In this paper, we present a novel controller for steering nanorobots in lattice-like vessel systems while avoiding potential obstacles such as the vessel walls without any prior knowledge of the obstacles' positions. The proposed control method consists of two sub-modules, namely a blind obstacle avoidance (BOA) and a model predictive control (MPC). In the case that a nanorobot might encounter an obstacle on its path, the BOA module is activated, which gives rise to a desirable heading angle to change the direction of the nanorobot's movement to bypass the obstacle. On the other hand, the MPC module offers a series of actuating field's directions that control the nanorobots' movement in the blood vessel with a grid structure representing potential paths of vascular growth, and introduces a repulsive boundary function to stop nanorobots from getting too close to the boundaries. This new formulation offers successful control and steering of nanorobots while avoiding obstacles in a blind manner by taking into account realistic in vivo physical constraints. Simulation results demonstrate the effectiveness of the proposed feedback control design.