Control and navigation problems for model bio-inspired microswimmers

Navigation problems for a model bio-inspired micro-swimmer, consisting of a cargo head and propelled by multiple rotating flagella or propellers and swimming at low Reynolds numbers, are formulated and solved. We consider both the direct problem, namely, predicting velocity and trajectories of the swimmer as a consequence of prescribed rotation rates of the propellers, and inverse problems, namely, find the rotation rates to best approximate desired translational and rotational velocities and, ultimately, target trajectories. The equations of motion of the swimmer express the balance of the forces and torques acting on the swimmer, and relate translational and rotational velocities of the cargo head to rotation rates of the propellers. The coefficients of these equations, representing hydrodynamic resistance coefficients, are evaluated numerically through a custom-built finite-element code to simulate the (Stokes) fluid flows generated by the movement of the swimmer and of its parts. Several designs of the propulsive rotors are considered: from helical flagella with different chirality to marine propellers, and their relative performance is assessed.