Geometric Motion Planning for a Three-Link Swimmer in a Three-Dimensional low Reynolds-Number Regime

Abstract

Purcell's three-link, two-joint planar swimmer is an iconic model of a simple mechanism that can locomote in the low-Reynolds number regime. In this paper, we consider a modification to the design of the planar swimmer by allowing yaw-pitch movements at the two actuated joints as opposed to the conventional yaw-yaw movements. We demonstrate that this design with only two active inputs is capable of swimming in three dimensions unlike the planar swimmer. Using analytical and visual tools from geometric mechanics, we design motion primitives that enable the swimmer to reorient itself and swim along canonical directions in the inertial frame. We also provide experimental results on a hardware testbed to show a comparison between the trajectories derived from simulated gaits and trajectory of the robot executing those gaits.