Analysis of efficient strokes for multi-legged microswimmers

We consider efficient controls for swimming with multiple rigid legs at low Reynolds number. We derive equations governing the translation and rotation of a general class of multi-legged swimmers, and we formulate energy-efficient controls of symmetric swimmers as a problem in geometric control theory. We then focus on the case of symmetric swimmers with multi pairs of legs. In the framework of sub-Riemannian geometry, abnormal geodescics are analyzed and shown to depend on the number of pairs of legs. Inspired by larval copepods possessing three pairs of legs, we compute various swimming strokes and explore optimal controls in that specific situation. We also compare our results to experimental measurements of larval copepod.