This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://www.springer.com/materials/mechanics/journal/11071.We present a novel analysis technique to understand the dynamics of a recently described locomotion mode called legless locomotion. Legless locomotion is a locomotion mode available to a legged robot when it becomes high-centered, that is, when its legs do not touch the ground. Under these conditions, the robot may still locomote in the plane by swinging its legs in the air, rocking on its body, and taking advantage of the nonholonomic contact constraints. Legless locomotion is unique from all previously studied locomotion modes, since it combines the effect of oscillations due to controls and gravity, nonholonomic contact constraints, and a configuration-dependent inertia. This complex interaction of phenomena makes dynamics analysis and motion planning difficult, and our proposed analysis technique simplifies the problem by decoupling the robot’s oscillatory rotational dynamics from its contact kinematics and also decoupling the dynamics along each axis. We show that the decoupled dynamics models are significantly simpler, provide a good approximation of the motion, and offer insight into the robot’s dynamics. Finally, we show how the decoupled models help in motion planning for legless locomotion
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