The system for moving and stabilizing (1) moves and stabilizes a mobile base (10), which is part of a robotic unit (100) for handling which is designed to move objects in an automated shop or an automated warehouse (200). The system (1) comprises: a linear guide element (5), which guides the mobile base (10) along operating trajectories; at least one rotatable shunting element (6), arranged at an end of the guide element (5) and designed to connect two or more guide elements (5) to one another, in order to shunt the mobile base (10) among various linear guides (5), or to enable the mobile base (10) to re-engage with the linear guide (5), with a modified orientation thereto; traction and positional control organs (20), arranged in a lower part of the mobile base (10) and designed to guide the mobile base along the guide elements (5) and shunting elements (6); stabilizer organs (30), arranged peripherally in the lower part of the mobile base (10) and destined to stabilize a position thereof during operations of handling of objects by the robotic unit (100). The mobile base (10) and the shunting element (6) are controlled by a computerised control unit, which manages the operations on the basis of the operating requirements of the automated shop or store (100).