The problems of stabilizing controlled motions and tracking the trajectory of a mobile robot with three roller-carrying wheels are investigated. The novelty of the results lies in the construction of control actions that solve the stabilization and tracking problems for a wide variety of programmed motions and trajectories of the robot taking into account the non-linearity and non-stationary nature of the system and its unknown mass-inertia characteristics. © 2016 Elsevier Ltd. All rights reserved.