Origami mechanisms are simple, lightweight, and can possess unique mechanical properties such as nonlinear tunable stiffness and multi-stability. Many studies have examined the use of these mechanical properties for adaptive and multi-functional structures and material systems. However, there are very few studies on how to exploit the mechanical properties of origami to generate or improve the locomotion of mobile robots. In this paper, we investigate the locomotion dynamics of a model origami robot system consisting of a bistable origami structure known as the generalized Kresling pattern attached to a Chaplygin sleigh, a canonical nonholonomic wheeled system. By applying a periodic torque on the Kresling segment we show that locomotion on a circle can be produced through the intrawell oscillations of the origami pattern. Furthermore, the bistability of Kresling pattern can be exploited to change the radius and speed of travel, producing two distinct modes of motion; and a control method is designed to switch the robot between these two modes. To the authors’ knowledge this is the first such study of dynamic locomotion using origami.