The invention concerns a neurosurgical assistance robot comprising a movable case (1), the chassis of which is provided with a rigid support arm (6) linked to a headrest (19) supporting the head of a patient lying on an operating table (18). According to the invention, said support arm (6) is movable relative to the chassis between a retracted position inside the volume of the case (1) and a plurality of deployed positions, means being provided for locking said arm (6) in any envisaged position.