Ultra sensitive ring laser gyroscopes are regarded as potential detectors ofthe general relativistic frame-dragging effect due to the rotation of theEarth: the project name is GINGER (Gyroscopes IN GEneral Relativity), aground-based triaxial array of ring lasers aiming at measuring the Earthrotation rate with an accuracy of 10^-14 rad/s. Such ambitious goal is nowwithin reach as large area ring lasers are very close to the necessarysensitivity and stability. However, demanding constraints on the geometricalstability of the laser optical path inside the ring cavity are required. Thuswe have started a detailed study of the geometry of an optical cavity, in orderto find a control strategy for its geometry which could meet the specificationsof the GINGER project. As the cavity perimeter has a stationary point for thesquare configuration, we identify a set of transformations on the mirrorpositions which allows us to adjust the laser beam steering to the shape of asquare. We show that the geometrical stability of a square cavity stronglyincreases by implementing a suitable system to measure the mirror distances,and that the geometry stabilization can be achieved by measuring the absolutelengths of the two diagonals and the perimeter of the ring
