Theory for controlling individual self-propelled micro-swimmers by photon nudging II: confinement

Photon nudging allows the manipulation and confinement of individual self-propelled micro-swimmers in 2D and 3D environments using feedback controls. Presented in this second part of a two-part contribution are theoretical models that afford the characterization for the positioning distribution associated with active localization. A derivation for the optimal nudging speed and acceptance angle is given for minimal placement uncertainty. The analytical solutions allow for a discussion on the physical underpinning that underlies controllability and optimality.