3D closed-loop swimming at low Reynolds numbers

In this paper, the mobility matrix of helical microswimmers is investigated to compute the magnetic torque as a function of the angular velocities of the helical robot to achieve a 3D path following in closed-loop. Thus, the helical swimmer kinematics are expressed in the Serret-Frenet frame considering the weight of the robot and lateral disturbances using the compensation inclination and direction angles, respectively. A new chained formulation is used to design a stable controller. The approach is simple and quite general and can be used for different non-holonomic autonomous systems. The 3D path following is validated by presenting experimental results using a scaled-up helical microswimmer actuated magnetically. Different trajectories were tested: a spatial straight line, a helix trajectory, and an inclined sinusoidal trajectory. Several conditions have been tested experimentally, namely: different velocity profiles, compensation inclination angles, liquid viscosities, control gains and boundary effects, and their impact on the performance of the path following. To illustrate the robustness and accuracy of the visual servo control to disturbances presenting in the environment such as the magnetic field gradient and boundary effects, it is compared with the open-loop control. The results show the robustness of the controller and a submillimetric accuracy during the path following.