Rolling is a frequently used high-efficiency motion pattern for articulated loop robots. An important issue is planning the angle of each joint to keep a loop closed on the fly and to roll forward stably. Most of the current approaches achieve a gait table by designing a few key postures or a numerical approximation of a special loop geometry (e.g., an ellipse), which is difficult to implement for non-experts and makes motion planning time-consuming. The change in joint angles for many current loop gaits is not smooth. The serpenoid curve, whose curvature changes sinusoidally, exhibits the advantage of making angle changes smooth. Based on this feature, a generalized Serpenoid Polygon model for loop gait is proposed, which extends Hirose's Serpenoid Oval to Polygon. Furthermore, we derive its scalable planning model for loop robots with different numbers of joints, which is easy to implement. The influence of key parameters on the performance of this model is investigated through numerous dynamics simulations with a general linkage-mechanism. In addition, loop forming and rolling-pattern switching are studied to facilitate the implementation of this model. In the end, the applications of the model are discussed, its effectiveness is validated through experiments using the UBot modular robot.
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