Model Predictive Control Strategy for Navigating Nanoswimmers in Blood Vessels Using Taxicab Geometry

In this paper, for the first time, a novel method of controlling nanoswimmers in blood vessels with a square lattice of discrete points that represent potential paths of vascular growth is proposed. The objective function of the proposed model predictive control (MPC) algorithm is comprised of the target cost function and the repulsive boundary function. The former is used to measure the Manhattan distance between the current position of the nanoswimmers and the targeted location to simulate the lattice-like vascular patterns inside the human body. Blood flow velocity may cause nanoswimmers to pass the target point where backward movement is not possible. Therefore, we introduce a repulsive boundary function which plays a crucial role in terms of avoiding nanoswimmers from getting too close to the boundaries. This new formulation, based on the Manhattan distance, is particularly successful in controlling and steering nanoswimmers while avoiding boundaries by taking into account realistic in vivo nanoswimmers' propagation. The proposed feedback control is validated through simulation.