A manipulator includes a main arm, of which the proximal end bears a drive, and a proximal manipulation structure, and of which the distal end bears a controlled distal structure that may itself bear a surgical tool. The main arm passes through a surgical trocar. The proximal manipulation structure includes two opposed contact zones and stress sensors positioned in a central zone between the two opposed contact zones. The stress sensors operate the drive as a function of the stresses applied to the contact zones in order to produce the pivoting and rotating movements of the surgical tool with respect to the main arm. This ensures that there is optimal decoupling of the movements in the various degrees of freedom, thus making it easier to obtain movements through stressing operations that are natural to the operating surgeon.