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Locomotion at low Reynolds numbers is a topic of growing interest, spurred byits various engineering and medical applications. This paper presents a novelprototype and a locomotion algorithm for the 3-link planar Purcell's swimmerbased on Lie algebraic notions. The kinematic model based on Cox theory of theprototype swimmer is a driftless control-affine system. Using the existingstrong controllability and related results, the existence of motion primitivesis initially shown. The Lie algebra of the control vector fields is then usedto synthesize control profiles to generate motions along the basis of the Liealgebra associated with the structure group of the system. An open loop controlsystem with vision-based positioning is successfully implemented which allowstracking any given continuous trajectory of the position and orientation of theswimmer's base link. Alongside, the paper also provides a theoreticalinterpretation of the symmetry arguments presented in the existing literatureto generate the control profiles of the swimmer.

Trajectory Tracking Using Motion Primitives for the Purcell's Swimmer