Title: Trajectory Tracking Using Motion Primitives for the Purcell's Swimmer,
Abstract: Locomotion at low Reynolds numbers is a topic of growing interest, spurred by
its various engineering and medical applications. This paper presents a novel
prototype and a locomotion algorithm for the 3-link planar Purcell's swimmer
based on Lie algebraic notions. The kinematic model based on Cox theory of the
prototype swimmer is a driftless control-affine system. Using the existing
strong controllability and related results, the existence of motion primitives
is initially shown. The Lie algebra of the control vector fields is then used
to synthesize control profiles to generate motions along the basis of the Lie
algebra associated with the structure group of the system. An open loop control
system with vision-based positioning is successfully implemented which allows
tracking any given continuous trajectory of the position and orientation of the
swimmer's base link. Alongside, the paper also provides a theoretical
interpretation of the symmetry arguments presented in the existing literature
to generate the control profiles of the swimmer.