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We analyse weak and strong controllability notions for the locomotion of the3-link Purcell's swimmer, the simplest possible swimmer at low Reynolds numberfrom a geometric framework. After revisiting a purely kinematic form of theequations, we apply an extension of Chow's theorem to analyze controllabilityin the strong and weak sense. Further, the connection form for the symmetricversion of the Purcell's swimmer is derived, based on which, thecontrollability analysis utilizing the Abelian nature of the structure group ispresented. The novelty in our approach is the usage of geometry and theprincipal fiber bundle structure of the configuration manifold of the system toarrive at strong and weak controllability notions.

Geometric Controllability of The Purcell's Swimmer and its Symmetrized Cousin