The disclosure relates to a robotic device for performing a medical intervention on a patient using a medical instrument, comprising: a robot arm having several degrees of freedom and having an end suitable for receiving the medical instrument, an image capture system suitable for capturing position information concerning the anatomy of the patient, a storage medium having a biomechanical model of the human body, a processing circuit configured to determine a position setpoint and an orientation setpoint for said medical instrument on the basis of the biomechanical model, on the basis of the position information and on the basis of a trajectory to be followed by the medical instrument in order to perform the medical intervention, and a control circuit configured to control the robot arm in order to place the medical instrument in the position setpoint and the orientation setpoint.