ABSTRACT
This chapter discusses the effect of nonholonomic constraints on the behavior of robotic systems. It emphasis the basic tools needed to analyze nonholonomic systems and the application of those tools to problems in robotic manipulation. The chapter discusses the problem of determining when constraints on the velocities of the configuration variables of a robotic system are integrate, and illustrate the problem in a variety of different situations. It develops some tools from differential geometry and nonlinear control. The chapter develop methods for planning paths compatible with nonholonomic constraints. Besides rolling constraints on multifingered hands, nonholonomic constraints play an important role in the study of mobile robot systems and space-based robotic systems. The complexity of the motion planning problem is related to the order of Lie brackets in its controllability Lie algebra. The growth vector for a regular filtration is a convenient way to represent complexity information about the associated controllability Lie algebra.
