3D closed-loop motion control of swimmer with flexible flagella at low Reynolds numbers

Previously, we developed a 3D path following algorithm to improve the microrobot performances to overcome the modeling errors and environmental disturbances in order to perform real tasks, tested experimentally in a scaled-up helical microswimmer. In this paper, we show that adapting the propulsion mode, the general path following algorithm can be used for any microswimmer behaving as a nonholonomic system. For that purpose, we study a magnetic robot with a flexible tail that mimics the spermatozoa locomotion mechanism. A frequency and amplitude characterization of the flexible swimmer using an oscillating magnetic field is shown. To adapt the propulsion mode, we develop a 3D magnetic field control based on the steering angular velocities which are computed from the path following algorithm in order to propel and steer the flexible robot to reach a desired location in space and achieve for the first time a 3D closed-loop motion control using a swimmer with flexible flagella.