Many important engineering systems accomplish their purpose using cyclic processes whose characteristics are under feedback control. Examples involving thermodynamic cycles and electromechanical energy conversion processes are particularly noteworthy. Likewise, cyclic processes are prevalent in nature and the idea of a pattern generator is widely used to rationalize mechanisms used for orchestrating movements such as those involved in locomotion and respiration. In this paper, we develop a linkage between the use of cyclic processes and the control of nonholonomic systems, emphasizing the problem of achieving stable regulation. The discussion brings to the fore characteristic phenomena that distinguish the regulation problem for such strongly nonlinear systems from the more commonly studied linear feedback regulators. Finally, we compare this approach to controlling nonholonomic systems to another approach based on the idea of an open-loop approximate inverse as discussed in the literature.