Abstract
The paper introduces the novel problem of the synchronization of a pair of identical mobile nonholonomic oscillators, the so-called Chaplygin sleighs, moving on a movable platform with springs. Each Chaplygin sleigh is actuated by a periodic torques of the same amplitude and frequency, resulting in a limit cycle in a reduced velocity space. The frictional constraint forces couple the motion of the two Chaplygin sleighs and the platform. The limit cycles of the coupled oscillators are dependent on the relative phase of actuation on the sleighs. We show that the coupled limit cycles become identical but with anti-phase synchronization, where the amplitude and frequency of oscillations and the average translational speeds of the two sleighs become equal. Moreover, in such anti-phase synchronization, the heading angle of both sleighs converge, producing motion in a formation.
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