System for monitoring stability of autonomous robot, including a GNSS navigation receiver including antenna, analog front end, plurality of channels, inertial measurement unit (IMU) and a processor, all generating navigation and orientation data for the robot; based on the navigation and orientation data, calculating position and direction of movement for the robot; calculating spatial and orientation coordinates z1, z2 of the robot, relating to the position and direction of movement; continuing with programmed path for the robot for any spatial and orientation coordinates z1, z2 within an attraction domain, where a measure V(z) of distance from zero in z1, z2 plane are defined by Lurie-Postnikov functions and is less than 1; for spatial and orientation coordinates outside the attraction domain with V(z)>1, terminating the programmed path and generating notification.