrate the problem in a variety of different situations. The emphasis of this chapter is on the basic tools needed to analyze nonholonomic systems and the application of those tools to problems in robotic manipulation. These tools are drawn both from some basic theorems in differential geometry and from nonlinear control theory.