Minimally invasive medical procedures are currently an active research aera. A drug targeted therapy and the possibility of establishing an accurate diagnosis through the use of miniaturized systems can greatly improve many medical practices. The use of untethered microrobots navigating in the cardiovascular system opens new perspectives. The objective of this PhD work is to provide a theoretical approach on i) the modeling of a microrobot navigating in the cardiovascular system, ii) the development of control laws and observers to ensure a fine tracking from the injection to a target area. Modeling such as system involves many forces : hydrodynamic forces, surface forces (electrostatic, van derWaals, steric), contact forces and apparent weight of the microrobot. This microrobot is controlled in the cardiovascular system by the application of magnetic fields or magnetic field gradients according to the design of the microrobot. The consideration of all the forces leads to a state representation in the form of a nonlinear system with many physiological uncertain parameters, but gives us sufficient informations to plan an optimal trajectory. The control approach is established based on stability consideration. A Lyapunov-stabilizing control is then developed using a backstepping approach. An adaptive backstepping control law estimates some physiological parameters. A high gain observer reconstructs the full state of the system required for implementing the control approach. Robustness and stability of the controller with respect to noise measurement, parameters variations and uncertainties are illustrated by simulations.
